JP3938915B2 - Drawing calculation apparatus, computer program, and recording medium - Google Patents

Description

  The present invention is a drawing calculation device that performs calculations required for drawing a three-dimensional object composed of a plurality of polygons, a computer program for realizing the device, and a computer on which the program is recorded can be read. The present invention relates to various recording media. More particularly, the present invention relates to a drawing calculation device such as a video game device for drawing a deformation of a three-dimensional object simulating a flexible object such as cloth, clothes, and hair, a computer program, and a recording medium.

  As a technique for drawing an image of a three-dimensional object, the surface of the three-dimensional object of various shapes is divided into minute polygons (polygons), and a pattern called a texture is pasted on each divided polygon. The method is widely used in the field of video games, for example.

  In a drawing calculation device such as a video game device that performs calculations required for drawing a three-dimensional object composed of a plurality of polygons, the deformation of the three-dimensional object imitating a flexible object such as cloth, clothes, and hair When performing cross-simulation processing to perform calculations required for drawing, a 3D object is composed of a plurality of quadrilaterals, each vertex of the quadrilateral is used as a mass point, and adjacent quadratic points are connected, and each side of the quadrilateral is a spring. Calculations required for drawing are performed using a simulation model that assumes a model to perform (see, for example, Non-Patent Document 1).

  The calculation required for drawing a three-dimensional object composed of a plurality of quadrilaterals is, for example, the calculation of the force received from the other four mass points adjacent to one mass point when each vertex of the quadrangle is the mass point, and This is a calculation of a normal vector at the vertex.

  When one mass point is the reference vertex M0 and four mass points adjacent to the one mass point M0 are the neighboring vertices M1, M2, M3, and M4, the force received by the reference vertex M0 is the respective neighboring vertices M1, M2, and M3. , M4, and the resultant force F1, F2, F3, and F4.

  When obtaining the forces F1, F2, F3, and F4 that the reference vertex M0 receives from the neighboring vertices M1, M2, M3, and M4, respectively, first, position vectors of the reference vertex M0 and the neighboring vertices M1, M2, M3, and M4 are respectively P0 and P1. , P2, P3, and P4, relative vectors X1, X2, X3, and X4 from the reference vertex M0 to the neighboring vertices M1, M2, M3, and M4 are obtained by the following equations.

X1 = P1-P0
X2 = P2-P0
X3 = P3-P0
X4 = P4-P0
X1: Relative vector from the reference vertex M0 to the neighboring vertex M1
X2: Relative vector from the reference vertex M0 to the neighboring vertex M2
X3: Relative vector from the reference vertex M0 to the neighboring vertex M3
X4: Relative vector from the reference vertex M0 to the side vertex M4 and using the obtained relative vectors X1, X2, X3, X4, the forces F1, F2, received by the reference vertex M0 from the side vertexes M1, M2, M3, M4, respectively F3 and F4 can be obtained by the following equations, and the force received by the reference vertex M0 can be obtained by calculating the resultant force of F1, F2, F3, and F4.

F1 = k * (| X1 | −L1) * (X1 / | X1 |)
F2 = k * (| X2 | −L2) * (X2 / | X2 |)
F3 = k * (| X3 | −L3) * (X3 / | X3 |)
F4 = k * (| X4 | −L4) * (X4 / | X4 |)
Where k is the spring constant
L1: Distance between reference vertex M0 and neighboring vertex M1
L2: distance between reference vertex M0 and neighboring vertex M2
L3: distance between reference vertex M0 and neighboring vertex M3
L4: Distance between the reference vertex M0 and the neighboring vertex M4 When obtaining the normal vector N0 at the reference vertex M0, first, the position vectors P0, P1, P2, respectively of the reference vertex M0, the neighboring vertices M1, M2, M3, and M4. P3 and P4 are obtained by the following equations.

N1 = (P1-P0) * (P2-P0) / | (P1-P0) * (P2-P0) |
N2 = (P3-P0) × (P1-P0) / | (P3-P0) × (P1-P0) |
N3 = (P2-P0) × (P4-P0) / | (P2-P0) × (P4-P0) |
N4 = (P4-P0) × (P3-P0) / | (P4-P0) × (P3-P0) |
The normal vector N0 at the reference vertex M0 can be calculated from the obtained position vectors P0, P1, P2, P3, and P4 by the following formula.

N0 = (N1 + N2 + N3 + N4) / 4
“C MAGAZINE” Softbank Publishing, September 2000, p. 10-42

  However, the calculation required for drawing, such as the conventional force calculation and normal vector calculation, has a problem that the processing load required for the calculation is large, and this problem also affects the drawing time of the three-dimensional object.

  The present invention has been made in view of such circumstances. For example, a calculation formula in a format capable of efficiently realizing parallel calculation using a matrix arithmetic processor for calculation required for drawing a three-dimensional object. A drawing calculation device capable of reducing the processing load required for calculation and shortening the drawing time by using or an approximate expression that simplifies the calculation, and a computer for realizing the device It is an object of the present invention to provide a program and a recording medium that can be read by a computer in which the program is recorded.

The present invention described in claim 1 is a drawing computing device for performing calculations necessary for the drawing of the three-dimensional object surface is formed by a plurality of polygons vertices of coordinates indicated by the polygon data, the matrix A matrix calculation processor that performs an operation on a given polygon, means for extracting one reference vertex of an arbitrary polygon and a plurality of side vertices adjacent to the reference vertex as mass points, and a reference vertex extracted as a mass point and coordinates of each side vertex Means for calculating from the polygon data; means for calculating a first matrix having a difference between the coordinates of the obtained reference vertex and the coordinates of each of the neighboring vertices using a matrix operation processor; and coordinates of the reference vertex and each of the neighboring vertices. the difference between the coordinates, the reference vertex of the vector to each neighbor vertex divided by the size, the second matrix with further reference vertex and a value obtained by multiplying the distance between the near vertex elements, matrix Starring Means for calculating with the processor, the calculated third matrix multiplied by a constant difference between the first matrix and a second matrix, and means for calculating using the matrix arithmetic processor, among the elements of the calculated third matrix And a means for performing a calculation required for drawing using a matrix operation processor, with the fourth matrix having the sum of the elements for each of the neighboring vertices as a resultant force of the forces from the plurality of neighboring vertices with respect to the reference vertex. This is a drawing calculation device.

