US 20060192779 A1 Abstract A hidden line processing method includes the steps of obtaining the maximum value PZ
_{max }of the Z-axis direction component of each vertex in a viewpoint coordinate system for each of the plurality of polygons; sorting the plurality of polygons in a descending order based on the obtained maximum values PZ_{max}; obtaining a value LZ_{min }that is the smaller of the Z-axis direction components in the viewpoint coordinate system of two end points of an arbitrary line obtained from the plurality of polygons; and comparing the maximum value PZ_{max }of the Z-axis direction component of the plurality of polygons with the value LZ_{min }that is the smaller of the above obtained Z-axis direction components of the arbitrary line, in the sorted order, wherein at the time when LZ_{min}≧PZ_{max}, determination of whether or not the lines are hidden lines is avoided for polygons subsequent to the plurality of polygons sorted. Claims(18) 1. A method for identifying as an internal line a ridge line or an contour line of a three-dimensional model, appearing when only the interior of the three-dimensional model is displayed in projecting the three-dimensional model consisting of a plurality of polygons onto a two-dimensional plane, comprising the steps of:
determining the value in the Z-axis direction of a normal vector belonging to each of two polygons having a ridge line or an contour line of the three-dimensional model as a common side; and determining the common side as an internal line if the value in the Z-axis direction of any of the normal vectors of the two polygons is determined zero (0) or less based on the determination of the direction of the normal vector. 2. The method for identifying an internal line according to determining the relation of the positions of the two polygons in the Z-axis direction in the case where the directions of the values in the Z-axis direction of the normal vectors belonging respectively to the two polygons differs from each other based on the determination of the direction of the normal vectors; and determining the common side as an internal line when the normal vector of a polygon present on the viewpoint side is negative. 3. The method for identifying an internal line according to determining the common side as an internal line when the senses of the values in the Z-axis direction of the normal vectors respectively belonging to each of the two polygons are different from each other based on the determination of the directions of the normal vectors, when a portion of a side of one of the two polygons is hidden by the other polygon and when the direction of the normal vector of the other polygon is negative. 4. A method for projecting a sectional view of a three-dimensional model consisting of a plurality of polygons onto a two-dimensional plane in a state that the model is stuffed, comprising the steps of:
determining the value in the Z-axis direction of the normal vector belonging to each of two polygons having a ridge line or an contour line of a three-dimensional model as a common side; and determining the common side as an internal line when the value in the Z-axis direction of any of the normal vectors of the two polygons is zero (0) or less based on the determination of the directions of the normal vectors, wherein the sectional view of the three-dimensional model is displayed such that the sectional view is displayed in a state that it is stuffed, by excluding the line determined as an internal line from the target to be displayed in a line image projected on the two-dimensional plane. 5. The method for projecting according to an internal line to be excluded from the target of display in a line image projected onto the two-dimensional plane is the common side determined as an internal line when the senses of the values in the Z-axis direction of the normal vectors respectively belonging to each of the two polygons are different from each other based on the determination of the directions of the normal vectors, when a vertex of a polygon of the two polygons is in the other polygon, when the value in the Z-axis direction of a vertex of a polygon is larger than the value in the Z-axis direction of a vertex of the other polygon and when the direction of the normal vector of the polygon is negative. 6. The method for projecting according to an internal line to be excluded from the target of display in a line image projected onto the two-dimensional plane is the common side determined as an internal line when the senses of the values in the Z-axis direction of the normal vectors respectively belonging to each of the two polygons are different from each other based on the determination of the directions of the normal vectors, when a portion of a side of one of the two polygons is hidden by the other polygon and when the direction of the normal vector of the other polygon is negative. 7. An information processing apparatus for creating a two-dimensional image by projecting a three-dimensional model consisting of a plurality of polygons onto a two-dimensional plane, comprising:
a memory storing a program for processing of avoiding projecting of lines hidden by the polygons, and program data; program executing and controlling means for executing reading out of the program stored in the memory: and a display apparatus for outputting and displaying a two-dimensional image created by the program executed and controlled by the program executing and controlling means, wherein the program executing and controlling means, in order to identify a ridge line or an contour line of the three-dimensional model appearing when only the interior of the three-dimensional model is displayed, as an internal line in projecting the three-dimensional model consisting of the plurality of polygons onto the two-dimensional plane, according to the program and based on the program data stored in the memory, determines the value in the Z-axis direction of a normal vector belonging to each of two polygons having a ridge line or an contour line of the three-dimensional model as a common side; and determines the common side as an internal line if the value in the Z-axis direction of any of the normal vectors of the two polygons is zero (0) or less based on the determination of the direction of the normal vector. 8. The information processing apparatus according to determines the relation of the positions of the two polygons in the Z-axis direction in the case where the senses of the values in the Z-axis direction of the normal vectors belonging respectively to the two polygons differs from each other based on the determination of the direction of the normal vectors; and determines the common side as an internal line when the normal vector of a polygon present on the viewpoint side is negative. 9. The information processing apparatus according to determines the common side as an internal line when the senses of the values in the Z-axis direction of the normal vectors respectively belonging to each of the two polygons are different from each other based on the determination of the directions of the normal vectors, when a portion of a side of one of the two polygons is hidden by the other polygon and when the direction of the normal vector of the other polygon is negative. 10. An information processing apparatus for creating a two-dimensional image by projecting a three-dimensional model consisting of a plurality of polygons onto a two-dimensional plane, comprising:
a memory storing a program for processing of avoiding projecting of lines hidden by the polygons, and program data; program executing and controlling means for executing reading out of the program stored in the memory: and a display apparatus for outputting and displaying a two-dimensional image created by the program executed and controlled by the program executing and controlling means, wherein the program executing and controlling means, according to the program and based on the program data, determines the value in the Z-axis direction of the normal vector belonging to each of two polygons having a ridge line or an contour line of a three-dimensional model as a common side; determines the common side as an internal line when the value in the Z-axis direction of any of the normal vectors of the two polygons is zero (0) or less based on the determination of the directions of the normal vectors; and is arranged to display the sectional view of the three-dimensional model such that the sectional view is displayed in a state that it is stuffed, by excluding the line determined as an internal line from the target to be displayed in a line image projected on the two-dimensional plane. 11. The information processing apparatus according to an internal line to be excluded from the target of display in a line image projected onto the two-dimensional plane is the common side determined as an internal line when the senses of the values in the Z-axis direction of the normal vectors respectively belonging to each of the two polygons are different from each other based on the determination of the directions of the normal vectors, when a vertex of a polygon of the two polygons is in the other polygon, when the value in the Z-axis direction of a vertex of a polygon is larger than the value in the Z-axis direction of a vertex of the other polygon and when the direction of the normal vector of the polygon is negative. 12. The information processing apparatus according to an internal line to be excluded from the target of display in a line image projected onto the two-dimensional plane is the common side determined as an internal line when the senses of the values in the Z-axis direction of the normal vectors respectively belonging to each of the two polygons are different from each other based on the determination of the directions of the normal vectors, when a portion of a side of one of the two polygons is hidden by the other polygon and when the direction of the normal vector of the other polygon is negative. 13. A program executed and controlled in an information processing apparatus for creating a two-dimensional image by projecting a three-dimensional model consisting of a plurality of polygons onto a two-dimensional plane, the program being operable to execute a process for avoiding projecting of lines hidden by the polygons, the program comprising the steps of causing program executing and controlling means to, based on program data read our from a memory:
in order to identify a ridge line or an contour line of the three-dimensional model appearing when only the interior of the three-dimensional model is displayed, as an internal line in projecting the three-dimensional model consisting of the plurality of polygons onto the two-dimensional plane, determine the value in the Z-axis direction of a normal vector belonging to each of two polygons having a ridge line or an contour line of the three-dimensional model as a common side; and determine the common side as an internal line if the value in the Z-axis direction of any of the normal vectors of the two polygons is zero (0) or less based on the determination of the direction of the normal vector. 14. The program according to determine the relation of the positions of the two polygons in the Z-axis direction in the case where the senses of the values in the Z-axis direction of the normal vectors belonging respectively to the two polygons differs from each other based on the determination of the direction of the normal vectors; and determine the common side as an internal line when the normal vector of a polygon present on the viewpoint side is negative. 15. The program according to determine the common side as an internal line when the senses of the values in the Z-axis direction of the normal vectors respectively belonging to each of the two polygons are different from each other based on the determination of the directions of the normal vectors, when a portion of a side of one of the two polygons is hidden by the other polygon and when the direction of the normal vector of the other polygon is negative. 16. A program executed and controlled in an information processing apparatus for creating a two-dimensional image by projecting a three-dimensional model consisting of a plurality of polygons onto a two-dimensional plane, and for executing a process for avoiding projecting of lines hidden by the polygons, comprising the steps of causing program executing and controlling means to, based on program data read out from a memory:
determine the value in the Z-axis direction of the normal vector belonging to each of two polygons having a ridge line or an contour line of a three-dimensional model as a common side; determine the common side as an internal line when the value in the Z-axis direction of any of the normal vectors of the two polygons is zero (0) or less based on the determination of the directions of the normal vectors; and display the sectional view of the three-dimensional model such that the sectional view is displayed in a state that it is stuffed, by excluding the line determined as an internal line from the target to be displayed in a line image projected on the two-dimensional plane. 17. The program according to an internal line to be excluded from the target of display in a line image projected onto the two-dimensional plane is the common side determined as an internal line when the senses of the values in the Z-axis direction of the normal vectors respectively belonging to each of the two polygons are different from each other based on the determination of the directions of the normal vectors, when a vertex of a polygon of the two polygons is in the other polygon, when the value in the Z-axis direction of a vertex of a polygon is larger than the value in the Z-axis direction of a vertex of the other polygon and when the direction of the normal vector of the polygon is negative. 18. The program according to an internal line to be excluded from the target of display in a line image projected onto the two-dimensional plane is the common side determined as an internal line when the senses of the values in the Z-axis direction of the normal vectors respectively belonging to each of the two polygons are different from each other based on the determination of the directions of the normal vectors, when a portion of a side of one of the two polygons is hidden by the other polygon and when the direction of the normal vector of the other polygon is negative. Description This application is a Divisional Application of and claims parent benefit under 35 U.S.C. §120 to application Ser. No. 10/808,534, filed Mar. 25, 2004, now pending, and claims priority benefit of Japanese Application Nos. 2003-093868 and 2004-022814, filed Mar. 31, 2003 and Jan. 30, 2004. 1. Field of the Invention The present invention relates generally to a hidden line processing method in converting three-dimensional image data into two-dimensional data. More particularly, the present invention relates to a processing method and an information processing apparatus for processing hidden lines, capable of processing at a high speed, in converting three-dimensional image data consisting of polygons into two-dimensional data, as well as to a program for controlling the processing method. 2. Description of the Related Art In these years, three-dimensional CADs and mechanism simulators have become widely used in development of industrial products. Along with this, the cases have been more frequently seen where shape recognition of products are handled as models having virtual three-dimensional space coordinate data. On the other hand, at production sites, it is the current state that displayed screens on displays or instruction manuals for assembling are often used when models are observed and grabbed. Therefore, it is desired that a line image is displayed or created as an image in an instruction manual for assembling is created through projecting a model represented by three-dimensional coordinate data onto the two-dimensional plane of the display from a direction. Here, in the case where a model projected onto a two-dimensional plane or a model created for an instruction manual for assembling is assembled from a plurality of parts and each of the parts consists of a plurality of polygons, the above model has data for polygons and lines constituting the parts that do not appear on the surface of its visible area. Therefore, in the case where the three-dimensional data of the polygons contained in the model are simply converted into two-dimensional data and are