WO2013049838A2

WO2013049838A2 - Systems and methods for displaying a golf green and a predicted path of a putt on the golf green

Info

Publication number: WO2013049838A2
Application number: PCT/US2012/058343
Authority: WO
Inventors: James U. JENSEN; Brandon Baker; James Wells; Robert M. VASHISTH; Brian Wells
Original assignee: My Line Golf, Inc.
Priority date: 2011-09-30
Filing date: 2012-10-01
Publication date: 2013-04-04
Also published as: US20130085018A1; WO2013049838A3

Abstract

A system for displaying information of a golf putt on a user device includes generating a digital terrain map of a golf green, determining a location of a cup, determining a location of a golf ball on the golf green in real time, calculating a projected path of a golf ball from the ball to the cup and displaying information of the ball location, cup location, projected path, aiming path and a flat surface equivalent distance on a user interface of the user device.

Description

SYSTEMS AND METHODS FOR DISPLAYING A GOLF GREEN AND A PREDICTED PATH OF A PUTT ON THE GOLF GREEN BACKGROUND OF THE INVENTION

Field of the Invention: The present invention relates generally to systems and methods for quantifying and visualizing the likelihood of a physical event. More specifically, the present invention relates to systems and methods for quantifying and visualizing the difficulty or likelihood of alternative outcomes of a physical event such as a feat in sports. Still more specifically, the present invention relates to systems and methods for capturing, estimating and displaying the theoretical course that a struck golf ball will travel on a golf green from any pre-determined point A toward any other pre-determined point B of alternative sizes.

Description of the Related Art: Mathematical models have been developed to simulate various events. Critics, sports fans, broadcasters, games-players and others debate and have written about the difficulty or likelihood of an event. Yet, there exists no systems or methods to accurately quantify the same for many applications. Furthermore, systems and methods to effectively provide a user with such information do not exist.

Systems and methods have been described in the art for providing a graphical representation of a path that a golf ball should travel to enter a cup on a putting green, where the projected path is superimposed on a live broadcast of a golf green from the resting position of a golf ball to the cup. Such a system provides a colored path or line from the golf ball to the hole while the camera is still. Any movement of the camera would necessarily cause the superimposed path to appear off target. In addition, the golfer cannot interact with the superimposed putting path or gain any information from it.

One attempt in the art to overcome the shortcomings of prior art methods and systems is disclosed in U.S. Patent Application Serial No. 12/775,944 to Sweeney, the entirety of which is incorporated by this reference. Sweeney discloses a method, apparatus and program for computing a path, starting velocity, aim angle and aim points for directing a putted golf ball for a point on a golf course to another point and incorporating such data into charts or electronic media. Sweeney also discloses a means of determining the initial launch conditions and actual path a putted golf ball traveled given its starting and ending ball positions. Sweeney, however, fails to teach or suggest how the position of the ball and cup are located, which is a critical aspect of providing a system in which the path of a putt from the ball to the cup can be accurately predicted. Moreover, Sweeney fails to teach or suggest any process for evaluating the difficulty of a particular putt or the locations on a green where the difficulty of a putt may increase or decrease.

Thus, there exists in the art a need to provide a system and method for providing real-time putting information to a golfer that is accurate, interactive, quickly accessible and easy to use. In addition, there is a need in the art to provide a system and method for providing predicted results of a putt from a putting location on a green to a cup in the green that utilizes accurate topographical data of the green to predict and display an optimal putting path on a graphical representation of the green where the graphical representation of the green may be a digital image of the green, a three dimensional image of the green or a graphical image of the green that provides contour information and predicted zones for putts that are not optimally struck by the golfer. Presentation of such three dimensional images in oral form or providing audible instruction would also be advantageous.

SUMMARY OF THE INVENTION

Accordingly, the present invention provides systems and methods for calculating, predicting, disclosing and displaying the likelihood of an event, such as a golf putt on a green. In a particular embodiment, a system and method is provided for displaying a virtual golf putt event or alternatively or in combination for announcing a textual, graphical and/or audible narrative representation of the virtual golf putt event comprising determining the location of the ball, the location of the target (e.g., a golf hole or a selected area adjacent to or surrounding a golf hole) determining the terrain of the green and displaying or otherwise conveying (e.g., graphical, textual and/or audibly announcing) information of the ball location, target location and green terrain on or through a user interface.

In another embodiment, a system and method according to the present invention provides determining the difficulty of the putt and/or determining the parameters for a desired outcome of a putt.

In yet another embodiment, a system and method according to the present invention includes means for allowing a user to indicate on a device the location of the golf ball, utilizing a device or plurality of devices that capture and/or transmit actual or estimated hole position information, photographing or otherwise capturing the relative location of the stationary ball and utilizing image processing and/or utilizing a device that transmits pre-determined position information and a device that determines orientation information.

In still another embodiment, a system and method according to the present invention includes displaying a representation of the terrain as a contour, color gradient, or vector field, determining the current hole location and displaying information relative to the putt.

In yet another embodiment, a system and method according to the present invention includes displaying results from the most recent attempt at the same hole, displaying results from a user selected past attempt or attempts at the same hole and/or displaying accumulated results from a plurality of past attempts at the same hole or plurality of holes.

In yet another embodiment, a system and method according to the present invention includes determining the difficulty of the putt by determining the solution space of a successful event defined as a single putt or a concatenation of putts, determining the solution space of all events and/or comparing the solution space of a successful event to the solution space of all events.

In still another embodiment, a system and method according to the present invention includes quantifying the solution spaces by an analytic method and/or a numerical method.

In another embodiment, a system and method according to the present invention includes quantifying the solution spaces by modeling non-linear dynamics associated with an event.

In yet another embodiment, a system and method according to the present invention includes modeling the non-linear dynamics by fitting sample data to a piecewise linear curve, fitting sample data to a quadratic curve, fitting sample data to a cubic spline, fitting sample data to a b-spline, fitting sample data to a linear combination of rational functions and/or fitting sample data to a linear combination of exponential functions.

In still another embodiment, a system and method according to the present invention includes modeling the terrain by utilizing accurate or approximate measurement data.

In yet another embodiment, a system and method according to the present invention includes displaying information pertaining to the quantified likelihood of accomplishing a successful single putt or successful concatenation of putts of a golf ball.

In another embodiment, a system and method according to the present invention includes providing a 3D simulation of an optimized line representing the ideal outcome, computing a line representing a straight line between the object at it's initial position and the position at the ideal outcome, rendering a target marker at a fixed or user defined distance from the object at its initial position at the desired angle to achieve the ideal outcome, rendering an optimized line representing the path of an optimized outcome, rendering the volume or surface area of the solution space of a successful event, rendering an animation of a 3D model representing the ideal outcome, rendering an animation of a 3D model representing the ideal outcome simultaneously with that of an actual outcome, comparing the path of an actual outcome to that of the solution space, comparing the path of an actual outcome to that of the ideal outcome and/or rendering parameters relative to achieving the successful outcome.

In yet another embodiment, a system and method according to the present invention includes providing information that comprises a force or plurality of forces applied to achieve a successful event compared to a set of reasonable limits to provide information regarding relative parameters (i.e., speed and direction) required to accomplish the event successfully.

In still another embodiment, a system and method according to the present invention includes providing information that comprises a flat surface equivalent distance (FSED) or plurality of FSEDs applied to achieve a successful event compared to a set of reasonable limits to provide information regarding relative velocity (which includes a speed component and a direction component) required to accomplish the event successfully.

In yet another embodiment, a system and method according to the present invention includes determining the FSED limits by utilizing the green topography for every hole location in a particular golf green, or subset of a golf green.

In another embodiment, a system and method according to the present invention includes determining the location of the ball by receiving data relevant to the ball, and the surroundings of the ball and/or computing the position of the ball relative to the surroundings. In still another embodiment, a system and method according to the present invention includes determining the position of the ball by receiving reflectance data of ball and the surroundings, receiving position data of the location of the target, receiving position data of the location where the reflectance data were acquired, receiving orientation data at the event of acquiring the reflectance data, comparing reflectance data at received position and orientation to precomputed model of reflectance data from said position and said orientation, refining parameters of received position and orientation to best match precomputed model, identifying the ball or plurality of balls in reflectance data and computing position of the ball or plurality of balls relative to the target.

In yet another embodiment, a system and method according to the present invention includes identifying the ball by selecting a desired ball from a plurality of identified balls.

In another embodiment, a system and method according to the present invention includes determining the position of the ball by receiving position data of the location of the target, determining the distance from the ball to the target, determining the orientation angle from the ball to the target, relative to a known orientation angle and determining the position of the ball from the received and determined information.

In still another embodiment, a system and method according to the present invention includes determining the position of the ball by receiving position data of the location of the ball, determining the orientation angle from the ball to the target, relative to a known orientation angle and determining the position of the ball from the received and determined information.

In yet another embodiment, a system and method according to the present invention includes determining the position of the ball by receiving a graphical representation of the ball and said surroundings and identifying the location of the ball relative to said surroundings.

In another embodiment, a system and method according to the present invention includes determining the position of the ball relative to the target by identifying the location of the target relative to said surroundings.

In another embodiment, a system and method according to the present invention includes determining the position of the ball relative to the target by receiving distance information relative to a plurality of known locations nearby the ball, receiving distance information of the ball to said plurality of known locations, receiving distance information of the target to said plurality of known locations and determining the position of the ball and target relative to the surroundings.

In yet another embodiment, a system and method according to the present invention includes determining the position of the ball relative to the target by receiving position information of a location where a ball may be placed relative to surroundings and receiving position information of the target relative to

surroundings.

In still another embodiment, a system and method according to the present invention includes graphically illustrating a parameter used in quantifying the likelihood of a successful event on a smartphone, a computer screen, a video game console, a television set, a hand held electronic device and/or a mechanism for providing visual information to a user.

In yet another embodiment, a system and method according to the present invention includes graphically illustrating the difficulty of a successful event as the inverse of the ratio of the size of the successful solution space to the total solution space.

In yet another embodiment, a system and method according to the present invention includes pre-determining a grid of ideal outcomes and using the grid of pre-determined ideal parameters to determine the ideal outcome for any position of ball on the green and any corresponding position of the target.

In another embodiment, a system and method according to the present invention includes determining the solution space for successful and all events by establishing a first test putt, applying first test putt to relevant green topography, calculating a line of variance, calculating sequential test putts and selecting an optimum sequential test putt.

In another embodiment, a system and method according to the present invention includes establishing a first test putt by establishing an orientation direction, establishing a cup position, establishing a first ball position and determine the first ball force stop position. Alternatively, a first test putt is established by establishing an orientation direction, establishing a cup position, establishing a first ball position and determine the ball speed at the location of the cup.

In yet another embodiment, a system and method according to the present invention includes selecting the optimum sequential test putt buy producing a series of sequential test putts using the same ball force or speed as applied on the first test putt only varying the angle, producing a series of sequential test putts using varied forces or speeds for each of the sequential tests putts performed previously and determining a single putt that most closely resembles the characteristics of the ideal angle and force or speed or a plurality of ideal angles and forces or speeds.

In still another embodiment, a system and method according to the present invention includes determining parameters for a desired outcome by determining an offset angle or plurality of offset angles associated with the ideal angle and force or speed and/or determining an offset force or speed or plurality of offset forces or speeds associated with the ideal angle and force or speed or a plurality of ideal angles and forces or speeds.

In yet another embodiment, a system and method according to the present invention includes determining parameters for a desired outcome by displaying an amoeba-like territory indicating where the ball may stop if the putt force or speed applied is slightly greater than or slightly less than the ideal force or speed and/or displaying an amoeba-like territory indicating where the ball may stop if the putt angle applied is slightly clockwise or slightly counter-clockwise relative to the ideal angle or plurality of ideal angles.

In still another embodiment, a system and method according to the present invention includes determining the ideal outcome by utilizing real-world coordinates for the actual location of the ball, the cup, or other necessary parameters.

In another embodiment, a system and method according to the present invention includes determining the parameters for a desired outcome of a putt by determining the parameters for an optimal putt, determining parameters for a 2-putt, at ball stop position, reverse engineer most likely path and/or at ball stop position, reverse engineer a plurality of likely paths.

In yet another embodiment, a system and method according to the present invention includes allowing a user or plurality of users to utilize displayed information and recording data relative to utilizing displayed information.

In another embodiment, a system and method according to the present invention includes a control and variable experiment to determine the degree of efficacy of the system and method of the present invention.

In still another embodiment, a system and method according to the present invention includes utilizing video media and adding or substituting narration. In yet another embodiment, a system and method according to the present invention includes determining the position of the ball relative to the target by receiving distance information relative to a plurality of known locations nearby the ball, receiving distance information of the ball to said plurality of known locations, receiving distance information of the target to said plurality of known locations and determining the position of the ball and target relative to the surroundings.

In another embodiment, a system and method according to the present invention includes determining the position of the ball relative to the target by receiving position information of a location where a ball may be placed relative to surroundings and receiving position information of the target relative to

surroundings.