According to the present invention, the drawing calculation device performs a calculation required for drawing a three-dimensional object whose surface is composed of a plurality of polygons whose vertex coordinates are indicated by polygon data. The drawing calculation device includes a matrix calculation processor that performs an operation related to a matrix, and extracts a reference vertex of an arbitrary polygon and a plurality of neighboring vertices adjacent to the reference vertex as a material point, and extracts as a material point Means for calculating the coordinates of the reference vertex and each side vertex from the polygon data; means for calculating a first matrix having a difference between the coordinates of the obtained reference vertex and the coordinates of each side vertex using a matrix processor ; The difference between the coordinates of the reference vertex and the coordinates of each side vertex is divided by the vector size from the reference vertex to each side vertex, and further multiplied by the distance between the reference vertex and each side vertex. 2 matrix, and means for calculating using the matrix arithmetic processor, a third matrix multiplied by a constant difference between the first matrix and the second matrix calculated using the matrix arithmetic processor calculates And a calculation required for drawing, in which the fourth matrix having the sum of the elements related to each of the neighboring vertices among the elements of the calculated third matrix is the resultant force of a plurality of neighboring vertices with respect to the reference vertex Means for performing the processing using a matrix arithmetic processor .

  In the drawing calculation apparatus of the present invention, as a calculation for drawing a deformation of a three-dimensional object imitating a flexible object such as cloth, clothes and hair, it is applied to an arbitrary vertex of a polygon constituting the three-dimensional object. When calculating the resultant force, the first matrix and the second matrix based on the coordinates of the reference vertex and the coordinates of each of the neighboring vertices are calculated, and the difference between the calculated first matrix and the second matrix is multiplied by a spring constant. The resultant force is calculated based on the three matrices.

  With this configuration, it is possible to calculate the resultant force by calculating a matrix, so that the matrix calculation processor or the like is compared with the conventional calculation that calculates the resultant force after obtaining the forces from adjacent vertices. As a result, it is possible to efficiently use a sub-processor specialized for the above calculation, so that it is possible to reduce the processing load required for the calculation performed by the main processor.

  According to a second aspect of the present invention, in the drawing calculation device according to the first aspect, the first matrix is represented by the following formula (A), and the second matrix is represented by the following formula (B): The third matrix is represented by the following formula (C).

  According to the present invention, the drawing calculation device calculates a first matrix represented by the following formula (A), calculates a second matrix represented by the following formula (B), and represents the following formula (C): A third matrix is calculated.

  In the drawing calculation apparatus of the present invention, the calculation is performed using a matrix arranged in a matrix data structure, as shown in Expression (A), Expression (B), and Expression (C).

  With this configuration, it is possible to efficiently use a matrix arithmetic processor provided in devices such as popular video game devices and personal computers, thereby realizing parallel computation, thereby reducing the load on the main processor. To reduce the overall calculation time.

  According to a third aspect of the present invention, in the drawing calculation apparatus according to the first or second aspect, the polygon is a quadrangle, and the number of the side vertices is four.

  According to the present invention, in the image drawing device, when calculating the deformation of the three-dimensional object, a polygon having a plurality of quadrangles is used as a calculation target, and the number of side vertices in the polygon is four.

  In the drawing calculation apparatus of the present invention, by setting the number of apexes to four, in particular, a homogeneous coordinate indicating a homogeneous coordinate indicating a projected plane in order to project a three-dimensional object onto a two-dimensional screen. When expressed in a system, a matrix such as the first matrix, the second matrix, and the third matrix can be expressed as a 4 × 4 matrix including x coordinates, y coordinates, z coordinates, and homogeneous coordinates. The matrix processor can be used efficiently by adapting to the standard specification of the matrix processor.

The present invention according to claim 4 is a drawing calculation device that performs calculations required for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data, A polygon is a quadrangle, means for extracting two to four neighboring vertices adjacent to one reference vertex of an arbitrary quadrilateral, and when the extracted neighboring vertices is four , a position based on the coordinates of the four neighboring vertices A means for obtaining a vector, a means for obtaining a position vector based on the coordinates of four side vertices, with the coordinates of the reference vertex being the coordinates of one side vertex when the number of extracted side vertices is 3, and In this case, the coordinate of the reference vertex is used as the coordinate of the second vertex, the position vector based on the coordinates of the four neighbors, the quadrangle formed by the extracted four neighbors , or the extracted neighbors and At the base vertex that is a neighbor vertex A vector outer product of two sets of vectors from one beside vertex at the position of the diagonal of the rectangle on the virtual computing towards the other near the apex normalized be made, the normal vector of the reference vertex, A drawing calculation apparatus comprising: means for performing calculation required for drawing.

According to the present invention, the drawing calculation device performs calculations necessary for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data. The polygon is a quadrangle, and means for extracting two to four neighboring vertices adjacent to one reference vertex of an arbitrary quadrilateral, and when the extracted neighboring vertices is four, the coordinates of the four neighboring vertices are A means for obtaining a position vector based on the above, a means for obtaining a position vector based on the coordinates of the four side vertices, with the coordinates of the reference vertex being the coordinates of the one vertex when the number of extracted vertexes is three,
When the extracted side vertices are two, the coordinate of the reference vertex is the coordinates of the second side vertex, a means for obtaining a position vector based on the coordinates of the four side vertices, and a rectangle formed by the four side vertices extracted , Or , normalize the outer product of two sets of vectors from one side vertex to the other side at the diagonal position of the hypothetical computational rectangle formed by the extracted side vertex and the reference vertex as the side vertex Means for performing a calculation required for drawing, wherein the normalized vector is a normal vector of a reference vertex.

  In the drawing calculation apparatus of the present invention, as a calculation for drawing deformation of a three-dimensional object imitating a flexible object, when calculating a normal vector of vertices of a quadrangle constituting the three-dimensional object, A vector obtained by normalizing the outer product of two sets of vectors from one side vertex to the other side vertex at the corner position is calculated as a normal vector of the reference vertex.

  With this configuration, the calculation is simplified as compared with the conventional calculation in which the calculation of the outer product and the normalization is performed four times, and the processing load required for the calculation can be reduced.

  According to a fifth aspect of the present invention, in the drawing calculation apparatus according to any one of the first to fourth aspects, the three-dimensional object in which the plurality of polygons are triangular before performing the calculation required for the drawing. A means to extract a plurality of triangles that form the surface of the object, and by removing the long sides of each extracted triangle, a surface is formed with a plurality of triangles, and a surface is formed with a plurality of rectangles. And a means for converting into a three-dimensional object.

