Hidden line processing method for erasing hidden lines in projecting a three-dimensional model consisting of a plurality of polygons onto a two-dimensional plane

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.

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  claim 1 , further comprising the steps of: 
 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  claim 1 , further comprising 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.    
   
   
       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  claim 4 , further wherein 
 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  claim 4 , wherein 
 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  claim 7 , wherein the program executing and controlling means, in compliance with the program, further: 
 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  claim 8 , wherein the program executing and controlling means further: 
 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  claim 10 , wherein 
 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  claim 11 , wherein 
 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  claim 13 , wherein the program further causes the program executing and controlling means 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  claim 14 , wherein the program further causes the program executing and controlling means 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  claim 16 , wherein 
 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  claim 17 , wherein 
 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.