In yet another embodiment, a system and method according to the present invention includes a method of acquiring utilization data by allowing a user or third party or plurality of users or third parties to record data by use with the system.

In still another embodiment, a system and method according to the present invention includes providing a control and variable experiment to determine the degree of efficacy of the system.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 illustrates a graphical display on a graphical interface graphically displaying a putting green and information relating to a putt of a golf ball on the golf green in accordance with the principles of the present invention.

FIG. 2 illustrates a graphical display on a graphical interface graphically displaying a first menu for selecting a golf course of an application operated on a smartphone in accordance with the principles of the present invention.

FIG. 3 illustrates a graphical display on a graphical interface graphically displaying a second menu for selecting a golf green of an application operated on a smartphone in accordance with the principles of the present invention.

FIG. 4 illustrates a graphical display on a graphical interface graphically displaying a third menu for selecting display settings of an application operated on a smartphone in accordance with the principles of the present invention.

FIG. 5 illustrates a graphical display on a graphical interface graphically displaying a fourth menu for selecting position settings of an application operated on a smartphone in accordance with the principles of the present invention. FIG. 6 illustrates a graphical display on a graphical interface graphically displaying a golf green displayed on a smartphone in accordance with the principles of the present invention.

FIG. 7 illustrates a graphical display on a graphical interface graphically displaying a golf green displayed on a smartphone in accordance with the principles of the present invention.

FIG. 7A is a graphical representation for determining the position of a golf ball on a green and a ball marker in accordance with the principles of the present invention.

FIG. 7B illustrates the ball marker shown in FIG. 7A at various orientations in accordance with the principles of the present invention.

FIG. 8 illustrates a graphical display on a graphical interface graphically displaying a golf green displayed on a smartphone in accordance with the principles of the present invention.

FIG. 9 illustrates a graphical display on a graphical interface graphically displaying a golf green displayed on a smartphone in accordance with the principles of the present invention.

FIG. 10 illustrates a graphical display on a graphical interface graphically displaying a golf green displayed on a smartphone in accordance with the principles of the present invention.

FIG. 1 1 illustrates a graphical display on a graphical interface graphically displaying a golf green and putt information in accordance with the principles of the present invention.

FIG. 12 illustrates a successful event and two alternative events relative to a golf putt in accordance with the principles of the present invention.

FIG. 13 illustrates three successful events relative to a golf putt in accordance with the principles of the present invention.

FIG. 14 illustrates three successful events relative to a golf putt in accordance with the principles of the present invention.

FIG. 15 illustrates a surface area describing the successful solution space of a golf putt in accordance with the principles of the present invention.

FIG. 16 illustrates a graph describing the successful and entire solution space of an event in accordance with the principles of the present invention. FIG. 17 illustrates a presentation of information relative to achieving a hypothetical or actual event in accordance with the principles of the present invention.

FIG. 18 illustrates a graphical display on a graphical interface graphically displaying a putting green in accordance with the principles of the present invention.

FIG. 19 illustrates a graphical display on a graphical interface graphically displaying a putting green in accordance with the principles of the present invention.

FIG. 20 illustrates a graphical display on a graphical interface graphically displaying a putting green in accordance with the principles of the present invention.

FIG. 21 illustrates a graphical display on a graphical interface graphically displaying a putting green in accordance with the principles of the present invention.

FIG. 22 illustrates a graphical display on a graphical interface graphically displaying a putting green in accordance with the principles of the present invention.

FIG. 23 illustrates a graphical display on a graphical interface graphically displaying a putting green in accordance with the principles of the present invention.

FIG. 24 illustrates a graphical display on a graphical interface of a digital level and reference points for calibrating the user interface according to the principles of the present invention.

FIG. 25 illustrates a graphical display on a graphical interface of a first measurement between a ball and a cup according to the principles of the present invention.

FIG. 26 illustrates a graphical display on a graphical interface of a second measurement between a ball and a cup according to the principles of the present invention.

FIG. 27 is a side view of a user device for measuring a first distance between a ball and a cup according to the principles of the present invention.

FIG. 28 is a side view of a user device for measuring a second distance between a ball and a cup according to the principles of the present invention. DETAILED DESCRIPTION OF ILLUSTRATED EMBODIMENTS

The present invention is directed to systems and methods of calculating, predicting and displaying various aspects of a putt to be made on a putting surface, including the computing, predicting and displaying the likelihood of such an event. The likelihood of successfully making a putt may comprise determining the solution space of a successful putt, determining the solution space of all putts, and then comparing the solution space of a successful putt to the solution space of all putts. One exemplary embodiment may include, without limitation, quantifying necessary input parameters to accomplish an ideal event, such as an ideal angle and force applied in or speed of a golf putt, given a model for the terrain of the green and the location of a ball and of the green-cup.

Quantifying the solution spaces may utilize an analytic method or a numerical method. Either method, analytic or numerical, may be based in part upon laws of physics such as Newton's Laws of motion, for example. There may also be non- linear dynamics that are difficult to quantify with basic physics. Such instances may require quantifying the solution spaces by mathematically modeling non-linear dynamics associated with an event. Some methods for modeling the non-linear dynamics may include: fitting sample data to a piecewise linear curve; fitting sample data to a linear combination of rational functions; and/or fitting sample data to a linear combination of exponential functions.

Equations describing the translational motion of a golf ball may be given by:

ma_y = f

Where m is the ball's mass, a_y is the translational acceleration and f is the force applied. The equation of rotational motion may be given by:

la_x= nr - fR_t

Where / is the moment of inertia, a_x is the rotational acceleration, n is the normal force applied to the surface of the ball; r is the perpendicular distance of the point of contact from the center of mass; and R_t is the perpendicular distance between the tangential component of the contact force and the center of mass of the golf ball.

The contact force (direction and magnitude) for a ball rolling on a non-level surface can be computed by:

p cos#cosg?sin β - I_b sin Θ

tan φ

p_g cos Θ cos g?cos β - I_b cos Θ sin φ and

p cos#cos ?sin β - I_b sin ?cos#

/ = ^mg

(l + I_b) cos<p respectively. The acceleration in 2-dimensions (x and y) may then be computed using:

ma_x = -mg sin Θ - f sin φ ,

and

ma_y = -mg cosd siri q) - f οο$ ,

respectively, so that the position at any point along the path may be easily determined, predicted and/or displayed. Moreover the determination of a

succession of such points will allow the prediction and/or display of the path of such object for initial resting point to ultimate resting point.

Furthermore, modeling and execution of physical parameters may be implemented by utilizing any one or combination of physics engines for predicting motion of three-dimensional objects as they interact.

In one such embodiment, an image-recording device, such as a video camera may be utilized to acquire motion data of a ball rolling across a green. Image processing algorithms may be employed to automatically track the motion of the ball, to identify the location of the center of mass at specific instances in time. The motion may then be modeled, and the resistive forces of the terrain may be quantified for various initial velocities or speeds. Furthermore, alternate methods may be employed, including without limitation, rational functions or exponential functions. Another exemplary embodiment may include a high definition image- sensing device to detect the rotation of the ball and similar non-linear dynamics may be modeled thereby.

Another exemplary embodiment of the present invention may include calculating a successful event wherein the successful event comprises attaining an acceptable outcome and/or the ideal outcome. In a golf putt, for instance, the ideal outcome may be described as the ball eventually stopping just inside and marginally below the top circumference of the hole, where the center of mass of the ball is slightly over the edge of the hole, so that the ball falls into the hole with an acceptable velocity and trajectory. Such a condition would ensure that if the angle of approach of the ball toward the hole were not ideal, the ball would not roll far past the hole. Knowing that all putts that end up short of the hole have no possibility of being made, the end location of a short putt is also of interest and may be computed, predicted and displayed using the current invention. In this exemplary embodiment, the ideal force and angle for a putt on a green based on a grid of ball locations on the green may be pre-computed to establish the ideal parameters for a putt, virtually anywhere on the green. A hand held device or pre-computed map will depict what line and what force to apply to any putt directed to any placed cup on any modeled green. The green may be modeled by using modern LIDAR scanning devices to produce a topographical map of the green at sub-centimeter accuracy the captured data may have points that are several centimeters (e.g., 10 to 20 cm) apart with vertical accuracy several centimeters apart (e.g., approximately 3-5 centimeters). Using this an interpolated DTM will be made and all computations will be made against the interpolated DTM. Such digital rendition of a green by LIDAR scanning may be referred to as a "digital terrain map or "DTM." And other methods of producing a DTM of a selected green are also incorporated into the current invention. Of course, no perturbations must be assumed between the date of scanning and the date of play, but largely that is acceptable, if the only "care" given to the green is watering, cutting and sanding. The presence of ball marks, foot prints or other real life perturbations may or may not be accounted for in the calculations of the present invention.

One particular embodiment of a learning algorithm uses the following abbreviations:

CP = Cup Placement

TN = True North or assumed True North

BP = Ball Placement

FTP = First Test Putt on the TN line

FBF = First Ball Force

FBF-SP = First Ball Force— Stop Position

FBL-SP = First Ball Line— Stop Position

RGT = Relevant Green Topography and is derived as the relevant part of the DTM of a given Green

LOV = Line of Variance from the assumed TN line and optimum FBF STP = Sequential Test Putt (STPs are multiples of a STP)

STP-SP = Sequential Test Putt-Stop Position

STP-BF = Sequential Test Putt-Ball Force

VL = Variable Line VF = Variable Force to "map" all putts to any cup placement position

("CP") one must start somewhere.

One may start by orienting the green to a chosen "True North" ("TN"), which need not be accurate but may be approximate. In fact, except for variations in friction due to orientation (such as direction of grass blade to or away from the sun) any orientation of the green is acceptable so long as one starts with a chosen TN line. The algorithm assumes a starting place for the first CP of an arbitrary distance, say 100 cm, inside the most northerly point on the scanned green. Then one may choose the same distance (100 cm) inside the fringe assuming that grounds keepers will place the cup, no nearer than that distance (100 cm) from the fringe. But any other starting distance will be acceptable. Then, for the first CP, draw a line running due south from the first CP. This line is called the True North line (the "TN"). On the TN line, each putt will come from a chosen Ball Placement ("BP") in a filigree of BPs as if pearls on a string running from north to south all the way to the fringe. One may choose to start at 50 cm from the center of the first CP and this position is the first Ball Position (the first "BP").

The ball will first be putted in the First Test Putt (the "FTP") on the TN line, from the chosen BP and assuming that the green is flat and that the First Ball Force (the "FBF") has been applied to the ball such that the FTP should stop at the First Ball Force Stop Position (the "FBF-SP").

It is shown below that the FBF-SP is a function of the FBF only for hypothetical putts on the TN line if one assumes constant friction and flat topography for each FTP on the TN line:

j j FBF-SP

-Ιω² + - mv² - C F_friction - s ds = 0 ,

^{1 1} BP

where Ffriction is the force of friction of the green that slows down the ball

(always acting in opposition to the velocity of the ball, so long as the velocity is nonzero), s is the path that the ball travels (with the variable of integration, c/s), / and m are the moment of inertia and mass for a golf ball, respectively; w is the angular velocity of a rolling golf ball; and v is the translational velocity of the ball.

The ab ve equation can be reduced to:

when friction is considered to be constant. This, in turn, yields:

when solving for FBF-SP, and substituting k FBF² for v² , due to the proportionality of velocity and force, from Newton's laws. Since all values in the equation above are known, except for FBF, the FBF-SP is clearly a function of only FBF.

Furthermore, the golf putt trajectory may be determined by utilizing analytic geometry and physics. First, a two-dimensional surface within a three-dimensional space can be characterized by

z = a(x, y).

One may assume that this is a single-valued function, that is, for every (x,y) point there is only one value of z, which is, of course, applicable for a golf green. One may define the function

G{x,y, z) = z - o{x,y)

Whose value is G = 0 on the surface.

Two important results from analytic geometry are the computation of the tangent plane and the normal vector to the tangent plane at an arbitrary point Po(xo,yo,s(xo,yo)) on the surface. These are

z = cr(x₀, y₀) + a_x(x₀,y₀)(x - x₀) + a_y(x₀,y₀)(y - y₀) (tangent plane)

n = VG = -o_x(x₀,y₀)x - o_y(x₀, y₀)y + z (normal vector)

Where s_x and s_y in the equations are defined to be

The unit normal vector is at (x₀,y₀).

Take the direction of the normal vector to be in the positive z direction for a flat, level plane (s(x,y) = const). The normal line that goes through the point Po and extends indefinitely in the same orientation as the normal vector and be

parameterized by t:

x = x₀ - o_x{x₀, y₀)t y = y₀ - <r_y(x₀,y₀)t

z = a(x₀,y₀) - t

The rolling motion of the ball may be accounted for as follows. A rolling sphere spinning about its center point will have a moment of inertia of

/ = wr²

where m is the mass of the sphere, r is its radius and the dimensionless coefficient x depends on the precise internal density profile of the sphere (x = 2/5 if uniform).