  According to the present invention, the drawing calculation device includes means for extracting a plurality of triangles forming a surface of a three-dimensional object in which a plurality of polygons are triangles before performing calculations required for drawing, and each extracted triangle And a means for converting a three-dimensional object whose surface is formed by a plurality of triangles into a three-dimensional object whose surface is formed by a plurality of quadrangles.

  In the drawing computing device of the present invention, the long side of the triangle that forms the surface of the three-dimensional object is compared to the three-dimensional object that is formed by a plurality of triangles formed as data for the video game device. In other words, a three-dimensional object whose surface is formed by a plurality of triangles by performing a pre-processing for converting a three-dimensional object whose surface is formed by a plurality of quadrilaterals by deleting the side corresponding to the diagonal of the quadrangle Since an object can be easily converted into a three-dimensional object whose surface is formed of a plurality of quadrangles, the three-dimensional object whose surface is formed of a plurality of triangles is also claimed. It becomes possible to apply the invention described in any one of claims 4.

The present invention of claim 6, the computer having a matrix arithmetic processor for performing operations on the matrix, the drawing of the three-dimensional object surface is formed by a plurality of polygons vertices of coordinates indicated by the polygon data A computer program for performing necessary calculations, a procedure for causing a computer to extract a reference vertex of an arbitrary polygon position and a plurality of neighboring vertices adjacent to the reference vertex as mass points, and a criterion extracted by the computer as a mass point Using a matrix calculation processor, the computer calculates a first matrix whose elements are the difference between the obtained coordinates of the reference vertex and the coordinates of each side vertex, and a procedure for obtaining the coordinates of the vertex and each side vertex from the polygon data. The procedure and the difference between the coordinates of the base vertex and the coordinates of each side vertex are transferred to the computer from the base vertex to each side vertex. Dividing at the magnitude of the vector, further a second matrix as a reference vertex and element value obtained by multiplying the distance of each neighbor vertex, the procedure to be calculated using the matrix arithmetic processor, a computer, a first matrix is calculated And a procedure for calculating a third matrix obtained by multiplying a difference between the second matrix and a constant by using a matrix processor, and causing a computer to calculate a sum of elements relating to the respective paravertices among the elements of the calculated third matrix. The computer program is characterized in that a fourth matrix is used as a resultant force of a plurality of side vertices with respect to a reference vertex, and a calculation operation required for drawing is performed using a matrix arithmetic processor. .

According to the present invention, a computer having a matrix operation processor that performs an operation relating to a matrix performs a calculation required for drawing a three-dimensional object composed of a plurality of polygons whose vertex coordinates are indicated by polygon data. The program causes the computer to extract a reference vertex of an arbitrary polygon position and a plurality of neighboring vertices adjacent to the reference vertex as mass points, and causes the computer to extract the reference vertex extracted as the mass point and the coordinates of each neighboring vertex. A procedure for obtaining from the polygon data, a procedure for causing the computer to calculate a first matrix having a difference between the coordinates of the obtained reference vertex and the coordinates of each side vertex using a matrix operation processor, and Divide the difference between the coordinates of and the coordinates of each side vertex by the size of the vector from the reference vertex to each side vertex. , Constant second matrix, and procedures to be calculated using the matrix arithmetic processor, the difference between the computer, the calculated first matrix and a second matrix for the further reference vertex and a value obtained by multiplying the distance of each neighbor vertex with elements a third matrix multiplied by a procedure which is calculated using the matrix arithmetic processor, a computer, a fourth matrix for the sum of the elements related to near the apex of each the element in the element of the calculated third matrix, reference A procedure for performing a calculation required for drawing, which is a resultant force of a plurality of side vertices with respect to the vertices , using a matrix arithmetic processor is executed.

  In the computer program of the present invention, a calculation required for drawing a three-dimensional object imitating a flexible object such as cloth, clothes and hair made up of a plurality of polygons by being executed by a computer such as a video game apparatus. When the computer operates as a drawing calculation device that performs the calculation, and when calculating the resultant force applied to any vertex of the polygon constituting the three-dimensional object as a calculation for drawing the deformation of the three-dimensional object, A first matrix and a second matrix are calculated based on the coordinates and the coordinates of each of the neighboring vertices, and a resultant force is calculated based on a third matrix calculated by multiplying the difference between the calculated first matrix and the second matrix by a spring constant.

  With this configuration, it is possible to calculate the resultant force by calculating a matrix, so that the matrix calculation processor or the like is compared with the conventional calculation that calculates the resultant force after obtaining the forces from adjacent vertices. As a result, it is possible to efficiently use a sub-processor specialized for the above calculation, so that it is possible to reduce the processing load required for the calculation performed by the main processor.

The present invention according to claim 7 is a computer program for causing a computer to perform calculation necessary for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data. the polygon is a square, the computer, the procedure for extracting any one of the reference vertex and phase Tonariru two to four beside the vertices of a square, the computer, if the extracted neighbor vertices four, four A procedure for determining the position vector based on the coordinates of the neighboring vertices, and when the extracted number of neighboring vertices is 3, the position based on the coordinates of the four neighboring vertices, with the coordinates of the reference vertex as the coordinates of the one neighboring vertex. The procedure for obtaining the vector and the computer, when the extracted two vertices are 2, the coordinates of the reference vertex are the coordinates of the second vertex and the position vector based on the coordinates of the fourth vertex is obtained. And procedures to fit the computer, quadrangle formed by the extracted fourth near the apex, or is formed by the reference vertex and the extracted neighbor vertex and neighbor vertex position of the diagonal of the rectangle on the virtual computing A method for performing a calculation required for drawing, wherein a vector obtained by normalizing the outer product of two sets of vectors from one neighboring vertex to the other neighboring vertex is set as a normal vector of the reference vertex. Is a computer program.