displayed on a display screen or are converted into an image for an instruction manual for assembling, the lines and faces hidden by the surface of the model are also displayed. In this case, the model image displayed or the model image drawn on the instruction manual for assembling is hard to understand. Thus, the function of processing the hidden lines and hidden faces for not displaying the lines and faces not necessary for displaying is an essential technique for making the shapes in the image more recognizable. As such a technique for processing hidden lines and hidden faces, Z-buffer method and scan-line method are known. The Z-buffer method is a method for displaying with priority the polygons having coordinates close to the viewpoint side by having a buffer memory corresponding to a three-dimensional space and sorting the three-dimensional coordinates that a plurality of polygons constituting the model have. Therefore, the polygons having the coordinates farther that those of the polygons displayed with priority are not displayed. That is, the hidden lines are processed such that they are erased. In addition, the scan-line method is a method for hidden-face-erasing processing by slicing the model in the vertical direction and scanning from the viewpoint the sectional views. However, in these conventional techniques, the following drawbacks are present. In the Z-buffer method described first, though it is possible to create an image in a short time by executing the hidden-line/hidden-face processing to the raster data using the known techniques such as the Z buffer, it is impossible to execute operations such as enlarging/reducing/color-changing of specific lines when creating drawings and instruction manuals for assembling. Because of such points, the method has problems in operability and display quality in the process for converting into the two-dimensional data. In the case of the scan-line method described secondly, it is a preferable method because the above problems in the Z-buffer method are avoided and the operability is excellent when vector data are used for creating drawings and instruction manuals for assembling. However, the method has problems that it is necessary to execute hidden-line/hidden-face processing analytically and a large amount of memory consumption and processing time are necessary and, therefore, it is difficult to apply the method to a large-scale three-dimensional coordinate model. Considering such points, a method for facilitating speedup of processing by reducing the number of polygons to be processed by selecting only the faces facing the front side against the viewpoint as the faces to be hidden-line processed has been proposed previously by the inventor (see Japanese Patent Application Laid-Open Pub. No. 1993-67219). In addition, as other techniques relating to hidden-face processing, an invention which has a circuit for, taking the image processing of a rotating object as a target, obtaining the inner product of the normal vector of a polygon face and a rotation-processed line-of-sight vector and determining whether the polygon is visible or invisible from the value of the obtained inner product (see Japanese Patent Application Laid-Open Pub. No. 1995-37120) and an invention for, providing a Z-buffer, executing hidden-face processing using the Z-buffer method when overlapping of representative values of coordinates in all the three directions of X, Y and Z is detected and executing hidden-face processing by overwriting when any overlapping is detected (see Japanese Patent Application Laid-Open Pub. No. 2000-268191) have been presented. Furthermore, as techniques proposed previously by the inventor, an invention in which, when three-dimensional shape information of a solid is converted into two-dimensional shape information, only the hidden lines present on the side in a specific direction against an arbitrary boundary plane crossing the solid are outputted is listed (see Japanese Patent Application Laid-Open Pub. No. 2003-1817263). The object of the present invention is, as an example, to provide a method for facilitating speedup of the hidden-line processing in which the polygons present on the front side are selected using the invention described in Japanese Patent Application Laid-Open Pub. No. 1993-67219 and, in addition, prohibiting displaying of lines hidden under the polygons present on the front side. A further object of the present invention is to provide a hidden-line processing method for facilitating speedup of processing by reducing the number of lines to be processed in the hidden-line processing for above-described prohibiting of displaying lines, as well as to provide an information processing apparatus to be applied with the method and a program for executing the hidden-line processing method. In order to achieve the above objects, according to a first aspect of the present invention there are provided a hidden line processing method and an information processing apparatus for executing a process for avoiding projection of lines hidden by a plurality of polygons in projecting a three-dimensional model consisting of the polygons onto a two-dimensional plane, the method comprising the steps of obtaining the maximum value PZ Preferably, for the plurality of polygons belonging to the arbitrary part, each of their normal vectors has a component in the opposite direction against the direction of the line of sight from the viewpoint of the viewpoint coordinate system. In order to achieve the above