The sphere is rolling along without slipping and no frictional losses with linear translation velocity v. On a flat, level surface and gravity is not acting on the sphere, the motion will be uniform with no acceleration. Thus, no torque will be applied that will cause the ball to speed up or slow down. However, when the sphere

experiences a change in incline, it will feel a component of gravity along its motion to cause it to accelerate. The linear acceleration a is related to the angular

acceleration a = a/r by necessity and the assumption of no slipping during the sphere's rolling.

In motion along one direction, the equations for rolling without slipping and no friction are

ma = F_g - F_torque

1— = r r

r

where Fg is the component of gravity along the motion direction, and Ftorque is the force applied to create a torque to generate the angular acceleration. Fg = mg sinq, where g = 9.80 m/s2 is the acceleration due to gravity, and q is the angle with which the normal vector to the surface has with respect to the z direction. These are two equations and two unknowns a and F_t0rque- The solution is m +—r \a = mg sin Θ .

r² )

Thus the motion is exactly the same as if it were a point particle except the additional inertia due to the energy of rolling is equivalent to adding an extra mass to the particle of size l/r². Including friction to the rolling equation above yields m = mg sin 0 - F_friction

Generalized equations to the two-dimensional motion on a s surface:

{l + i)m5 = mgQ - F_friction

Since I = zmr2, the rolling of the sphere compared to a point particle is modeled here as an effective increase of mass m:

m→ (1 + ξ)τη

where x = 2/5 if the sphere is of uniform density. The vector Q may be define

For small angles s_x, s_y « 1 then we can approximate Q as

e = -Vcr.

Friction may be modeled as the force that causes the slowing down of the ball due to loss of energy (microscopically through heat dissipation), based on the normal force acting on the ball from the surface pushing up times a dimensionless coefficient of rolling friction C_r.

Where v is the direction of motion. Neglecting the additional effective normal force that the ball experiences by pushing against the green as it first begins to curve up hill or "lifting" off the green as it first begins to curve down hill.

Simply ignoring the velocity dependence of frictional effects gives us a constant coefficient of rolling friction. The frictional force can be modeled as:

F fnoion = C_rmgv , where

0.05≤C_r≤ 0.15

where the lowest values of C_r are the fastest greens and the highest values are the slowest greens. Standard techniques known to those skilled in the art can be employed to solve the differential equation along the putt path.

Assuming the ball is at an initial position r„ the present invention is capable of determining the final position /> upon stopping (e.g., a few inches past the cup). To do so, the correct initial velocity must be chosen. A first choice may not be the correct answer in general, and so various iterations of the initial velocity will occur in order to converge to the final answer. A useful first guess may be to assume that the green is perfectly flat and solve the equation analytically. The putt direction would be a straight line to the final position A>.

Another option may be to assume the putt to be at a specified non-zero speed at the cup position r_cup. If the green is curved then specifying the ball come to rest a foot beyond the cup, for example, means that the center of the cup position may not be in the ball's path.

A first guess on the ball's speed using this criteria may be accomplished by:

K ⁼ + E _riction

which implies

1 2 1 2 2 1 2

— mv, +— Ιω. = \mV f +— 1ω₍ + C mgd

2 2 ^f 2 ^f

where

is the distance to the cup. However, we know that w = v/r, and we know that / = xmr², so we can solve the above equation for v, simply as

2C_rgd

l + £

This should be the initial velocity choice, with the initial direction being pointed straight at the hole. Iterations of changing v, and the direction would be required to converge on the solution when the specific topography of s(x, y) is included.

It will also be shown that the FBF-SP is a function of the FBF and the

Relevant Green Topography (the "RGT" or "DTM") for all putts after the FTP. For example, a FBF may be chosen to cause the ball to stop at, say, 20cm past the center of the CP for the FTP and RGT may cause this FTP to miss the CP such that (due to the RGT of up-hill, for example) the FBF-SP is actually 10cm in front of the CP and 10cm to the right.

The result of this FTP will then be applied to the RGT and the Line Of Variance to the line of the FTP (the "LOV") will be noted and the corresponding FBF- SP will be noted. Now, similar putts to the FTP will be performed, each called a Sequential Test Putt and collectively called Sequential Test Putts (the "STP" and the "STPs"). The STPs will be repeated an optimum number of times as STPs and each such will be numbered sequentially, or alternatively numbered with a code of variance of direction and force from the FTP. The repeat STPs will be performed using a sequence of variances of the two variables of Variable Line (the "VL") and Variable Force (the "VF") from the FTP and the variances of the line produced and the BS position produced by the adjustments in VL and the VF will be noted.

From these multiple STPs the program will chose an optimum STP or a group of nearly optimum STPs using the selection criteria described below.

Here follows an exemplary embodiment:

First: Produce the FTP and apply it to the RGT. Note the LOV and the FBF- SP and the corresponding FBL-SP. Note that there will be no VF or VL in this first FTP, because it starts with the FTP and the assumed FBF-SP.

Second: Produce a set of 6 STPs using the same FBF as in the FTP but varying the line from the TN line by 1 , 2 & 3 degrees to the right and 1 , 2 &3 degrees to the left of the TNL each of these will have a LOV and a VL but no VF because of the use of the same test force, the FBF, as in the FTP and again note the LOV and the STP-SP.

Third: Produce a second set of 24 STPs using 2 incrementally and marginally greater forces or speeds and using 2 incrementally and marginally lesser forces or speeds than the FBF applied thus 24 times in total, 4 times to each of the first set of 6 STPs and again note the LOV and the STP-SP for each of these STPs.

Fourth: Now, from the 30 STPs choose a single putt that most closely resembles the characteristics of the Ideal Wide Line Putt (the "IWLP").

Note the LOV and the STP-SP of the chosen IWLP. If this results in an IWLP, then move to the next sequential BP (say a new BP of about 5 cm further South if the original BP was within 3 centimeters of the center of the CP and new BP of about 10cm if the original BP was further distant than the chosen 10cm adjustment) and repeat. It will be seen that a different movement variable can be selected. If review of the 30 STPs does not result in an IWLP, then repeat the previous steps using the optimal near-IWLP as the replacement TN line as the FTP.

When an IWLP is shown, the chosen IWLP will then serve as the Substitute FTP (the "SFTP") and substitute TN line and the process is repeated at 5 cm, 10 cm and so on to the South, placing the new BP on the original TN line but using the most recent LOV as the new substitute TN line for each successive SFTP until all IWLP's on that TN line have been produced. This process will then be repeated for all radiating lines to the East and to the West of the TN line for the particular CP. And the process is further repeated for each new CP on the TN line. It will be seen that as the CP moves south on the TN line, the radiating lines to the East and West of the TN line will expand from upwards of 90 degrees to approaching 180 degrees in each direction as the possible putts to that CP expand around the CP for putts of direction East and West and up to putts of South direction and all directions in between.

A new CP will then be chosen on a grid built a chosen distance to the East and to the West of the TN line and repeated until all such substitute TN lines have been utilized and all CP on all such substitute TN lines have been used and all FTP and STPs on all such CP on all such substitute TN lines have been computed to get the IWLP for each such combination. Specifications for the IWLP must be set. These can include characteristics of probability of the ball falling in the hole within certain parameters of location, direction and speed. Such that with a force of 3 traveling on a path due East and exactly parallel to the North edge of the cup, the ball will not drop unless that path is inside said edge by 3 cm, whereas if the ball is traveling not due East, but is curving in a southerly direction it will drop if it is inside the said edge by only 2 centimeters, even up to a force of 4. And so on.

Also, the wide line of the IWLP may show the greater force applied to the right side of the line and the lesser force applied to the left side of the line and so on. And probabilities can be produced from the evaluation of the number and magnitude of variations in the FBF and the LOV that can approximate the IWLP without actually being an IWLP. For example a 30 foot putt on a relatively flat slope may have a greater number of variables that will still result in an IWLP than a 15 foot down hill with a curve to the left. This is so, because of the increase in influence of the RGT over the LOV and the FBF.

Since any practical grid of ideal values has a limited number of points from which the ideal parameters were calculated, an estimation technique may be employed to estimate in real time, fluctuations in ideal solutions for actual ball placement between grid points. Other embodiments an optimum line can be retrieved from a data base containing a plurality of stored, predetermined lines from a plurality of points A to a plurality of points B on the DTM for a specific green DTM. One of the predetermined lines can then be retrieved from the database

corresponding that most closely approximates the actual position of the ball (point A) and cup (point B) on the green. These calculations can be performed using linear, quadratic, cubic, sinusoidal or other interpolation techniques. One particular embodiment may comprise the calculation of bare-eccentric coordinates of the ball relative to the nearest control points on the DTM. Then one may compute a weighted average on the neighboring ideal parametric values for force and angle for the actual ball location as in:

where F is the ideal force at the actual ball position, F? , F₂, and F3, are the pre-computed forces at the three closest control points on the DTM; a_? , a₂ , and a₃ are the pre-computed weighting factors that may be determined by computing the bare-eccentric coordinates, or some other method; Q is the ideal angle at the actual ball position; and Qi, Q₂, Q₃ are the pre-computed ideal angles at the three closest control points on the DTM. Although the pre-calculation of the ideal parameters for all the grid points may require significant computational execution, one can clearly see that a simple hand-held device can easily calculate a very accurate estimate of the ideal force and angle for any actual ball position by utilizing the pre-determined parameters. Alternatively, of course, all of the pre-computed IWLP can be stored in a database, computational grid or matrix. Then, for any given cup placement and ball placement, the map or device need not "compute the IWLP, but rather it need only retrieve it from the stored cup placement and ball placement— just as a chess player does not "compute" the path of a rook's move, but rather refers to pre- computed available moves for each given situation.

It will be seen that the program can compute the relative difficulty of any putt over any other putt, thus allowing teachers to caution students away from putting from selected BP to selected CPs, with less than predetermined force, allowing players to make similar choices, allowing broadcasters to advice viewing audiences of such relative probabilities among several players, and allowing bookies and odds makers to wager on the probability of success of alternative putts. For example, during a live golf tournament, once a golf ball lands on a green, utilizing the DTM information and difficulty of the ensuing putt from the ball to the cup on that particular green, the odds of the likelihood that the putt will be made, given for example the putting accuracy of the golfer that will be attempting the putt, the contour of the green between the ball and the cup, the resulting amount of break of the putt, the speed of the green, the slope of the green between the ball and the cup, and other similar factors and conditions.

Incorporation of a training golf ball that will record and calculate and report relative force would add to the program by allowing students to practice relative force putts on chosen IWLPs thereby honing FBF capabilities.

In order to display the IWLP, several aspects are present in the system for a given set of conditions.

First, a digital representation or approximation of the topography of the green of choice is created. For example, the green is scanned using modern LIDAR scanning cameras. The LIDAR scanning cameras may be mounted on aircraft for aerial scanning of greens or tripod mounted for ground scanning of greens to collect laser scan data. An Airborne LIDAR system is typically composed of three main components: a laser scanner unit, a global positioning system (GPS) receiver, and an inertial measurement unit (IMU). The GPS receiver is used to record the aircraft trajectory and the IMU unit measures the attitude of the aircraft (roll, pitch, and yaw or heading). The position and orientation information obtained from the GPS and IMU are used to determine target location with high accuracy in three-dimensional spaces. The three dimensional LIDAR points are transformed into global coordinate system (GCS) data. While GPS data is primarily used for latitudinal and longitudinal location of a point, the GCS data is particularly applicable in a three-dimensional geo coordinate system. After processing, the GCS data is used to create a digital elevation model (DEM). In order to generate the DEM from the GCS data, the LIDAR points are separated into ground (terrain) and non-ground (non-terrain) points, and as a result all the points are classified to a bare earth model which contains the GCS information. The GCS information, which includes GPS information, allows the data for a particular green to be easily linked to a particular golf course.

The data files are converted into color elevation map, contour files and a Geotiff file. The DEM are used to create the digital terrain maps (DTMs) of the simulated golf greens of the present invention. The raw LIDAR data can be several gigabytes of data. Once converted into the DEM, the Geo reference images are relatively small in storage size that can then be used on a user device that may be limited in its internal computing power and/or memory, such as a smartphone. By using LIDAR scanning, the topography of the green is measured and approximated using a significantly large number of data points from a stationary or moving location where the LIDAR scanning camera is located. When creating the DTM from LIDAR data, it is possible that the green could be scanned using fewer data points and, by using extrapolation techniques, the DTM can be created at points between those actually measured. Likewise, other methods known in the art could be used to capture the topography of the green. From such "real world" data a CAD model of the green will be created and the portion of the green that is relevant to a chosen LOV will be concentrated to allow focus on the Relevant Green

Topography.

Next, the program will calculate and display the FBF and LOV for each Sequential Test Putt-STP, leading to the display, estimate or computation of an IWLP for every variable of CP and BP.