According to the present invention, a computer program for causing a computer to perform calculations necessary for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data is performed on a polygon that is a rectangle. Applied to the computer and causes the computer to extract two to four neighboring vertices adjacent to one reference vertex of an arbitrary quadrilateral, and if the extracted number of neighboring vertices is four , the computer A procedure for obtaining a position vector based on coordinates, and having the computer obtain a position vector based on the coordinates of the four side vertices with the coordinates of the reference vertex set as the coordinates of the one side vertex when the number of extracted side vertices is three Procedure and let the computer find a position vector based on the coordinates of the four neighboring vertices, using the coordinates of the second neighboring vertex as the coordinates of the second neighboring vertex when the extracted neighboring vertex is two And instructions, on the computer, a square formed by the extracted fourth near the apex, or is formed by the extracted neighbor vertex and neighbor vertex with the reference vertex while in the position of the diagonal of the rectangle on the virtual computing A procedure for performing a calculation required for drawing is performed by setting a vector obtained by normalizing the outer product of two sets of vectors from one side vertex to the other side vertex as a normal vector of the reference vertex.

  In the computer program of the present invention, the computer operates as a drawing calculation device that performs calculations necessary for drawing a three-dimensional object imitating a flexible object by being executed by a computer such as a video game device, and the three-dimensional object. When calculating the normal vector of the vertices of the quadrangle that constitutes the three-dimensional object as the calculation for drawing the deformation of the object, two pairs from one side vertex at the diagonal position to the other side vertex A vector obtained by normalizing the outer product of the vectors is calculated as the normal vector of the reference vertex.

  With this configuration, the calculation is simplified as compared with the conventional calculation in which the calculation of the outer product and the normalization is performed four times, and the processing load required for the calculation can be reduced.

The present invention of claim 8, the computer comprising a matrix arithmetic processor for performing operations on the matrix, the drawing of the three-dimensional object surface is formed by a plurality of polygons vertices of coordinates indicated by the polygon data A computer-readable recording medium in which a computer program for performing necessary calculations is recorded, and a computer is provided with a reference vertex of an arbitrary polygon position and a plurality of adjacent vertices adjacent to the reference vertex. The procedure for extracting as the mass point, the procedure for causing the computer to obtain the coordinates of the reference vertex and each side vertex extracted as the mass point from the polygon data, and the computer for the difference between the obtained coordinates of the reference vertex and each side vertex a first matrix having a procedure for calculating using the matrix arithmetic processor, a computer, reference vertex The coordinate and difference of coordinates of each neighbor vertex, from a reference vertex of the vector to each neighbor vertex divided by the size, the second matrix whose elements further reference vertex and a value obtained by multiplying the distance of each neighbor vertex, a procedure for calculating using the matrix arithmetic processor, a computer, a third matrix multiplied by a constant difference between the first matrix and the second matrix determined, the procedure to be calculated using the matrix arithmetic processor, a computer, calculates A matrix calculation processor that performs a calculation required for drawing, with the fourth matrix having the sum of the elements related to each of the neighboring vertices as the resultant force of the plurality of neighboring vertices among the elements of the third matrix A computer-readable recording medium on which is recorded a computer program that executes a procedure to be performed using the computer.

According to the present invention, a computer having a matrix operation processor that performs an operation related to a matrix performs a calculation required for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data. A computer-readable recording medium on which a computer program to be recorded is recorded, the computer having a computer to extract a reference vertex of an arbitrary polygon position and a plurality of neighboring vertices adjacent to the reference vertex as mass points; , Causing the computer to obtain the coordinates of the reference vertices extracted as the mass points and the coordinates of each side vertex from the polygon data, and the computer to obtain a first matrix having the difference between the coordinates of the obtained reference vertices and the coordinates of each side vertex as elements. , a procedure for calculating using the matrix arithmetic processor, a computer, a reference vertex coordinates and Kakusobaitadaki Difference and dividing by the magnitude of the vector to each neighbor vertex from a reference vertex, a second matrix with further reference vertex and element value obtained by multiplying the distance of each neighbor vertex, using the matrix arithmetic processor of the coordinates a procedure for calculating Te, a computer, a third matrix multiplied by a constant difference between the first matrix and the second matrix determined, the procedure to be calculated using the matrix arithmetic processor, a computer, the calculated third matrix The matrix calculation processor is used to perform the calculation required for drawing, with the fourth matrix having the sum of the elements related to each of the neighboring vertices as the combined force of the forces from the plurality of neighboring vertices with respect to the reference vertex . And execute the procedure.

  In the recording medium that can be read by the computer of the present invention, the recorded computer program is executed by a computer such as a video game device, so that cloth, clothes, hair, and the like composed of a plurality of polygons can be obtained. The computer operates as a drawing calculation device that performs calculations required to draw a three-dimensional object imitating a flexible object, and as a calculation for drawing the deformation of the three-dimensional object, the polygons constituting the three-dimensional object are calculated. When calculating the resultant force on an arbitrary vertex, the first matrix and the second matrix are calculated based on the coordinates of the reference vertex and the coordinates of each of the neighboring vertices, and the spring constant is set as the difference between the calculated first matrix and second matrix. The resultant force is calculated based on the third matrix calculated by multiplication.

  With this configuration, it is possible to calculate the resultant force by calculating a matrix, so that the matrix calculation processor or the like is compared with the conventional calculation that calculates the resultant force after obtaining the forces from adjacent vertices. Since it is possible to efficiently use a sub-processor specialized for the above calculation, the calculation performed by the main processor is simplified, so that the processing load required for the calculation can be reduced.

The present invention according to claim 9 records a computer program for causing a computer to perform calculations necessary for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data. A computer-readable recording medium, wherein the polygon is a quadrangle, and the computer causes the computer to extract two to four side vertices adjacent to one reference vertex of an arbitrary quadrangle; When the computer has 4 extracted apexes , the computer determines the position vector based on the coordinates of the 4 adjacent vertices . The procedure for obtaining the position vector based on the coordinates of the four neighboring vertices as the coordinates of the neighboring vertices, and when the extracted number of neighboring vertices is two, the reference vertex coordinates are As the coordinates of the point, the procedure causes obtain the position vector based on the coordinates of the four beside vertex, the computer, quadrangle formed by the extracted fourth near the apex, or by the reference vertex and the extracted neighbor vertices and near the vertex A vector obtained by normalizing the outer product of two sets of vectors from one side vertex to the other side vertex at the diagonal position of the formed virtual calculation rectangle is defined as a normal vector of the reference vertex. A computer-readable recording medium on which a computer program for executing a procedure for performing a calculation required for drawing is recorded.