objects, according to a second aspect of the present invention there are provided a hidden line processing method and an information processing apparatus for executing a process for avoiding projection of lines hidden by a plurality of polygons in projecting a three-dimensional model consisting of the polygons onto a two-dimensional plane, the method comprising the steps of, for a priority polygon group including a predetermined number of polygons obtained in the order of large projection area made when each of a plurality of polygons constituting a three-dimensional model is projected onto a two-dimensional plane, and for a plurality of polygon groups constituting a part to which a line undergoing determination to be a hidden line or not; and in the order of the priority polygon group and the plurality of polygon groups constituting the part, obtaining the maximum value PZ Preferably, the arbitrary line is a side common to polygons adjacent to each other, of which the angle formed by respective normal vectors is not equal or close to 0°. The method may further comprise the steps of defining an inclusive circle including vertices of the polygon when each of the plurality of polygons is projected onto a two-dimensional plane; determining whether a portion of an arbitrary line is present in the inclusive circle corresponding to the polygon for the polygons for which determination of whether or not the line is an internal line is not avoided; and erasing hidden line portions on the two-dimensional plane when the portion of the arbitrary line is present in the inclusive circle. In order to achieve the above objects, according to a third aspect of the present invention there are provided a method and an information processing apparatus for identifying as an internal line a ridge line or an contour line of a three-dimensional model, appearing when only the interior of the three-dimensional model is displayed in projecting the three-dimensional model consisting of a plurality of polygons onto a two-dimensional plane, the method comprising the steps of determining the value in the Z-axis direction of a normal vector belonging to each of two polygons having a ridge line or an contour line of the three-dimensional model as a common side; and determining the common side as an internal line if the value in the Z-axis direction of any of the normal vectors of the two polygons is determined zero (0) or less based on the determination of the direction of the normal vector. The method may further comprise the step of determining the common side as an internal line when the senses of the values in the Z-axis direction of the normal vectors respectively belonging to each of the two polygons are different from each other based on the determination of the directions of the normal vectors, when a portion of a side of one of the two polygons is hidden by the other polygon and when the direction of the normal vector of the other polygon is negative. According to the present invention, it is possible to facilitate speedup in hidden-line processing for prohibiting displaying of lines hidden under polygons, and to reduce considerably the time necessary for the entire processing. The above and other objects, aspects, features and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings, in which: Embodiments of the present invention will now be described with reference to the drawings. It is to be noted however that the embodiments shown in the drawings are for understanding the present invention and that the technical scope of the present invention is not limited thereto. Inputting means [Pre-Treatment] As a precondition for the process, a pre-treatment (Process Step P First, the elements constituting the three-dimensional model are broken up in a tree-like system as shown in In The CD-ROM drive apparatus (CD-ROM) Furthermore, the moving assembly (Asm_Move) Here, the cover elements A (Cover_A) Then, only each of such minimum-unit parts has data of a plurality of polygons, constituting each of the parts, having vertex data containing three-dimensional position coordinates at their vertices. Therefore, an upper-order part containing minimum-unit parts contains the data of a plurality of polygons constituting these minimum-unit parts. The CD-ROM apparatus The present invention expedites the process for erasing the above unnecessary lines and executes a hidden-line erasing process with the following pre-treatment as a precondition. As a precondition, first, in the case where a CD-ROM apparatus Here, as the method for selecting the only polygons of which the surfaces are facing toward the line of sight, the method described in the above-described, Japanese patent Application laid Open Pub. 1993-67219 can be applied. That is, only the polygons for which the sign of the component in the Z-axis direction of the normal vector of a plurality of polygons (in Next, the projected area and the inclusive circle made when the polygon Next, as shown in Then, for each part (in [Obtaining Lines] Lines are obtained following the above pre-treatment (Process Step P When polygons adjacent to each other having a common side are on a plane, said common side is defined not as a line on the polygons because the faces of polygons adjacent to each other having an angle equal or close to 0° formed by the normal vectors of each of the polygons at the center of gravity of each of the polygons are regarded as an approximately continuous plane. On the contrary, when the angle formed by the normal vectors of each