Additionally, in one variation of the invention, a means for real time capture of the actual CP and BP for each putt is provided, so that the foregoing capabilities can be made available to the specified user in real-time. Real-time capturing of the CP and BP on a green may be provided by using GPS technologies and/or radio frequency tags. For example, two portable tags (the size of a poker chip or smaller) may be used. One will be used to mark the player's ball as the BP in the test case - placed when the player picks-up his/her ball for cleaning- and the other will be used to mark the location of the cup, the CP— placed in the bottom of the cup when the player removes the flag, on in a more sophisticated scheme, placed in the bottom of the cup or on the pin by the grounds keeper when the cup was set that morning. Alternatively, the location of the cup could be calculated by using a laser light directed to the pole of the flag before the flag is removed from the cup. Assuming that the location of the CP is know thru one or more of these or other means, each of the players would then use his/her companion player chip to mark his/her respective BP. In rapid order, these locations would be transmitted to a receiver, ground, portable or airborne and the IWLP for the respective BP's would be broadcast to the hand held device used by each player, to the broadcaster's booth and/or to other audiences. Because all possible IWLP had been previously calculated, the program needs only to know the two locations, CP and BP and the IWLP would be displayed. Alternatively, a touch screen could be used and the player would be asked to estimate by touch the location of the CP and BP and then the IWLP would be displayed.

Alternatively, a paper map could be produced with chosen colors to suggest the relative LOV and FBF needed from any neighborhood to any other neighborhood and difficulty could be depicted.

In an additional iteration of the invention, the system or method would be applied to select the Sequential Test Putts-Stop Position of the ball for various preselected failed putts. For example one such STP-SP might be near the golfer's original BP on a putt up-hill that lacked sufficient ball force or speed to reach the cup and thus regressed downhill after coming to a stop. Then the area of the several failed STPs could be noted and color-coded to suggest worst to best near-miss outcomes, thus warning a golfer away from a too weak putt or a too severe line putt in favor of a less risky choice.

Alternatively, it will be seen that the invention will allow the golfer to select a cup of larger size when selecting a "two-putt" strategy. In this iteration, the ameba of possible area chosen will optimize the golfer's selected favorite second putt position within the ameba of choice.

It can be seen that a method of business is available to the party having these capabilities. That method might include the components of scanning the greens, computing all possible IWLPs, capturing the CP each day for said green and capturing serially the BP of several players or of storing predetermined ball lines and velocity. The resulting IWLP would then be broadcast to the appropriate site (booth, hand held, and so on) and the course, the player or both, as applicable, would pay the business. The business would include the system of capturing the scanned greens and automating the topographical maps to harmonize with the algorithm for calculating all possible IWLPs in the manner described above.

An additional system or method of the invention is presented at an early time and date before the method of capture of actual ball placement is perfected. For example, if a user were interested in golfer impression or marketplace feed-back, the invention can be deployed to set on a test green a number, such as 20 for illustration, of small ball markers, placed in a manner of relative stability and without disruption to any golfer or path of any given putt. Then, manual computation of the IWLP could be calculated for these few test putts. A golfer could be invited to test his/her own read of the green with out viewing the IWLP and the compare with using the IWLP. Alternatively, a course management could be invited to calculate the average time needed by four golfers to line-up their several putts when not-using and alternatively when using the IWLPs for the test BPs. The results can be recorded and allocations of capital and marketing approaches can be established with the information gained at this early stage in deployment of the invention into commerce.

A variation of this early testing application of the invention could be had when the user wanted to test the use of the IWLP from any place of BP on a given test green. Here, instead of transmitting the exact location of the Ball to a GPS satellite, the user would arrange for installation (for a short period and only for the benefit of this test case) of sub stations around the green, from which, by triangulation, the exact location of the BP could be computed real time with the IWLP then computed manually without the need or expectation of complete automation.

In one embodiment, the present invention is embodied in a golf-related software application (APP) that can be accessed and operated via a smartphone, such as the smartphone 10 illustrated in FIG. 1 . The smartphone 10 includes a touch screen 1 1 that allows a user to view calculated information regarding the distance and direction of a put that is displayed on the touch screen 1 1 and to select and/or manipulate certain features of the APP 12. As shown in FIG. 1 , the position of a golf ball 14 and cup 15 on a golf green 16 is illustrated in two graphical representations. In the first graphical representation, a bird's eye view is presented in which a straight distance line 17, a ball trajectory line 18, an aiming line 19 and an aiming point line 20 are displayed relative to the golf ball 14 and cup 15.

Accompanying the straight distance line 17 is a distance measurement representing the actual distance between the ball 14 and the cup 15. Accompanying the aiming point line 20 is an aiming point distance and arrow which provides the location of the aiming point 21 at which the user should aim in order to make the putt assuming that the user putts the ball at an appropriate speed.

An important aspect of the invention is the "Plays Like" feature 22, which provides a distance at which the putt will play like depending on the slope of the green between the ball 14 and the cup 15. In this example, as shown in the second graphical representation 23, the ball 14 is above the cup 15 by 6 inches resulting in a downhill putt. This Plays Like feature 22 displays a distance measurement that takes into consideration the distance between the ball 14 and the cup 15 and the slope of the green. The plays like feature 22 distance thus provides a recalculated distance based on whether the putt is uphill or downhill, where plays like distances for downhill putts will be less than the actual distance 17 and uphill putts will be greater than the actual distance. The user can then adjust the force of their putter to add or decrease the effective distance of the putt according to the plays like distance displayed.

The plays like distance is also represented in the second graphical representation 23 in which a second cup 24 is illustrated at a distance from the cup 15. In this example, the second cup 24 may be displayed in a different color in a shaded form so as to be visually distinguishable from the cup 15. Furthermore, in the second graphical representation 23, a cross-sectional contour of the green 25 is shown that illustrates the surface of the green 25. All of the information presented on the screen 1 1 of the smartphone 10 provides the user with sufficient information to increase the likelihood that a putt of an actual golf ball on an actual green in the same position as represented on the screen will be made. This information is provided to the user in real-time so that the user can use the information in for an actual putt. The system is adaptable so that the cross-sectional line 25 can be calculated on line 23 or on line 18 as is most suitable to the user or other audience.

As illustrated in FIG. 2, the APP 12 includes various menus and submenus displayed on the screen 1 1 that allow a user to first select a particular golf course that is to be played. A number of courses 26-30 may be provided and stored in memory of the smartphone 10 and selectable via the touchscreen 1 1 . Additional courses can be accessed by scrolling to reveal courses listed below Course 5.

Once a particular course has been selected, the data representing the contours of the greens for that particular golf course that are stored in memory on the

smartphone 10 are used to provide information to the user, such as aiming points, trajectory lines and other information as shown in FIG. 1 . As shown in FIG. 3, once the course has been selected, the user can select a particular green to be accessed, including for example, the practice green 31 as well as holes 1 -18. Once a particular green has been selected, the smartphone will display a view of the green as selected by the user. In order to alter or customize the image of the green and information displayed, the user can access the display settings menu illustrated in FIG. 4. The display settings allow the user to toggle on and off the various feature and information sets provided by the APP 12. For example, by turning on the "Basic" setting 32, the display will provide basic information in text form only, such as distance to hole, amount (in distance) of right or left break of the putt, and the amount (in height) of incline or decline in the putt, that the change in elevation of the putt. The "Trajectory" setting 33 will add a graphical representation of the position and direction of an aiming point relative to the cup at which the user should aim given a particular ball position and cup position on the green in order to have the correct line of the putt. The "Line" setting 34 will display the curved or straight path of the putt from the ball to the cup that will allow the ball to enter the cup. The "Heat/Grid" setting 35 will display a color gradient in various locations on the green, for example, from red to green, with shades of yellow and orange in between, that indicate locations on the green where putts will likely be more difficult. The

Heat/Grid setting can be chosen to display contours, difficulty or vector fields over the DTM of the green.

As such, the Heat/Grid setting 35 can display locations on the green where a second putt is more likely to be makeable so that the user can err on a side of a cup where, if necessary, a second putt will likely be easier to make. The "Elevations" setting 36 provides a display of the green in cross-section from the ball to the cup so that the user can see the elevational changes in green between the ball and the cup.

As illustrated in FIG. 5, the APP 12 provides various position settings that can be toggled on or off by the user. In some instances, only one position setting can be activated if that position setting would necessarily override another position setting. In the GPS setting 37, the position of the cup and ball on the green are determined by GPS. In using the GPS setting, the user (as shown in FIG. 6) is provided with a plan view of the green 38. Buttons 39 and 40 are provided for the cup and ball respectively as well as a mark button 41 . When the user steps on the actual live green, the user can walk to the location of the actual cup, press the cup button 39 so that the APP 12 knows that the user is going to mark the location of the cup 39. Pressing the mark button 41 causes the APP 12 to mark the location of the cup using GPS data. The mark button 41 once pressed provides a countdown timer in which an arm will sweep in a circular motion within the mark button 41 to indicate to the user that the APP 12 is measuring the location of the cup. If the APP detects that the GPS location is changing during the measurement, the countdown timer will slow so as to provide a more accurate measurement. That is, if the APP 12 detects that the GPS position is changing, either the user (i.e., the smartphone 10) is moving or the GPS location is still being calibrated based on the data being received from the GPS satellites. In either case, the location will not be determined until the GPS data has stabilized for a predetermined period of time (e.g., 10 seconds). Once the GPS location of the cup has been marked, the user can then walk to the location of the ball and repeat the process for the ball. Once the APP 12 has determined, via GPS calculations, the location of the cup and ball, the putt data selected by the user will be displayed. Of course, those of skill in the art will appreciate that other geo locating systems may be employed in addition to or in replacement of use of GPS to locate the position of the ball and cup. In the case of a graphical representation of the green as shown in FIG. 6, the ball 14 and cup 15 will be shown at their measured locations relative to the graphical representation of the green 38.

As illustrated in FIG. 7, the use of electronic markers to mark the location of the cup and ball is also contemplated according the to principles of the present invention. The marker or markers may use radio frequency technology or laser distance measurement to determine a distance from the cup to the ball and the location of the ball relative to the cup. In this embodiment, the location of each cup has been predetermined for that given day for a particular golf course. Upon reaching the golf course, the user downloads the pin locations to their smartphone 10 so that the pin locations are predetermined for the APP 12. When a user walks onto a green, the user marks the ball with an electronic ball. The ball marker may include a digital compass to allow the ball marker to know the direction of true north. By knowing true north, the distance from the cup and the angle between true north and the direction of the marker to the cup, the APP 12 can calculate the relative position of the ball to the cup. If the cup position is predetermined, the ball location can be calculated and displayed.

As illustrated in FIGS. 7A, a ball marker 50 includes on one side thereof an alignment arrow 51 to be pointed at the direction of the cup. The ball marker 50 further includes an electronic compass 53 that can detect the direction of True North and a processor/transmitter 54 to determine the angle between True North and the straight line between the ball and the cup and transmit that angle information to a smartphone running an APP according to the principles of the present invention. As illustrated in FIG. 7A, where the ball marker 50 is positioned adjacent the ball (X2, Y2) and the distance D1 to the cup and the location of the Cup at (X1 , Y1 ) is known, the position of the ball at (X2, Y2) can be calculated. Moreover, if the position of the cup at (X1 , Y1 ) on the green is known, the precise position of the ball at (X2, Y2) can be calculated as illustrated in FIG. 7B. As shown in FIG. 7B, the cup direction arrow will vary depending on the direction of the ball to the cup at any angle between 0 degrees and 360 degrees. The all ball positions (X2, Y2) relative to the cup (X1 , Y1 ) can be calculated for any measured angle Am between True North and the Cup Direction according to the following equations.

If 270 > Am > 180,

A2 = Am-180,

X2= -(sin A2/D1 ) and

Y2= (cos A2/D1 ).

If 180 > Am > 90,

A2 = 180 - Am,

X2= (sin A2/D1 ) and

Y2= (cos A2/D1 ).

If 90 > Am > 0,

A2 = Am,

X2= (sin A2/D1 ) and

Y2= -(cos A2/D1 ).

Using these equations, some sample calculations (set forth in Table I) illustrate that the location of the ball (X2, Y2) can be calculated for any measured angle Am when the distance D1 between the ball and the cup is known.

Table I

Am A2 PI X2 Y2

360 0 20 0 -20.0

340 20 20 -6.8 -18.8

270 90 20 -20 0.0

250 70 20 -18.8 6.8

180 0 20 0.0 20.0 150 30 20 10.0 17.3

90 90 20 20.0 0.0

30 30 20 10 -17.3

0 0 20 0 -20.0 As shown in FIG. 8, the ball marker may also or alternatively include an RF chip therein that may be accompanied by a RF chip in the cup. When the marker is placed on the green, the location of the marker can be triangulated relative to the cup where a RF beacon is provided near the green or at a central location on the golf course. The RF beacon provides a third reference point for triangulating the position of the marker on the green relative to the cup. This information is then transmitted to the APP 12. The APP 12 then displays the location of the ball on the green 38 since the location of the cup 15 is already known and displayed. Again, since there is some time involved in making the distance measurement and calculation, a countdown timer in the marker button 41 may be provided to let the user know when the calculations have been completed.