According to the present invention, a computer program for causing a computer to perform calculations necessary for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data is recorded. The recording medium that can be read by the method is applied to a polygon that is a rectangle, and causes the computer to extract two to four neighboring vertices adjacent to one reference vertex of an arbitrary rectangle; When the number of extracted apexes is 4, the procedure for obtaining the position vector based on the coordinates of the 4 adjacent vertices, and when the number of extracted apexes is 3, the coordinate of the reference vertex is set as the coordinate of the one adjacent vertex. The procedure for obtaining the position vector based on the coordinates of the four neighboring vertices and the computer, if the extracted neighboring vertices are two, the coordinates of the reference vertex are And a procedure for obtaining a position vector based on the coordinates of the four side vertices and a computer formed by a quadrature formed by the extracted four side vertices, or a reference vertex that is the extracted side vertices and side vertices. Necessary for drawing, with the normal vector of the reference vertex set as the normal vector of the two sets of vectors from one side vertex to the other side vertex at the diagonal position of the virtual calculation rectangle And a procedure for performing the calculation.

In the recording medium readable by the computer of the present invention, a calculation required for drawing a three-dimensional object imitating a flexible object by executing a recorded computer program on a computer such as a video game apparatus. When the computer operates as a drawing calculation device that performs the calculation and calculates the normal vector of the vertices of the quadrangle constituting the three-dimensional object as a calculation for drawing the deformation of the three-dimensional object, the diagonal position A vector obtained by normalizing the outer product of two sets of vectors from one side vertex to the other side vertex is calculated as a normal vector of the reference vertex.

  With this configuration, the calculation is simplified as compared with the conventional calculation in which the calculation of the outer product and the normalization is performed four times, and the processing load required for the calculation can be reduced.

According to the present invention described in any one of claims 1 to 3, 6, and 8, a plurality of vertex coordinates are indicated by polygon data imitating a flexible object such as cloth, clothes and hair. As a calculation for drawing the deformation of a three-dimensional object whose surface is formed by a polygon, particularly a three-dimensional object whose surface is formed by a plurality of rectangles, one reference vertex of the arbitrary rectangle and the reference The four neighboring vertices adjacent to the vertex are extracted as mass points, and a first matrix having the difference between the reference vertex extracted as the mass point and the coordinates of each neighboring vertex is calculated using a matrix arithmetic processor , Dividing the difference between the coordinates and the coordinates of each side vertex by the magnitude of the vector from the reference vertex to each side vertex, and further multiplying the distance between the reference vertex and each side vertex by the second matrix , calculated using the matrix arithmetic processor, A third matrix multiplied by a spring constant to the difference between the first matrix and a second matrix out, calculated using the matrix arithmetic processor, the sum of the elements for near the vertex of each in the elements of the calculated third matrix The matrix calculation processor is used to calculate the fourth matrix as an element as the resultant force of the four side vertices with respect to the reference vertex.

  With this configuration, it is possible to calculate the resultant force by calculating a matrix, so that the matrix calculation processor or the like is compared with the conventional calculation that calculates the resultant force after obtaining the forces from adjacent vertices. As a result, it is possible to efficiently use a sub-processor specialized for the above calculation, so that it is possible to reduce the processing load required for the calculation performed by the main processor.

  In particular, in order to project a three-dimensional object onto a two-dimensional screen, the first matrix, the second matrix, the third matrix, etc., when expressed in a homogeneous coordinate system showing the homogeneous coordinates indicating the projected plane Can be expressed as a 4 × 4 matrix including x-coordinate, y-coordinate and z-coordinate and homogeneous coordinates, so that a matrix arithmetic processor provided in devices such as popular video game devices and personal computers can be used. Since the parallel calculation can be realized by using it efficiently, it is possible to reduce the load on the main processor and reduce the calculation time of the entire apparatus.

  In this way, the drawing time of the three-dimensional object is shortened by reducing the time for calculating the force applied to a plurality of vertices of the three-dimensional object that is a polygon image. It is possible to express the smooth movement of the 3D object by increasing the number of frames, and by reducing the size of each quadrangle and increasing the total number of squares, It has excellent effects such as being capable of being expressed.

According to the present invention of claim 4, claim 7, and claim 9, the surface is made up of a plurality of polygons whose vertex coordinates are indicated by polygon data, imitating flexible objects such as clothes and hair. As a calculation to draw the deformation of a three-dimensional object to be formed, particularly a three-dimensional object whose surface is formed by a plurality of quadrangles, the normal vector of the vertexes of the quadrangle that forms the surface of the three-dimensional object is used. When calculating, extract two to four neighboring vertices adjacent to one reference vertex of an arbitrary rectangle, and when the extracted neighboring vertices is four, obtain a position vector based on the coordinates of the four neighboring vertices, If the number of extracted side vertices is 3, if the coordinates of the base vertex are the coordinates of the one side vertex, the position vector based on the coordinates of the four side vertices is obtained. Based on the coordinates of the four neighboring vertices. While in the Ku position seek vector, rectangle formed by the extracted fourth near the apex, or extracted neighbor vertices and diagonal positions of virtual computational quadrangle formed by the reference vertex and neighbor vertex A vector obtained by normalizing an outer product of two sets of vectors from one side vertex to the other side vertex, that is, a pair of diagonal vectors, is calculated as a normal vector of the reference vertex.

  With this configuration, the calculation is simplified and the processing load required for the calculation can be reduced compared to the conventional calculation in which the calculation of the outer product and the normalization is performed four times for each vertex.

  In this way, the drawing time of the 3D object is shortened by reducing the time for calculating the normal vectors of the vertices of the 3D object which is a polygon image. It is possible to express the smooth movement of the 3D object by increasing the number of frames of the image, and by reducing the size of each rectangle and increasing the number of the entire rectangle, Excellent effects such as being able to express precisely.

  According to the present invention described in claim 5, calculation of resultant force, calculation of normal vector, etc. for a three-dimensional object whose surface is formed by a plurality of triangles formed as data for a video game apparatus. When performing calculations required for drawing, extract multiple triangles from a three-dimensional object whose surface is formed by multiple triangles and delete the vertices of each extracted triangle before performing the calculations required for drawing Thus, a three-dimensional object whose surface is formed by a plurality of triangles is converted into a three-dimensional object whose surface is formed by a plurality of quadrangles.