of the polygons adjacent to each other at the center of gravity of each of the polygons is not equal or close to 0°, the common side of the polygons is obtained as a line because the polygons adjacent to each other continues from each other forming an angle between them over the common side as the border. On the other hand, in the case shown in [Line-Erasing Process by a Polygon Group] A line-erasing process by a polygon group is executed to the line obtained as above. That is, for the line hidden by polygons projected and displayed onto the two-dimensional plane Here, a polygon group is a set of one (1) or more polygons and refers to the priority polygon group, the self-part polygon group and the plurality of other's-part polygon group obtained in the above pre-treatment. The priority polygon group means the plurality of priority polygons described in the above [Pre-Treatment) The self-part polygon group means the plurality of polygons constituting the parts (the parts Then, the erasing process of a line by a polygon group is an erasing process by the priority polygon group (Process Step P Especially, the erasing process by the priority polygon group uses one or more polygons selected in the order of large area of the shape of a polygon projected onto a two-dimensional plane (screen) (projected area) among the polygons to be hidden-line-processed. This is because the possibility of erasing a line is higher for the case where an erasing process is executed with a polygon having a large projected area than the case with a polygon having a small projected area. When the whole portion of one (1) obtained line is completely erased, it is not necessary to execute any erasing process using another polygon and the speedup of the process to proceed to the next line-erasing process is facilitated. As an embodiment, as described above, among the polygons constituting a three (3)-dimension model, ten (10) polygons having the largest projected areas among the polygons which are present within the output range of the final drawing and of which the surfaces are facing toward the viewpoint are obtained. However, application of the present invention is not limited to the order of the polygon groups for the above erasing of lines. Then, the procedures of the hidden-line erasing by the above polygon groups (Process Steps P [Erasing Process by the Priority Polygon Group] First, the erasing process by the priority polygon group (Process Step P In Therefore, an erasing process for a polygon belonging to a polygon group is avoided when LZ In [Simplified Determination of Hidden-Line Processing] Next, a simplified determination of hidden-line processing (Process Step P The inclusive circle When considered on a screen (two-dimensional plane) if the line L is present outside a polygon inscribed in the inclusive circle In the hidden-line processing for the corresponding polygons (Process Step P On the other hand, when a portion of the line is not erased, as far as the polygon to be the target is present, the process is proceeded to a hidden-line processing by the next polygon (Process Step P [Erasing Process by the Self-Part Polygon Group] In As described above, the self-part polygon group means the polygons belonging to the same part as the part to which the obtained line belongs. For example, in [Avoidance of Process by Part-Inclusive Circle/Assembly-Inclusive Circle] Furthermore, in the case where a visible portion also remains (Process Step P A three-dimensional model for a three-dimensional CAD or a simulator usually has a tree-like composition consisting of the assembly parts Therefore, even in the case where the line-erasing process for the self-part polygon group (Process Step P In the assembly (part) circle check process (Process Step P Then, If not present, hidden-line processing of all the parts at the node and at all the nodes under the node is avoided (Process Step P In the case where a portion of the part circle is included, an erasing process by the polygon group according to the flow shown in In the case where, in the assembly part (Asm_Move) However, though some three-dimensional CAD or simulators have part globes or assembly globes including parts and their assemblies in a three-dimensional space, these globes include parts even when projected from any position. Therefore, they can be regarded as part circles and it is possible to apply a response S in the process described above. [Display of Visible Portion] The portion not having been erased after undergoing the step of the above assembly (part) circle check (Process Step P [High-Speed Conversion of Three-dimensional Model into Line Image Information] Here, in the above description for the processes, the (Obtaining Line) is executed (Process Step P As the first consideration, the process time of this [Line-Erasing Processes by Polygon Groups] is in proportion to the product of the number of lines created from a three-dimensional model to be processed and the number of polygons necessary for the hidden-line processing. Therefore, the cost for calculation for the case where line images are created from a large-scale three-dimensional model is very high. Thus, a technique that reduces the number of the lines to be processed for line-erasing and expedite the processes is desired. As the second consideration, as shown in In this case, it is possible to create a line image in which the interior of the model is observed on a solid plane Furthermore, as the third consideration, in the above three-dimensional model