As illustrated in FIG. 9, the user setting allows the user to simply drag and drop the approximate location of the ball using a ball pin 14' and a cup pin 15'. This is particularly useful and can be relatively accurate when an accurate representation of the green 38 and an adjacent geographical object, such as a sand bunker 38' is presented to provide the user with proper green orientation relative to the location of the pin and the ball. Once the user has set the ball pin 14' and the cup pin 15', pressing the mark button 41 will cause the pins 14' and 15' to be set in place and the APP 12 to calculate the various putt information of the present invention.

Alternatively, in one configuration of the invention, this ball placement information is superimposed on the heat map or other graphical representation of the DTM and the user can then more accurately suppose the line of the putt and the force required to make the putt.

As shown in FIG. 10, the photo setting, the user, upon approaching a green, will take a photograph of the green, for example, from a marked photo spot adjacent the green. The APP 12, knowing that the photo is taken from a particular location and detecting the location of the ball and the cup from the photograph will then position the ball 14 and cup 15 on the green at their actual locations. This is done using image recognition software that determines the presence and location of the ball and presence and location of the cup. For example, once the photo is taken, the image recognition software locates a circular object having a particular relative size and color that would likely be a golf ball. Similarly, the photo recognition software locates an elongate straight object indicating the pin and locates the bottom of that object to determine the location of the cup. Once those two points are known, the software can then determine the relative position of the cup and the ball on the green and use that data for the APP in displaying the ball, cup and putt information to the user.

Regardless of the method employed to determine the ball and cup location on the green, once determined, the APP 12 uses this data to calculate and display information to the user regarding the proper path for the putt. As shown in FIG. 1 1 , the location of the ball 14 and cup 15 are displayed on a graphical or photographical representation of the green 38. In addition, putt information, such as distance between the ball 14 and cup 15, amount of break in the putt, position of an aiming point for making the put, plays like information depending on the slop of the green between the ball 14 and the cup 15 and true putting path are displayed on or superimposed over the green 38. As will be discussed in additional embodiments, the green 38 may also be displayed as a contour map, heat grid or other graphical representation in combination with the putt information shown in FIG. 1 1 .

In order to calculate the proper path of a putt that is most likely to be successful, FIG. 12 illustrates an example of three golf putt paths 1 10, 120 and 130. The ball at its initial position 140 travels along one of the three paths 1 10, 120, 130. Paths 1 10 and 130 represent unsuccessful events since the ball does not touch the circle representing the cup 100. The path 120 represents a successful putt if the ball stops just past the edge of the cup 100 so that it falls within the cup 100. In this particular embodiment, the paths 1 10, 120 and 130 indicate that the surface of the green is sloped from right to left, causing the path of a rolling golf ball 140 to curve from right to left. Each path 1 10, 120 and 130 begins at the ball 140 with the angle of departure of each path relative to the ball being the same. The variance of each path 1 10, 120 and 130 is a result of the ball having a different initial velocity with the path 1 10 representing a putt that has too little initial velocity and thus falls to the left of the 100, the path 130 representing a putt that has too much initial velocity and thus ends above the hole 100 and path 120 representing a putt that has the correct initial velocity and thus ends within the boundaries of the cup 100. It should be noted that while specific reference is made herein to the cup 100 as the end target for the ball, the present invention further contemplates that the target may be a space chose by the user or calculated by the system of the present invention so as to allow for predetermined favoritism for a two-putt strategy, especially when the user is faced with a more difficult first putt and/or when the system predicts that more than two-putts is likely.

FIG. 13 illustrates three successful putt events wherein it may be described as keeping the angle of departure constant while varying the initial speed of the ball or force applied. The ball at initial position 240 approaches the hole 200 through paths 210, 220, and 230. Path 210 may represent the minimum force required for success at a given angle, while path 230 may represent the maximum force or speed required for success at that same angle. Path 220 may represent the optimum solution at the illustrated angle of departure.

FIG. 14 also illustrates three successful putting events; yet in this exemplary embodiment, the initial angle of departure is varied as well as the initial speed or impact force. The ball at position 340 approaches the hole 300 through paths 310, 320, and 330. Path 310 may represent the minimum force required for success at a first given angle. The path 330 may represent the maximum force or speed allowed for success at an angle that is greater than the angle of departure for path 310. Path 320 may represent the optimum solution at an angle that is between the angles of departure for paths 310 and 330 and at an initial velocity that is between the minimum and maximum velocities for paths 310 and 320.

Referring again to FIG. 1 , to facilitate successful completion of a sporting event, such as a golf putt, a straight line 17 may be rendered between the object at its initial position and the position at the ideal outcome, such as the hole. The present invention may also render a target marker 21 at a fixed or user defined distance from the object at its initial position at the desired angle to achieve the ideal outcome. Another exemplary embodiment of the present invention may render a target 24 marked at a flat surface equivalent distance (FSED) (Plays Like distance) along the optimal angle of initial velocity. The FSED is the distance at which the ball would travel along a straight line, if the ideal initial velocity were applied to the ball on a perfectly flat golf green. The FSED quantity or Plays Like distance may provide the user useful (i.e., practical) information as to how hard he or she needs to hit the ball to complete a successful putt. The FSED may be determined by utilizing the present invention on a virtual model of a surface that is perfectly flat. The equations for the trajectory of the ball may be identical and the topography of the green may be simplified.

FIG. 14 illustrates a possible solution space, represented by the area A between paths 410 and 430 for a given initial speed of a golf ball rolling on a green. The ball 440 approaches the hole 400 at any space between paths 410 and 430. The lined region between 410 and 430 represents a successful solution space, or the solution space for a given initial speed that results in a successful event, such as making a putt.

FIG. 16 illustrates a graphical representation of an exemplary solution space.

The two-dimensional graph 500 shows a successful solution space 520 based on two parameters: p1 530 and p2 540. The ideal solution 590 for 530 and 540 is represented as a dot 590 within the successful solution space 520.

FIG. 17 illustrates an exemplary embodiment of visually representing information relative to the solution space of a successful event. In this particular embodiment, an absolute minimum force (Fmin) 610 appears at the left end and an absolute maximum force (Fmax) 650 appears at the right end of FIG. 6. It is to be assumed for this particular embodiment that these limits are representative of lower and upper bounds typical for putting on a golf green, respectively. A relative minimum force (Fa) 630 and a relative maximum force (Fb) 640 illustrate the lower and upper limits to attain a successful putt, given other known pre-set or user chosen parameters such as the speed of a green (Stemp meter reading), time of day, time of year, grass orientation or other local conditions and/or the location of the hole and the location of the ball on the terrain surrounding the hole. It should be noted that the system of the present invention may or may not account for any or all of such local conditions. A line 620 is also provided to connect the peaks of all lines representing each force to provide clarity to the viewer. A user may then view the provided information to assist in determining parameters such as angle or initial speed to better achieve a desired outcome, such as making a putt.

The information may be a flat surface equivalent distance, an initial speed, or other quantity. Furthermore, the visual representation may be a line on a 2D plane, a bar graph, a pie chart, or any other form.

The FSED limits may be pre-calculated based on the green topography for every hole in a particular course, or subset of a course. For example, the farthest distance on the green at a particular hole may be used as the upper limit for the FSED. Or, the farthest distance on a particular set of holes, front 9, back 9, all 18 for an entire course, additionally may be utilized as the upper FSED limit.

As illustrated in FIG. 18, a graphical representation, generally indicated at 700, of a putting green 702 is represented as a two dimensional contour map of the green 702. Such a graphical representation of the putting green 702 may be displayed on a smartphone 704 or other handheld device, such as a tablet PC or the like, which comprises a display screen 705 and internal electronic components which may include but are not limited to a processor, memory, a GPS chip, a transceiver, a two-way communication device, such as BLUETOOTH technologies, a speaker, a camera, such as the devices illustrated and describe in U.S. Patent 7,479,949 to Jobs et al., the entirety of which is incorporated by this reference. The contour map of the green 702 is provided with contour lines 710-716, where each contour line represents a particular change in elevation in the surface of the green 710, such as 2, 4, 6 or 12 inch changes in elevation of the surface of the green 702 similar to elevational changes represented in topographical maps.

As illustrated in FIG. 19, a graphical representation, generally indicated at 800, of a putting green 802 is represented as a two dimensional gradient map of the green 802. Such a graphical representation of the putting green 802 may be displayed on a smart phone 804 or other handheld device, such as a tablet PC or the like. The gradient map of the green 802 is provided with color coded areas 810- 816 representing areas of incline within the green 802, wherein each color coded area represents a particular inclination change in the elevation in the surface of the green 810, such as a change of 2, 4, 6 or 12 inches over a particular distance, such as 6, 12, 24 or 36 inches. The hole is represented by circle 818 with an arrow 820 indicating the general direction of the slope of the green relative to the hole 818.

As illustrated in FIG. 20, a graphical representation, generally indicated at 900, of a putting green 902 is represented as a two-dimensional difficulty map of the green 902. Such a graphical representation of the putting green 902 may be displayed on a smart phone 904 or other handheld device, such as a tablet PC or the like. The difficulty map of the green 902 is provided with color-coded areas 910- 914 representing areas of difficulty of the putt based on various factors. The factors may include both variable factors, such as the initial speed and direction of the putt involved as well as constant factors, such as the speed of the green, the distance from the cup 915, graphically represented by pin or flag 915, and the slope of the green between any actual, possible or assumed ball location and the cup 915, incline within the green 902, wherein each color coded area represents a particular inclination change in the elevation in the surface of the green 810, such as a change of 2, 4, 6 or 12 inches over a particular distance, such as 6, 12, 24 or 36 inches. The various areas of difficulty from the area 914 surrounding the hole 915 to the areas 910 and 913 that may represent the most difficult putts for a ball residing within one of these areas for a pin placement within the area 914 may be based upon a calculation in which a range of percentages of making a putt from within a particular area or zone can be predetermined. For example, the areas 910 and 913 may represent the area in which a putt from that area has a relatively high probability of being missed, while area 91 1 represents the area in which a putt has a moderate probability of being missed, area 912 represents the area in which a putt has a moderate probability of being made and area 914 has a high probability of being made. Having this information prior to hitting a golf shot to a green can provide a golfer with invaluable information. In most instances, when a golfer is hitting a golf ball to a green the golfer would like to know the positions on the green where a putt has a better chance of being made and the positions on the green where a putt has a greater chance of being missed. The golfer can then aim to attempt to land the ball in the preferred areas and avoid the less-preferred areas. It should be noted that it may often be the case that the a most preferred area may not necessarily be concentric around the hole 915 as greens often slope around the hole and thus, for example, may result in the preferred area extending more below the hole than above the hole. Likewise, the difficulty may be measured by, for example, the size of the target area, whether the target area comprises an around or proximate the cup or just the cup itself or the relative difficulty of several ball locations relative to the cup location on the display.

In calculating the difficulty of a particular putt for displaying the difficulty map as illustrated, several factors may be taken into consideration, some of which may be variable factors and some of which may be constant factors. For example, the predicted likelihood that a particular putt from Point A, where the ball resides, to Point B, where the cup resides may depend on the distance D from Point A to Point B, the speed S (Stemp reading) of the green, the change in elevation Δ E between Point A and Point B, whether the change in elevation is positive or negative, the transverse slope (AS) of the surface of the green between point A and Point B, the added difficultly -S if the putt is a downhill putt, the number of discrete elevation changes (NE) between Point A and Point B, the number of discrete transverse slope changes (NS) of the surface of the green between Point A and Point B, the proficiency (P) of the particular golfer attempting the putt for putts of similar distance, the percentage of made putts (%M) from locations similar to Point A, etc.