  With this configuration, for example, data of a three-dimensional object whose surface is formed by a plurality of rectangles created at the stage of designing the three-dimensional object using CG (Computer Graphics) software is used for a video game device. Even if the data is converted into the data of a three-dimensional object whose surface is formed by a plurality of triangles, the surface of the three-dimensional object is converted from the three-dimensional object whose surface is formed by a plurality of triangles. The long side of the triangle to be formed, that is, the side corresponding to the diagonal of the quadrangle, can be deleted to easily form a three-dimensional object whose surface is formed by a plurality of quadrilaterals. The present invention has an excellent effect that the invention described in any one of claims 1 to 4 can be applied to a three-dimensional object on which a surface is formed.

  Hereinafter, the present invention will be described in detail with reference to the drawings illustrating embodiments thereof.

  FIG. 1 is a block diagram showing a configuration of a drawing calculation apparatus 100 according to the present invention.

  The drawing computing device 100 is a kind of computer using a home video game device, and includes a CPU (Central Processing Unit) 101 which is a main processor for controlling the entire device, generation and processing of image data and audio data, and the like. A signal processing processor 102 that performs signal processing of the matrix, a matrix operation processor 103 that performs calculations relating to a 4 × 4 matrix, various sub-processors that operate based on the control of the CPU 101 such as an image drawing processing processor 104 that performs image drawing processing, Slot for reading various information from a recording medium 200 such as a ROM (Read Only Memory) cartridge, a CD-ROM (Compact Disc Read Only Memory), and a DVD (Digital Versatile Disc) in which various information such as the computer program 201 and data is recorded. , CD-ROM drive and DVD drive etc. An auxiliary storage means 105 and a RAM (Random Access Memory) 106 for temporarily storing information such as calculation data and display image data are provided.

  Then, various information such as the computer program 201 and data of the present invention recorded on the recording medium 200 is read by the auxiliary storage means 105, stored in the RAM 106, and executed based on the control of the CPU 101. The computer used operates as the drawing calculation apparatus 100 of the present invention.

  The drawing calculation apparatus 100 includes an input unit 108 such as a dedicated controller connected via an input interface circuit (input I / F) 107.

  Further, the drawing calculation apparatus 100 includes an audio output interface circuit (audio output I / F) 109 used for outputting audio data, and audio data that is a digital signal output from the audio output interface circuit 109 is: The analog signal is converted into an analog signal by an audio D / A converter (audio D / A) 110, and the analog signal converted by the audio D / A converter 110 is amplified by the pre-main amplifier 111, and then based on the audio data. The sound is output to sound output means 120 such as a speaker that outputs sound.

  Further, the drawing calculation device 100 includes an image output interface circuit (image output I / F) 112 used for outputting image data, and image data that is a digital signal output from the image output interface circuit 112 is: It is converted into an analog signal by an image D / A converter (image D / A) 113 and sent to display means 130 such as a television monitor that outputs an image based on the image data.

  A single television monitor may be used as a device that serves as both the audio output means 120 and the display means 130.

  Next, processing performed to represent a three-dimensional object in the game space using the drawing calculation apparatus 100 of the present invention will be described.

  In the drawing calculation apparatus 100, the signal processor 102 and the matrix calculation processor 103 perform various calculation processes based on the control of the CPU 101, and the display area that is a part of the image drawing processor 104 and the RAM 106 based on the calculation result. Write processing of image data to be drawn on the (frame buffer).

  The RAM 106 has a non-display area and a display area. The non-display area stores intermediate calculation data in image drawing processing such as polygon data and texture data, and the display area is displayed on the display means 130. The image data to be stored is stored, and the stored image data is sent to the display means 130 via the image D / A converter 113.

  Polygon data is data indicating the spatial coordinates of the vertices of polygons (polygons) such as a plurality of quadrilaterals that form the surface of a three-dimensional object set in the game space, and the three-dimensional object indicated by the polygon data An image indicating the surface such as a pattern and material indicated as texture data is pasted on the surface of the object, thereby showing various virtual objects in the game space.

  When an image showing a three-dimensional object in the game space is displayed on the display unit 130, a surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data by processing of each processor based on the control of the CPU 101. By converting the spatial coordinates of the three-dimensional object to be converted into plane coordinates and further performing perspective projection processing, the plane coordinates of each vertex of the polygon in two dimensions are calculated, and the texture data is converted into the polygon based on the calculated plane coordinates. Is generated, and the generated image data is stored in the display area of the RAM 106.

  The image data stored in the display area of the RAM 106 is sent to the display means 130 via the image D / A converter 113 and displayed on the display means 130 as described above.

  Next, calculations required for drawing a three-dimensional object in the drawing calculation apparatus 100 of the present invention will be described.

  Three-dimensional objects that imitate flexible objects such as cloth, clothes, and hair are required to move in various shapes when rendered as moving images. Various dynamics are required to express natural movement. Calculation is required.

  FIG. 2 is an explanatory view schematically showing a three-dimensional object in the drawing calculation apparatus 100 of the present invention.

  FIG. 2A is an explanatory diagram showing a plurality of quadrilaterals that form a three-dimensional object imitating a flexible object. FIG. 2A shows a three-dimensional object simulating a square cloth, which is formed by a plurality of quadrangles.

  FIG. 2B is an explanatory diagram illustrating a dynamic model that is assumed when performing calculations necessary for drawing the three-dimensional object illustrated in FIG. When the calculation required for drawing the three-dimensional object shown in FIG. 2A is performed, the vertexes of each square are used as mass points as shown in FIG. A dynamic model is assumed in which each mass point is connected by this spring and receives a force from four adjacent mass points (two or three adjacent mass points at the end of the fabric).

  By assuming such a dynamic model, for example, when drawing the movement of pulling the end of the cloth, the force applied to the mass point corresponding to the end of the cloth, the force applied to the mass point adjacent to the mass point, Further, it is possible to calculate the force applied to the mass point adjacent to the mass point, and it is possible to obtain the change in the shape of the three-dimensional object imitating the cloth by calculation.

  Furthermore, as one of the calculations required for drawing a three-dimensional object, for example, when generating image data in which texture data is pasted on a three-dimensional object, the direction of light reflected on the surface of the three-dimensional object is calculated. Therefore, it is necessary to calculate a normal vector at each vertex.

  Next, calculations required for drawing a three-dimensional object in the drawing calculation apparatus 100 of the present invention will be described.

  In the drawing calculation apparatus 100 of the present invention, the matrix arithmetic processor 103 is effectively used when the plurality of polygons forming the surface of the three-dimensional object formed as data for the video game apparatus are triangles. Therefore, before calculating the resultant force required to draw the three-dimensional object and calculating the normal vector, the surface of the three-dimensional object formed with a plurality of triangles is formed with a plurality of rectangles. A process of converting into a three-dimensional object is performed.