display apparatus having a sectional-view-display function that processes a side of an arbitrary reference plane, in the case where a three-dimensional model is projected as a line image from an arbitrary direction, a method is used, in which a line image for easily grabbing the shape of the sectional portion and the entire model is created by outputting the portion of the side to be processed from the reference plane A in a predetermined format such as a dotted line. In this case, processes as follows are executed. First, as shown in Next, as shown in In the above third consideration, as described above, the calculation cost of (the number of the ridge/outline liens) X (the number of polygons necessary for hidden-line processing) is necessary for creating a hidden-line-processed line image geometrically with polygons. In addition to this, all the constituent lines of the line image to display the entire model, determination of the position of the reference plane and creation of the sectional lines are necessary. As the model becomes larger-scale, the cost for creating the hidden-line-processed line image becomes high. Therefore, a method for creating a line image reducing the amount of the calculation for hidden-line processing as far as possible is desired. Yet furthermore, as the fourth consideration, in order to express the parts interfering with each other in a two-dimensional line image into which a three-dimensional mode has been projected, the interfered portions are reflected by checking the interference using three-dimensional shapes and displaying marks and comments indicating the interfered points on the drawing (line image). In contrast, as shown in Therefore, in view of the above first to fourth considerations, further feature of the present invention observed from a different aspect is to facilitating the speedup considered commonly in the above first to fourth considerations by executing a process for reducing the number of lines to be hidden-line processed. An example of the process according to the present invention for reducing the number of lines to be hidden-line processed will be described as follows. Among these lines, the lines of the second group are internal lines. Those internal lines are surely not displayed on the two-dimensional screen. Therefore, according to the further feature of the present invention, only the lines represented by thick lines in Here, the line to be a common side of polygons adjacent to each other in a three-dimensional model will be considered. For polygons adjacent to each other having a common side, aspects A, B, C and D of the direction of four (4) normal lines in a first group I shown in Here, polygons adjacent to each other having a common side are shown in Based on the above preconditions, However, it is possible to execute the process flow, shown in Describing referring back to In Process Step P If a condition that both of the normal vector values N When the side L corresponds to either IIc- Furthermore, in the case where the side L corresponds to either IIc- Next, in the case where the z-component Nf On the contrary, in the case where the z-component Nf By identifying an internal line in advance and not obtaining it as described above, it is possible to exclude it from the targets to be line-erased and to expedite [Line-Erasing Processes by Polygon Groups] (Process Steps P That is, it is possible to realize the speedup by approximately 50% by the above process of Furthermore, since it is possible to determine internal lines appearing when the interior of the model is displayed by utilizing the method for detecting internal lines according to Furthermore, as described referring to First, the polygons constituting a three-dimensional model are distinguished as those present on the side to be processed and as those present on the side not to be processed from the reference plane. Then, the polygons crossing the sectional view lines are distinguished as the portions present on the side to be processed and the portions present on the side not to be processed. Ridge lines/contour lines are created from the polygons on the side to be processed and hidden-line processing is executed by the polygons on the side to be processed. Thereby, a line image on the side to be processed from the reference plane is created by hidden-line processing according to the process flow shown in That is, the case where 1.2×10 According to the method of the present invention, in the case where there are 5.0×10 Furthermore, in relation to the fourth consideration, utilizing the method for detecting internal lines according to As set forth hereinabove referring to the drawings, according to the present invention, it is possible to reduce the amount of data to be processed in handling shape recognition etc. as a model having virtual three-dimensional space coordinate data by a three-dimensional CAD and a mechanism simulator. Thereby, it is possible to facilitate speedup of the processing speed in the three-dimensional CAD and a mechanism simulator. Therefore, the industrial contribution of the present invention is great. While illustrative and presently preferred embodiments of the present invention have been described in detail herein, it is to be understood that the inventive concepts may be otherwise variously embodied and employed and that the appended claims are intended to be construed to include such variations except insofar as limited by the prior art. Referenced by
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