Accordingly, the odds O in percentage of success of a particular putt may be calculated as:

O = ((P + %M)/2) (1 /D)(1/AE)(1 /-S)(1/AS)(1/NE)(1/NS) That is, the Odds O are equal to the proficiency P of the golfer plus the percentage of putts actually made by other golfers from a similar location divided by 2 with each of D, ΔΕ, AS, -S, NE and NS being inversely applied so as to decrease the odds O as each of the factors that affect the likelihood of a successfully made putt increases. It should be noted that each of the factors D, ΔΕ, AS, -S, NE and NS may not be in absolute numbers but included as determined functions based on real world measurements. For example, the difficulty of a putt for a putt between 2 feet and 20 feet may not be a linear function. Moreover, the effect on the odds for a change in elevation may be represented by a range of numbers from, for example, 1 - 5, where no change in elevation is represented by the number 1 so as to have no effect on the calculation, while a sever elevation change (e.g., greater than five feet) is given a factor of 5. Likewise the change in slope may also be represented by a range of numbers from 1 -5 for example, with a sever slope given a factor of 5, while no transverse slope to the putt is given a factor of 1 so as to not affect the odds O. The number of elevation NE and/or slope changes NE between Point A and Point B may also be represented by a range of numbers in which no changes are

represented by the number 1 so as to not affect the odds, while 2 actual measured changes may be represented by a number between 1 and 2 in that the effect on the odds O by the NE or NS are never greater than 50%. It is noted that not all of the various factors may be included in determining the odds. For example, it may be desired and sufficient to only use such factors as the golfers proficiency, if known, the distance and the transverse slope. For generating the difficulty map, various points, such as in a grid of Points A separated by a small distance (e.g., 6 inches) are applied to the DTM of the green. Based on at least the distance D and change in transverse slope AS (i.e., the amount of projected break of the putt) from Point A to Point B, the difficulty map is calculated, where locations of a higher odds O are presented in a first color (e.g., green) and locations of lower odds O are presented in a second color (e.g., red). The difficulty map can then be provided to the user before an approach shot to the green. This allows the user to see where to land the ball in order to have higher odds of making the subsequent putt. It is often known on golf courses that balls left at certain locations relative to the cup result in putts that are virtually impossible to make. In some instances, the best location on the green is not directly at the pin. Knowing where to land the ball on the green can, in some circumstances, make the difference between a par and a double bogie. As such, the difficulty map of the present invention can be viewed by the user prior to hitting a golf ball onto the green. Once the ball is on the green, the plot of the projected path in order to make the putt can be superimposed over the difficulty map, or provided in other graphical ways as described and shown herein.

As illustrated in FIG. 21 , a graphical representation, generally indicated at 1000, of a putting green 1002 is represented as a two-dimensional difficulty map of the green 1002. Such a graphical representation of the putting green 1002 may be displayed on a smart phone 1004 or other handheld device, such as a tablet PC or the like. The difficulty map of the green 1002 is provided with color-coded areas 1010 and 101 1 , with area 101 1 representing an area of likely misses relative to the hole 1013 based on the initial ball position 1015. Factors used to calculate and display the area of likely misses 101 1 may include both variable factors, such as the initial speed and direction of the putt involved to be made as well as constant factors, such as the speed of the green, the distance from the hole 1015 and the slope of the green between the ball 1015 and the hole 1013. The area of likely misses 101 1 may be based on a percentage deviation from an ideal putt having a particular direction and speed. By varying one or both factors by a predetermined percentage, e.g., 5% or 10%, the graphical representation of this area 101 1 of dispersion can be calculated and displayed. This information can provide the golfer with information such as what factors can have the most dramatic effect on a miss. For example, by allowing the golfer to fix the speed to the preferred speed and display misses based on a 10% variance in direction, the golfer can see the preferred side of the hole 1013 to miss the putt and end up closer to the hole at the end of the putt. Likewise, the golfer could fix the direction to that of the preferred direction and vary the speed by 10% to see whether it is better to err by leaving the putt short or by putting the ball past the hole 1013. The area 1012 may be shaded in a gradient manner across the green 1002 from one color, such as green nearest the hole 1013 to another color, such as yellow, at locations 1014 furthest from the hole 1013 where the difficulty of a putt from that area is most difficult. As such, both the area of likely misses can be represented around the hole 1013 while the putt difficult of putts from any location on the green can be simultaneously displayed.

Accordingly, the target may comprises a target area, represented by the circle surrounding the cup or hole 1013, which may be concentric with the hole 1013 as illustrated or offset relative to the hole 1013 so that, for example, the user is left with an uphill and relatively straight putt for a second putt if the first putt is missed. In other words the target may be a target area for a user that is interested in

determining a good position to leave the ball after a first putt in order to have a better chance of making a second putt. It is often the case that a hole 1013 is placed in a location where a missed putt to one side of the hole 1013 results in an easier second putt than if the first putt is left on the other side of the hole 1013. For example, when the green is severely sloped, a second putt that is from a location below the hole 1013 is generally easier to make than a putt of equivalent distance that is above the hole 1013. In such an instance, the area below the hole 1013 would be indicated as the target area.

Likewise, the present invention may determine the difficulty attaining an optimal initial velocity of a golf ball to best achieve a two-putt event. The two-putt event may be characterized by achieving a first putt ending position of the ball to be within a desired distance from the target or hole. All estimations in determining the likelihood of an event, the solution space, or any other parameter disclosed herein may be applied to a two-putt event. In this instance, the target may be estimated to be a circle of a larger radius (a desired distance away from the hole) or a segmented space or ameba-like space adjacent to the cup. Since the target for golf putts is already a circle, the radius parameter for the target may be changed, and all equations applied analogously to the two-putt event calculation. The present invention may determine the position of the ball relative to a target or hole by receiving data relevant to the ball, and the surroundings of the ball, and computing the position of the ball relative to the surroundings. There are many different ways to determine the position of the ball. Some exemplary embodiments of the present invention may include photography and image processing, global positioning systems (GPS), ball marker devices, radio frequency identification tags, a digital compass, or other method.

While technology is rapidly advancing for scanning of golf greens and the creation and display of associated "digital terrain maps" ("DTM"), a significant impediment has arisen to full utilization. To date, no one has offered a simple method to capture the location of the ball during real-time play as a player approaches or enters upon the green. The present invention provides a simple method that captures the location of the ball and displays that location on the DTM (e.g., large and remote or small and local) with both the DTM and ball location displayed on a media device such as a smartphone. The present invention may be seamlessly integrated into any putting aid or visualization tool and in a manner that will not retard the pace of play. Additionally, the present invention can capture and depict the ball location of more than one player. Users of the present invention may include golfers, instructors (class room or live), broadcasters, gaming houses and pin placement workers.

In one embodiment, the location of the pin or cup on each DTM of a scanned green may be assured through other means and that is included in the system or method by other methods. In another embodiment, a golfer or other person may capture and insert into the DTM the location of the cup. The present invention utilizes the capabilities of current "phone camera" technology to align selected camera capture points within the applicable DTM. After the golfer's ball is on the green, the camera operator (golfer, broadcast media, caddie or other person) positions the camera in such location as to capture on camera a 2-D image showing the golf ball of interest and the cup. The system and method can be employed either before the pin is removed or during the time that the pin remains in the cup (as when an "on-green" player awaits a pitch shot from an "off-green" player. The scene is then captured with the camera. The camera also captures and integrates, using known art, the bearing of the captured scene; that is, the scene is labeled with its facing direction, such as in land conveyancing descriptions, "North, 30 degrees, seven minutes and 18 seconds West" where such description is chosen as the midline of the captured image. It is not necessary that the ball or pin be exactly on such mid line, just that each be visible in the scene. Also, other orientation methods could also be deployed.

The camera operator then taps on the scene depicted on the camera (or moves a cursor or icon) showing the location of the ball shown in the captured visualization (or "picture") of the green. In one iteration of the invention, the operator does the same to capture the location of the cup. Alternatively the course manger could have determined the location of the cup and conveyed that data to the method or data set of the method prior to the initiation of play. Using applications already available in current cameras, the associated X and Y location of the ball point (and alternatively also the cup point) is sent to the associated program application. Note, this conveyance is not of the GPS location but rather is just of the X and Y location within the relative scene captured by the camera. It is this X and Y location information that is superimposed into the DTM.

In at least one embodiment of this invention, a third point on the green or its parameter can be similarly designated to give the system a third reference point, or the system can be so configured as to designate the location of the camera as such designated point. For example, a small permanent marker could be placed adjacent each putting green to designate the designated camera point for that green so that the system would automatically know the orientation of the ball and cup relative to that point once the picture was taken. The location of each permanent marker could be provided on the graphical representation of the green on the user interface so that the user will know prior to approaching the green the location of the permanent marker. The permanent marker may be placed at a location where the entire green can be photographed within a single picture and where all portions of the green are visible. Visual alignment markers on the screen may be provided to allow the user to align the captured image with a predetermined position of the green on the display screen so that the user can properly position the green within the display. For example, for a given green at a given golf course, a graphical representation of the outline of the green may be superimposed on the screen as the picture is being taken. The user would then simply align the outline of the green with the actual green in the image to be taken. Once the green is photographed, the ball and cup location may be automatically determined by the software as by utilizing image recognition software or by allowing identification of the ball and cup by the user as by utilizing movable icons on the display to be positioned on the photo of the green at the locations of the ball and cup. By knowing relatively precisely the location of the ball and the cup relative to the green, the system of the present invention can quickly and accurately calculate or retrieve from stored prior calculations and display the optimum putting path for making the putt.

Once gathered, the reference points are then conveyed into the application and converted to be imposed into the DTM that has been previously captured and recorded. The applicable DTM may be provided by various means. Such means might include, by way of illustration and not limitation, a sensing unit built into the camera, being previously coded to align with that DTM within the method that is closest to the camera. Or the camera operator could choose a green from depicted alternatives shown on the screen using technology outside the scope of this invention. A prior designation may also be used.

Confidence intervals can be utilized in the method using computations previously accomplished and stored in a library of possible locations A and B on any given green, the media screen can be informed that the level of confidence of the computed putting path is within X percent, irrespective of whether the exact location has been captured within a chosen variance. For example, the method may inform the user that the computed line is reliable up to 90% for a variance of ball placement up to 6 inches. Or for example, that the computed putting path is reliable up to only 50% for any putt to the right of the hole for up to 3 inches.

Determining the position of the ball with photography and image processing may comprise receiving reflectance data of ball and the surroundings; receiving position data of the location of the target; receiving position data of the location where the reflectance data were acquired; receiving orientation data at the event of acquiring the reflectance data; comparing reflectance data at received position and orientation to a precomputed model of reflectance data from said position and said orientation; refining parameters of received position and orientation to best match precomputed model; identifying the ball or plurality of balls in reflectance data;

computing position of the ball or plurality of balls relative to the target.

The user may identify the ball by selecting a desired ball from the plurality of balls identified. The user may indicate graphically, select from a numerical list, use a touch screen, or other method. The position of the ball may be determined by utilizing GPS data sufficiently nearby the flag and utilizing a device that may be placed on the hole as a golfer places for a ball marker as he or she waits to complete the putt. The ball may be located by then receiving position data of the location of the target, determining the distance from the ball to the target; determining the orientation angle from the ball to the target, relative to a known orientation angle.; and determining the position of the ball from the received and determined information.

Determining the position of the ball may comprise a radio frequency identification (RFID) tag and a digital compass. First, the present invention receives position data of the location of the ball, then determines the orientation angle from the ball to the target, relative to a known orientation angle. Third, the present invention may determine the position of the ball from the received and determined information. Determining the position of the ball may comprise utilizing user input. A user may identify the location of the ball relative to said surroundings.

As illustrated in FIG. 22, once the position of the ball 1 1 15 and hole 1 1 13 is determined or inputted relative to the green 1 102, a graphical representation 1200 of the ball 1 15 and hole 1 13 can be displayed over a graphical representation 1 100 of the green 1 102 on a smartphone 1 104. The graphical representation 1 100 of the green 1 102 may be a two-dimensional representation of the green as previously described, an aerial photograph of the green, a three-dimensional model of the green or other representation. Once the ball 1 1 15 and hole 1 1 13 are graphically represented on the green 1 102, the preferred path 1 1 1 1 of the putt can be calculated and displayed on the green 1 102. Other features can be toggled between the putting line representation 1 1 14 currently being displayed and, for example, the 2-putt calculation 1 1 12. Other options, maps and stats may also be provided and selectable with various buttons 1 1 16, 1 1 17 and 1 1 18, respectively, on the smartphone 1 104 or other similar device.

Determining the position of the ball relative to the target, such as the cup on the green, may comprise receiving distance information relative to a plurality of known locations nearby the ball, receiving distance information of the ball to the plurality of known locations, receiving distance information of the target to the plurality of known locations, and determining the position of the ball and target relative to the surroundings. To do so, a RFID tag may be embedded in a ball marker. A second RFID tag may be placed in the cup or in a marker placed near the cup. Signals from the RFID tags can provide distance information to determine the location of each of the golf ball and cup and relative distance apart.

The position of the ball may be determined relative to the target by receiving position information of a location where a ball may be placed relative to surroundings and receiving position information of the target relative to surroundings. This may be accomplished by GPS, differential GPS, total station, or other methods known to those skilled in the art. For example, the user could position himself near the ball to obtain a first GPS position and near the hole for a second GPS position, each GPS position being associated with the relative position on the putting green.

The present invention may also acquire utilization data such as market or product research, data for product enhancement, product promotion or other marketing utilization, or for any other use. Data may be acquired by recording data as a user utilizes the system and methods of the present invention. Control and variable experiments may also be performed to determine the degree of efficacy of the present invention. For example, one user may perform a task relative to a golf putt without the use of the system and methods of the present invention while another user utilizes the systems and methods of the present invention. The results could then be compared to determine the efficacy of the system and methods of the present invention. Data acquired may be recorded, such as voice or video recording, to utilize the present invention in marketing training or other uses.