  FIG. 3 is a flowchart showing polygon conversion processing of the drawing calculation apparatus 100 of the present invention.

  In the drawing calculation apparatus 100, based on the control of the CPU 101 that executes the computer program 201 stored in the RAM 106, before performing calculation such as calculation of resultant force and normal vector calculation required for drawing of the three-dimensional object, A plurality of triangles included in a three-dimensional object whose surface is formed by a plurality of triangles are extracted (S101), and a long side of each extracted triangle is deleted, whereby a surface is formed by the plurality of triangles. The three-dimensional object is converted into a three-dimensional object whose surface is formed by a plurality of squares (S102). In step S102, the long side of the triangle is deleted and converted to a quadrangle, but the deletion here means to remove from the data to be calculated, and the data itself is deleted to form a plurality of triangles. It does not make it impossible to restore the 3D object.

  FIG. 4 is an explanatory diagram showing conversion of a polygon of a three-dimensional object by polygon conversion processing of the drawing calculation apparatus 100 of the present invention. FIG. 4 shows a three-dimensional object whose surface is formed by a plurality of triangles before performing the polygon conversion processing described with reference to FIG. 3, and is indicated by a dotted line among the three sides of each triangle. The long side is the long side of each triangle deleted in step S102 in FIG.

  As shown in FIG. 4, the long side of the triangle before performing the polygon conversion process is a side corresponding to the diagonal of the quadrangle after the conversion, and a tertiary whose surface is formed by a plurality of triangles by deleting the long side. It is possible to easily perform the process of converting the original object into a three-dimensional object whose surface is formed by a plurality of quadrangles.

  Next, a description will be given of a method for calculating the resultant force from another mass point applied to one mass point corresponding to the vertex of a quadrangle constituting the three-dimensional object in the drawing calculation apparatus 100 of the present invention.

  FIG. 5 is a flowchart showing the resultant force calculation process of the drawing calculation apparatus 100 of the present invention. FIG. 6 shows the reference vertex M0 and the four adjacent to the reference vertex M0 in the resultant force calculation process of the drawing calculation apparatus 100 of the present invention. It is explanatory drawing which shows typically the connection relation of near vertex M1, M2, M3, and M4.

  In the drawing calculation apparatus 100, based on the control of the CPU 101 that executes the computer program 201 stored in the RAM 106, one reference vertex M0 that forms the surface of the three-dimensional object, and the reference vertex M0. The four neighboring vertices M1, M2, M3, and M4 are extracted as mass points (S201), and the reference vertex M0 extracted as the mass point and the coordinates of each of the neighboring vertices M1, M2, M3, and M4 in the three-dimensional space are extracted from the polygon data. Obtained (S202).

  The coordinates in the three-dimensional space of the reference vertex M0 and the neighboring vertices M1, M2, M3, and M4 obtained in step S202 are shown as follows.

P0 = (x0, y0, z0, w0)
P1 = (x1, y1, z1, w1)
P2 = (x2, y2, z2, w2)
P3 = (x3, y3, z3, w3)
P4 = (x4, y4, z4, w4)
However, P0: coordinates of the reference vertex M0
P1: Coordinates of the near vertex M1
P2: coordinates of the near vertex M2
P3: Coordinates of the near vertex M3
P4: Coordinates of the near vertex M4 x0, x1, x3, and x4 are the values of x on the three-dimensional coordinates indicated by the x-axis, y-axis, and z-axis, and y0, y1, y3, and y4 are y The values z0, z1, z3, and z4 indicate the values of z, and P0, P1, P2, P3, and P4 indicate the reference vertex M0 and the side vertices M1, M2 by showing in such a coordinate system. , M3, and M4.

  Further, w0, w1, w2, w3, and w4 are homogeneous coordinates indicating a plane to be projected when a three-dimensional object is projected onto a two-dimensional screen. For example, a two-dimensional plane indicated as w = 1. Assuming that the image is projected upward, a value of w0 = w1 = w2 = w3 = w4 = 1 is used.

  In the drawing calculation apparatus 100, based on the control of the CPU 101 that executes the computer program 201 stored in the RAM 106, the difference between the obtained coordinates of the reference vertex M0 and the coordinates of the respective neighboring vertices M1, M2, M3, and M4 is used as an element. The first matrix MX shown in the following equation (1) is calculated (S203).

  Further, in the drawing calculation apparatus 100, based on the control of the CPU 101 that executes the computer program 201 stored in the RAM 106, the difference between the coordinates of the reference vertex M0 and the coordinates of the neighboring vertices M1, M2, M3, and M4 is determined as the reference vertex. Divide by the magnitude of the vector from M0 to each of the neighboring vertices M1, M2, M3, M4, and further multiply by the distance L1, L2, L3, L4 between the reference vertex M0 and each of the neighboring vertices M1, M2, M3, M4 The second matrix ML shown in the following formula (2) having the obtained value as an element is calculated (S204). In equation (2), the distances L1, L2, L3, and L4 between the reference vertex M0 and the neighboring vertices M1, M2, M3, and M4 are always constant because they indicate the distances between the vertices that do not expand and contract.

  In the drawing calculation device 100, the difference between the first matrix MX and the second matrix ML is multiplied by the spring constant k based on the control of the CPU 101 that executes the computer program 201 stored in the RAM 106, and the following equation (3) 3 is calculated (S205). In the expression (3), the reference vertex M0 and the neighboring vertices M1, M2, M3, and M4 are regarded as mass points, and the attractive force acting between the reference vertex M0 and the neighboring vertices M1, M2, M3, and M4 is calculated. For the sake of convenience, the force is calculated on the assumption that the reference vertex M0 and each side vertex M1, M2, M3, M4 are connected by a virtual spring having a spring constant k. Since the distances L1, L2, L3, and L4 between the vertices M1, M2, M3, and M4 are constant, the virtual spring that connects between the reference vertex M0 and the neighboring vertices M1, M2, M3, and M4 does not expand and contract. Shall.

Third matrix MF = k * (MX−ML) (3)
However, k: spring constant In the drawing calculation device 100, each of the neighboring vertexes M1, M2, and M2 among the calculated third matrix elements based on the control of the CPU 101 that executes the computer program 201 stored in the RAM 106. A fourth matrix F having the sum of elements relating to M3 and M4 as elements is calculated (S206).