In an exemplary embodiment, the terrain may be modeled by utilizing accurate measurement data from a 3D spatial data acquisition device such as a LiDAR scanner.

The present invention may furthermore utilize likelihood information wherein information pertaining to the quantified likelihood of accomplishing an event is visually presented to a viewer. This may comprise a 3D simulation, for example. A non-exhaustive list of information that may be visually presented may include:

recording a 3-dimensional line representing the ideal outcome; rendering a 3- dimensional line representing the ideal outcome; rendering a line representing the path of an actual outcome; rendering the volume or surface area of the solution space of a successful event; rendering an animation of a 3D model representing the ideal outcome; rendering an animation of a 3D model representing the ideal outcome simultaneously with that of an actual outcome; comparing the path of an actual outcome to that of the solution space; comparing the path of an actual outcome to that of the ideal outcome; or rendering parameters relative to achieving the successful outcome. Such renderings may include renderings of the terrain or other objects to properly orient a viewer.

For example, as illustrated in FIG. 23, the terrain of the green 1202 may be modeled by utilizing representative measurement data from a 3D spatial data acquisition device such as a LIDAR scanner. In the case of capturing data representative of the terrain of the green, when the LIDAR scanner is being used, the permanent marker previously discussed could be placed at the location of the LiDAR scanning for each green. That way, the resulting terrain data can be easily matched and utilized to calculate the break of a putt between the golf ball and the cup. The graphical representation 1200 of the green 1202 may include an overlaying grid or mesh 1204 that illustrates contours on the green 1202 based on varying spacing between grid lines. In addition, the green 1202 may comprise a three dimensional surface model that can be manipulated by the user as by rotating and tilting the image of the green 1202 to allow the user to view the green from different angles and viewpoints, including viewing from directly behind the ball 1206 or hole 1208. Rotational or tilting of the green may be controlled by various gesturing on a touch screen display of the smartphone 1203 such as two-finger rotation, two-finger splitting and combinations thereof. The graphical representation 1200 also displays a preferred putting path line 1210 as well as an aim point 1212 for the putter. In addition, the graphical representation 1200 may include written instructions 1214 that include aiming direction and relative speed of the putt. The relative speed of the put may be a number representing a number within a scale. For example, a speed of 5 may represent a speed of a putt on a flat surface, whereas a speed of 7 may represent a speed of a putt that is downhill. Likewise, the smartphone 1203 may provide an audio cue with the same information. For example, the smartphone could provide audio instructions to the golfer such as, "Aim eighteen inches to the right of the hole. Putt is slightly downhill." Other audio cues may also be used.

Referring now to FIGS. 24 - 28, there is illustrated another embodiment for determining relatively precisely the distance from the ball to the cup. The process utilizes the camera, accelerometer, digital compass and processor of the electronic handheld device, in this case a smartphone 1300. As a first step, as shown in FIG. 24, the user is provided with a means for determining the height that the phone is to be held in order to get the most accurate distance measurements using the smartphone 1300. To do so, two marks are placed at a precise distance apart (e.g., 3 feet, 5 feet, etc.) on the floor. A virtual bubble level 1302 is displayed on the smartphone 1300 while the camera application is activated. The virtual bubble 1302 may also be calibrated by operating a calibration mode in which the smartphone is placed on a level surface and so that the virtual bubble 1303 will be centered in the cross hairs 1304. The user, while maintaining the virtual bubble 1303 in the center of the cross-hairs 1304, raises or lowers the phone relative to the floor until Point A cross hairs 1306 are centered on Point A and Point B cross hairs 1307 are centered on Point B. At this point, which may be at approximately waist height, the user is instructed to remember and/or record the precise height of the smartphone 1300 so that in the field, the height of the phone for measuring a distance from a ball to the cup can be repeated. It is also contemplated that a custom height H could be calibrated so that the user can place the phone 1300 at, for example, belt buckle height, and the distance between cross-hairs 1306 and 1307 can be manually adjusted by the user as by dragging and dropping so as to be a precise distance apart (e.g., 3 feet apart when the phone 1300 is level at height H.

As shown in FIGS. 25 and 27, once calibrated, the system knows the precise distance between Point A and Point B when viewed through the smartphone camera at the set height H and when viewed from any of a plurality of positions selected from the environment of points A and B. That is, in use, when the smartphone is held at height H corresponding to the calibrated height previously discussed and level to the horizon, the distance between the cross hairs 1306 and 1307 will indicate a distance of, for example, 3 feet or 5 feet, when the distance D1 between the ball 1308 and cup 1310 is three feet or 5 feet respectively, in order to properly align the cross hairs 1306 and 1307 at height H. In this configuration, the phone will be substantially level to the horizon. In a refined configuration, the need for level presentation may be avoided and the smart phone will compute the delta from level as to be plus in one direction and negative in the opposite direction such that these differences are taken into account using trigonometry computations known to those of skill in the art.

As show in in FIGS. 26 and 28, in order to accommodate and measure different distances (e.g., greater than three feet) from the ball to the hole, the smartphone 1300 will be angled at an angle A1 chosen from a plurality of angles starting at a relative minimum angle to capture both objects and extending to a less acute angle within the needed tolerances of the smart phone so as to be able to view both the ball 1308 and the cup 1310. Furthermore, in order to place the ball 1308 in the cross hairs 1306 and the cup in the cross hairs 1307, because of limitations in the field of view FV of the camera, the user may need to step back from the ball 1308 in order to have both the ball 1308 and cup 1310 in view. The distance D2 between the smartphone 1300 and the ball as shown in FIG. 28 can be calculated. That is, because the smartphone is a predetermined height H and at a detectable angle A to the horizon using the accelerometer of the smartphone, the distance D2 can be calculated as D2 = sin A1 . The angle A2 between cross hair lines 1306' and 1307' is also known. As the angle A1 is increased in order to increase the viewable area between the ball 1308 and the hole 1310, the distance D1 from the ball 1308 to the cup 1310 is calculated as D2 = sin (A1 + A2) - D2.

Once the distance D1 between the ball 1308 and the cup 1310 is calculated, if the position (i.e., coordinates) of the cup 1310 are known relative to the DTM of the green, the system can then utilize the digital compass of the smartphone 1300 to calculate and determine the position of the ball 1308 relative to the cup as previously described herein. To do so, the user would return the phone to a substantially horizontal orientation so that the digital compass can determine the direction of True North N in order to triangulate the position of the ball relative to the cup on the DTM. The system of the present invention can then utilize this information to graphically display the ball on a graphical representation of the DTM on the display of the smartphone and plot and display other information for the user regarding a putt from the ball to the cup as previously described herein.

As set forth herein, the present invention provides a system for determining ball and cup locations on a green and projecting, conveying or otherwise displaying information relating to a putt from the ball to the cup. According to the present invention, the system for displaying information on a user interface relating to a golf putt on a golf green comprises generating a digital terrain map of a golf green, determining a first approximate location of a cup in the golf green and generating cup coordinates relative to the digital terrain map, inputting cup coordinates of the approximate location of the cup for placement of the cup at a representative location on the digital terrain map, storing the digital terrain map and the cup coordinates in memory of a user device, determining a second approximate location of a golf ball on a golf green in real time and generating ball coordinates relative to the digital terrain map, calculating a projected path of a golf ball from the ball coordinates to the cup coordinates in which the golf ball is most likely to travel from the ball coordinates to the cup coordinates, the projected path based on a contour of the green represented by the digital terrain map, velocity of the golf ball when traveling from the ball coordinates to the cup coordinates and angle between a first straight line between the ball coordinates and the cup coordinates and a second straight line between the ball coordinates and an aiming point that is at a distance from the cup coordinates that is calculated to be the location where a putt to the aiming point will most likely result in a successful putt as a result of the effect of the contour of the green, and displaying information of the ball location, cup location, projected path, aiming path and a plays like distance on a user interface of the user device.

The system further includes determining the difficulty of the putt based on the location of the golf ball relative to the cup and the contour of the digital terrain map and displaying information regarding the difficulty of the putt on the display of the user device. The information regarding the difficulty of the putt on the display of the user device may comprise a probability of success of the putt. The information regarding the difficulty of the putt on the display of the user device may comprises a color gradient comprising a first color indicating an easier location on the green for a successful putt and a second color indicated a harder location on the green for a successful putt. The displayed information may also include results from the most recent attempt at the same hole, results from a user selected past attempt at the same hole and/or accumulated results from a plurality of past attempts at the same hole or plurality of holes.

The method for determining the location of the ball may comprise providing means for a user to indicate on a device a location of a golf ball, utilizing a device or plurality of devices that transmit pre-determined position information, photographing the ball and surroundings and utilizing image processing or utilizing a device that transmits pre-determined position information and a device that determines orientation information. Determining the location of the ball may also comprise generating a photograph of the ball and the cup with the user device, and

determining a distance between the ball and the cup from the photograph.

Determining the location of the ball may also comprise detecting an angle of incline of the user device relative to a horizon and using the angle of incline to accurately determine the distance from the ball to the cup in from the photograph.

The location of the ball may also be determined by receiving data regarding the ball, and the surroundings of the ball and computing the position of the ball relative to the surroundings. Likewise, the position of the ball may be determined by receiving reflectance data of ball and the surroundings, receiving position data of the location of the cup, receiving position data of the location where the reflectance data were acquired, receiving orientation data when acquiring the reflectance data and comparing the reflectance data at the received position and orientation to a precomputed model of reflectance data from a position and orientation substantially equivalent to the received position and orientation data, refining parameters of received position and orientation to best match the precomputed model, identifying a ball in reflectance data and computing position of the ball relative to the cup. as

The location of the ball may also be determined by receiving position data of the location of the cup, determining the distance from the ball to the cup, determining the orientation angle from the ball to the cup, relative to a known orientation angle and determining the position of the ball from the received position data and determined distance and orientation angle. Likewise the position of the ball may be determined by receiving position data of the location of the ball, determining the orientation angle from the ball to the target, relative to a known orientation angle and determining the position of the ball from the received and determined information. The position of the ball may be further determined by receiving a graphical representation of the ball and the surroundings and allowing a user to identify the location of the ball and the cup relative to the surroundings. Likewise, determining the position of the ball relative to the cup may include receiving distance information relative to a plurality of known locations nearby the ball, receiving distance information of the ball to the plurality of known locations, receiving distance information of the cup to the plurality of known locations and determining the position of the ball and cup relative to the surroundings.

In various aspects of the invention, the system determines and displays information regarding the difficulty of the putt by determining the solution space of a successful event, determining the solution space of all events and comparing the solution space of a successful event to the solution space of all events. When determining the solution space, non-linear dynamics associated with an event may be modeled by fitting sample data to a piecewise linear curve, fitting sample data to a quadratic curve, fitting sample data to a cubic spline, fitting sample data to a b- spline, fitting sample data to a linear combination of rational functions and fitting sample data to a linear combination of exponential functions.

Additional information provided to the user may include at least one flat surface equivalent distance (FSED) to achieve a successful putt compared to a set of reasonable limits to provide information regarding relative strength required to accomplish the successful putt. The FSED limits are determined by utilizing the green topography for every hole location in a particular golf green, or subset of a golf green. Additional information may include graphically illustrating a parameter used in quantifying the likelihood of a successful event, graphically illustrating a difficulty of a successful putt as the inverse of the ratio of the size of the successful solution space to the total solution space, such as a grid of ideal outcomes used to determine the ideal outcome for any position of ball on the green.

To determine a solution space for successful and all events the system may include establishing a first test putt, apply first test putt to relevant green topography, calculating a line of variance, calculating sequential test putts and selecting an optimum sequential test putt. In addition, establishing a first test putt may include establishing an orientation direction, establishing a cup position, establishing a first ball position and determining the first ball stop position based on at least one of force or velocity.

Selecting the optimum sequential test putt may comprise producing a series of sequential test putts using the same ball force or speed as applied on the first test putt only varying the angle, producing a series of sequential test putts using varied forces or speeds for each of the sequential tests putts performed previously and determining a single putt that most closely resembles the characteristics of the ideal angle and force or speed.

To determine the parameters for a desired outcome the system of the present invention determines an offset angle or plurality of offset angles associated with the ideal angle and force or speed and determines an offset force or speed or plurality of offset forces or speeds associated with the ideal angle and force or speed.

Subsequently, an amoeba-like territory indicating where the ball may stop if the putt force or speed applied is slightly greater than or slightly less than the ideal force or speed can be displayed and an amoeba-like territory indicating where the ball may stop if the putt angle applied is slightly clockwise or slightly counter-clockwise relative to the ideal angle.

To determining an ideal outcome, real-world coordinates for the actual location of the ball, the cup, or other necessary parameters may be used. Likewise, the system of the present invention may be configured to determine the parameters for an optimal putt, determine parameters for a 2-putt, at ball stop position, reverse engineer most likely path, and at ball stop position, reverse engineer a plurality of likely paths.

It is contemplated that the information displayed by the system of the present invention may include displaying a virtual golf putt and allowing a user or plurality of users to utilize the displayed information and recording data relative to the utilization of displayed information. The plurality of users can then utilize the system for determining a golf ball location, a target location and terrain information of a putting green and recording data as the plurality of users utilize the system.

According to the present invention a constant coefficient of rolling friction may be used by computing a friction force with the formula _ί,_αοη = C_rmgvwhere C_r is the coefficient of rolling friction (typically between 0.05 and 0.15), m is the mass of the ball, g is the gravitational constant and v is the velocity of the ball.

It is further contemplated that a desired outcome may comprise utilizing a calculated first guess for initial velocity. Utilizing a calculated first guess for initial

I ^" 2C sd

velocity may include employing the formula v_; = \v_f + ^ ^r ^ , where v, is the initial velocity, Vf is the final velocity, C_r is the coefficient of rolling friction (typically between 0.05 and 0.15), g is the gravitational constant, d is the distance from the ball to the hole, and ξ is the factor used in calculating the moment of inertia based on the properties of the ball.

In determining parameters for a desired outcome a moment of inertia for the golf ball may be utilized, which is determined by at least one of the formulas:

/ = ^mr²

I = r hm

where ξ is a factor determined by experimentation, m is the mass of the ball, r is the radius of the ball, p is the density function of the ball (mass per unit volume) and V \s volume, and where Y suggests a numerical solution and f suggests an analytic solution.

Furthermore, the present invention may utilize information by graphically illustrating a parameter used in quantifying the likelihood of a successful event. An example of such a parameter may include a force or plurality of forces applied to achieve a successful event, compared to a set of reasonable limits to provide information regarding relative strength required to accomplish said event

successfully.

Alternately, presenting information may include graphically illustrating the difficulty of a successful event as the inverse of the ratio of the size of the successful solution space to the total solution space. Such a quantity infers the difficulty of accomplishing an event. If such a quantity is very large, the likelihood of

accomplishing said event is very small. Contrarily, if the quantified difficulty is small, the likelihood of accomplishing the event is relatively high.

Determining parameters for a desired outcome may comprise in an exemplary embodiment: determining an offset angle or plurality of offset angles associated with the ideal angle and force or speed; determining an offset force or speed or plurality of offset forces or speeds associated with the ideal angle and force or speed; displaying an amoeba-like territory indicating where the ball may stop if the putt force or speed applied is slightly greater than or slightly less than the ideal force or speed; or displaying an amoeba-like territory indicating where the ball may stop if the putt angle applied is slightly clockwise or slightly counter-clockwise relative to the ideal angle. Such parameters may assist a golfer in deciding whether he or she should over or under strike the ball to prevent a large deviation relative to the ideal outcome and an actual outcome. If, for example, over-striking the ball would most likely occur in a large deviation between the ideal and actual outcomes, a golfer may choose to under-strike the ball to avoid taking an extra hit if the ball does not fall into the hole. Likewise, the angle may cause large deviations if hit too far clockwise, relative to the ideal angle, yet small deviations if hit too far counter-clockwise, based on the green terrain, green speed, or other factors. Graphically illustrating the information may include displaying pixels on a computer screen, a video game, a television set, a hand held electronic device, or other mechanism for providing visual information to a user. Thus, while specific examples and embodiments of the present invention employ the use of a

smartphone upon which an APP may be operated, the present invention is not so limited and may be employed using various electronic devices, including, but not limited to tablets, personal computers, a smartphone, a computer screen, a video game console, a television set, a hand held electronic device, an electro-mechanism for providing visual and audible information to a user and the like.

The illustrated embodiments of this invention are not limited to any particular individual feature disclosed herein, but include combinations of them distinguished from the prior art in their features, functions, and/or results achieved. Features of the invention have been broadly described so that the detailed descriptions that follow may be better understood, and so that the contributions of this invention to the arts may be better appreciated. Those skilled in the art who have the benefit of this invention, its teachings, and suggestions will appreciate that the conceptions of this disclosure may be used as a creative basis for designing other methods and systems for carrying out and practicing the present invention.

While there have been described various embodiments of the present invention, those skilled in the art will recognize that other and further changes and modifications may be made thereto without department from the spirit of the invention, and it is intended to claim all such changes and modifications that fall within the true scope of the invention. It is also understood that, as used herein and in the appended claims, the singular forms "a," "an," and "the" include plural reference, unless the context clearly dictates otherwise.

Unless defined otherwise, all technical and scientific terms used herein have the same meanings as commonly understood by one of ordinary skill in the art to which this invention belongs. While various methods and systems of the present invention are described herein, any methods ore systems similar or equivalent to those described herein may be used in the practice or testing of the present invention. All references cited herein are incorporated by reference in their entirety and for all purposes. In addition, while the foregoing advantages of the present invention are manifested in the illustrated embodiments of the invention, a variety of changes can be made to the configuration, design and construction of the invention to achieve those advantages including combinations of components of the various embodiments. Hence, reference herein to specific details of the structure and function of the present invention is by way of example only and not by way of limitation.

Claims

CLAIMS What is claimed is:

1 . A system for displaying information on a user interface relating to a golf putt on a golf green comprising:

generating a digital terrain map of a golf green;

determining a first approximate location of a target area on the golf green and generating target area coordinates relative to the digital terrain map;

inputting cup coordinates of the approximate location of the cup for placement of the cup at a representative location on the digital terrain map;

storing the digital terrain map, the first approximate location of the target area and the cup coordinates in memory of a user device;

determining a second approximate location of a golf ball on the golf green in real time and generating ball coordinates relative to the digital terrain map; calculating a projected path of a golf ball from the ball coordinates to the cup coordinates in which the golf ball is most likely to travel from the ball coordinates to the cup coordinates, the projected path based on a contour of the green represented by the digital terrain map, velocity of the golf ball when traveling from the ball coordinates to the cup coordinates and angle between a first straight line between the ball coordinates and the cup coordinates and a second straight line between the ball coordinates, an aiming point that is at a distance from the cup coordinates that is calculated to be a location where a putt to the aiming point will most likely result in a successful putt as a result of the effect of the contour of the green,;

displaying information of the ball location, cup location, projected path, aiming path, target area and a flat surface equivalent distance (FSED) on a user interface of the user device.

2. The system of claim 1 , further comprising determining the difficulty of the putt based on the location of the golf ball relative to the cup and the contour of the digital terrain map and displaying information regarding the difficulty of the putt on the display of the user device.

3. The system of claim 2, wherein the information regarding the difficulty of the putt on the display of the user device comprises a probability of success of the putt.

4. The system of claim 2, wherein the information regarding the difficulty of the putt on the display of the user device comprises a color gradient comprising a first color indicating an easier location on the green for a successful putt and a second color indicated a more difficult location on the green for a successful putt.

5. The system of claim 1 , wherein determining the location of the ball comprises at least one of:

providing means for a user to indicate on a device a location of a golf ball; utilizing a device or plurality of devices that transmit pre-determined

position information;

photographing the ball and surroundings and utilizing image processing; and

utilizing a device that transmits pre-determined position information and a device that determines orientation information.

6. The system of claim 5, wherein determining the location of the ball comprises generating a photograph of the ball and the cup with the user device, and determining a distance between the ball and the cup from the photograph.

7. The system of claim 6, wherein determining the location of the ball comprises detecting an angle of incline of the user device relative to a horizon and using the angle of incline to accurately determine the distance from the ball to the cup in from the photograph.

8. The system of claim 1 , wherein displaying information further comprises at least one of:

displaying results from the most recent attempt at the same hole;

displaying results from a user selected past attempt at the same hole; and displaying accumulated results from a plurality of past attempts at the

same hole or plurality of holes.

9. The system of claim 2, wherein determining the difficulty of the putt comprises:

determining a first solution space of a successful event;

determining a second solution space of all events; and

comparing the first solution space of a successful event to the solution second space of all events.

10. The system of claim 6, wherein determining the first and second solution spaces comprises modeling non-linear dynamics associated with an event.

1 1 . The system of claim 8, wherein modeling the non-linear dynamics comprises at least one of:

fitting sample data to a piecewise linear curve;

fitting sample data to a quadratic curve;

fitting sample data to a cubic spline;

fitting sample data to a b-spline;

fitting sample data to a linear combination of rational functions; and fitting sample data to a linear combination of exponential functions.

12. The system of claim 1 wherein the information comprises at least one flat surface equivalent distance (FSED) applied to achieve a successful putt compared to a set of reasonable limits to provide information regarding relative strength required to accomplish the successful putt.

13. The system of claim 12, wherein the FSED limits are determined by utilizing the green topography for every hole location in a particular golf green, or subset of a golf green.

14. The system of claim 1 wherein determining the location of the ball comprises:

receiving data regarding the ball, and the surroundings of the ball; and computing the position of the ball relative to the surroundings.

15. The system of claim 1 , wherein determining the position of the ball further comprises:

receiving reflectance data of ball and the surroundings;

receiving position data of the location of the cup; receiving position data of the location where the reflectance data were acquired;

receiving orientation data when acquiring the reflectance data;

comparing the reflectance data at the received position and orientation to a precomputed model of reflectance data from a position and orientation substantially equivalent to the received position and orientation data;

refining parameters of received position and orientation to best match the precomputed model;

identifying a ball in reflectance data; and

computing position of the ball relative to the cup.

16. The system of claim 15 wherein determining the position of the ball further comprises:

receiving position data of the location of the cup,

determining the distance from the ball to the cup;

determining the orientation angle from the ball to the cup, relative to a known orientation angle; and

determining the position of the ball from the received position data and determined distance and orientation angle.

17. The system of claim 16, wherein determining the position of the ball further comprises:

receiving position data of the location of the ball;

determining the orientation angle from the ball to the target, relative to a known orientation angle; and

determining the position of the ball from the received and determined

information.

18. The system of claim 17 wherein determining the position of the ball further comprises:

receiving a graphical representation of the ball and said surroundings; and allowing a user to identify the location of the ball relative to the

surroundings.

19. The system of claim 18, wherein determining the position of the ball relative to the cup further comprises allowing the user to identify the location of the cup relative to the surroundings.

20. The system of claim 1 , wherein determining the position of the ball relative to the cup comprises:

receiving distance information relative to a plurality of known locations nearby the ball;

receiving distance information of the ball to the plurality of known

locations;

receiving distance information of the cup to the plurality of known

locations; and

determining the position of the ball and cup relative to the surroundings.

21 . The system of claim 1 , wherein displaying information comprises graphically illustrating a parameter used in quantifying the likelihood of a successful event.

22. The system of claim 1 , further comprising pre-determining a grid of ideal outcomes and using a grid of pre-determined ideal parameters to determine an ideal outcome for any position of ball on the green.

23. The system of claim 2 wherein determining parameters for a desired outcome further comprises at least one of:

determining an offset angle or plurality of offset angles associated with the ideal angle and force or speed; and

determining an offset force or speed or plurality of offset forces or speeds associated with the ideal angle and force or speed.

24. The system of claim 23, wherein determining parameters for a desired outcome further comprises at least one of:

displaying an amoeba-like territory indicating where the ball may stop if the putt force or speed applied is slightly greater than or slightly less than the ideal force or speed; and displaying an amoeba-like territory indicating where the ball may stop if the putt angle applied is slightly clockwise or slightly counterclockwise relative to the ideal angle.

25. The system of claim 6 wherein determining the ideal outcome further comprises utilizing real-world coordinates for the actual location of the ball, the cup, or other necessary parameters.

26. The system of claim 2 wherein determining the parameters for a desired outcome of a putt comprises at least one of:

determining the parameters for an optimal putt;

determining parameters for a 2-putt;

at ball stop position, reverse engineer most likely path; and

at ball stop position, reverse engineer a plurality of likely paths.

27. The system of claim 1 , further comprising acquiring utilization data comprising a plurality of users utilizing a system for determining a golf ball location, a target location and terrain information of a putting green and recording data as the plurality of users utilize the system.

28. The system of claim 1 , wherein calculating a projected path comprises utilizing a constant coefficient of rolling friction by computing a friction force with the formula F_friction = C_rmgvwhere C_r is the coefficient of rolling friction, m is the mass of the ball, g is the gravitational constant and v is the velocity of the ball.

29. The system of claim 2, wherein calculating a projected path comprises utilizin lculated first guess for initial velocity according to the formula

where i , is an initial velocity, Vf is a final velocity, C_r is a coefficient of rolling friction, g is a gravitational constant, d is a distance from the ball to the hole, and £ is a factor used in calculating the moment of inertia based on the properties of the ball.

30. The system of claim 1 , wherein calculating parameters for a desired outcome further comprises utilizing a moment of inertia for the golf ball determined by at least one of the formulas: / = ξτην²

/ = ^ r² m

I = pr²AV

where £is a factor determined by experimentation, m is a mass of the ball, ris a radius of the ball, p is a density of the ball and V is volume.