  The fourth matrix F calculated in step S206 is a column vector whose element is the sum of the columns of the third matrix MF, and the force from the plurality of neighboring vertices M1, M2, M3, M4 with respect to the reference vertex M0. Is a vector indicating the resultant force.

  FIG. 7 is an explanatory diagram schematically showing the connection relationship between the ends of the three-dimensional object in the drawing calculation apparatus 100 of the present invention. FIG. 7 shows an end portion of a three-dimensional object simulating a square cloth shown in FIG. 2, for example. FIG. 7 (a) is an end portion corresponding to a square side, and FIG. ) Is the end corresponding to the apex of the square.

  At the end shown in FIG. 7A, there is no vertex that should become the side vertex M4 among the four side vertices M1, M2, M3, and M4 with respect to the reference vertex M0.

  Even in such a case, it is assumed that four neighboring apexes M1, M2, M3, and M4 are connected to the reference vertex M0, and calculation is performed using the coordinate P0 of the reference vertex M0 as the coordinate P4 of the neighboring vertex M4. I do.

  At the end shown in FIG. 7B, there are no vertices that should become the side vertices M3 and M4 among the four side vertices M1, M2, M3, and M4 with respect to the reference vertex M0.

  Even in such a case, it is assumed that the four neighboring vertices M1, M2, M3, and M4 are connected to the reference vertex M0, and the coordinates P0 of the reference vertex M0 are used as the coordinates P3 and P4 of the neighboring vertices M3 and M4. Calculate using.

  These resultant force calculation processes are performed on all quadrangular vertices constituting the three-dimensional object, but the first matrix MX, the second matrix ML, and the third matrix MF are expressed as 4 × 4 matrices. Therefore, since the matrix arithmetic processor 103 is effectively used for the calculation and is performed by parallel calculation, the load on the other CPUs 101 and various processors is reduced, and the calculation time of the entire apparatus is shortened.

  When actually tested, it was found that the calculation could be completed in 70 to 90% of the time of the conventional method.

  Next, a method for calculating the normal vectors of the vertices of the quadrangle constituting the three-dimensional object in the drawing calculation apparatus 100 of the present invention will be described. FIG. 8 is a flowchart showing normal vector calculation processing of the drawing calculation apparatus 100 according to the present invention. FIG. 9 shows the reference vertex V0 and the reference vertex V0 in the normal vector calculation processing of the drawing calculation apparatus 100 according to the present invention. It is explanatory drawing which shows typically the connection relation of four adjacent vertexes V1, V2, V3, and V4.

  In the drawing calculation apparatus 100, based on the control of the CPU 101 that executes the computer program 201 stored in the RAM 106, one reference vertex V0 of an arbitrary quadrilateral that forms the surface of the three-dimensional object, and the reference vertex V0 are combined. The four neighboring vertices V1, V2, V3, V4 are extracted (S301), and position vectors P1, P2, P3, P4 based on the coordinates of the extracted neighboring vertices V1, V2, V3, V4 in the three-dimensional space are obtained. Obtained (S302).

  The position vectors P1, P2, P3, and P4 based on the coordinates of the neighboring vertices V1, V2, V3, and V4 obtained in step S302 are the coordinates obtained in step S202 of the resultant force calculation process described with reference to FIG. P1, P2, P3, and P4.

  In the drawing computing device 100, based on the control of the CPU 101 that executes the computer program 201 stored in the RAM 106, one of the four diagonal vertices formed by the four side vertices extracted in step S301 is located at the diagonal position. A vector N0 represented by the following equation (4) obtained by normalizing the outer product of two sets of vectors from the neighboring vertex to the other neighboring vertex is calculated (S303).

Normal vector N0
= (P1-P3) × (P2-P4) / | (P1-P3) × (P2-P4) |
...... Formula (4)

  The vector N0 calculated in step S303 is used as a normal vector of the reference vertex V0.

  In addition, the two sets of vectors from one side vertex to the other side vertex at the diagonal position are a vector from the side vertex V1 to the side vertex V3 and a vector from the side vertex V2 to the side vertex V4 in FIG. is there.

FIG. 10 is an explanatory diagram schematically showing the coupling relationship between the ends of the three-dimensional object in the drawing calculation apparatus 100 of the present invention. FIG. 10 shows, for example, an end of a three-dimensional object simulating a square cloth shown in FIG. 2, and FIG. 10 (a) is an end corresponding to a square side, and FIG. ) Is the end corresponding to the apex of the square.

  At the end shown in FIG. 10 (a), there are no vertices that should become the side vertices V4 among the four side vertices V1, V2, V3, V4 with respect to the reference vertex M0.

  Even in such a case, it is assumed that four neighboring apexes M1, M2, M3, and M4 are connected to the reference vertex M0, and calculation is performed using the coordinate P0 of the reference vertex V0 as the coordinate P4 of the neighboring vertex M4. I do.

  In the end portion shown in FIG. 10B, there are no vertices that should become the side vertices V3 and V4 among the four side vertices V1, V2, V3, and V4 with respect to the reference vertex M0.

  Even in such a case, it is assumed that the four neighboring vertices V1, V2, V3, V4 are connected to the reference vertex M0, and the coordinates P0 of the reference vertex M0 are used as the coordinates P3, P4 of the neighboring vertices V3, V4. Calculate using.

  It is possible to shorten the calculation time by the normal vector calculation process described above, and when the test is actually performed, the result that the calculation can be completed in 20 to 25% of the time of the conventional method is obtained. It was.

  In the best mode for carrying out the invention, an embodiment has been shown in which a calculation relating to drawing of a three-dimensional object whose surface is formed by a plurality of quadrangles is performed. However, the present invention is not limited to this, and a plurality of triangles are used. It is also possible to apply to the calculation of the resultant force for the vertexes of polygons other than a quadrangle such as a three-dimensional object on which the surface is formed.

It is a block diagram which shows the structure of the calculation apparatus for drawing of this invention. It is explanatory drawing which shows typically the three-dimensional target object in the calculation apparatus for drawing of this invention. It is a flowchart which shows the polygon conversion process of the calculation apparatus for drawing of this invention. It is explanatory drawing which shows conversion of the polygon of the three-dimensional target object by the polygon conversion process of the calculation apparatus for drawing of this invention. It is a flowchart which shows the resultant force calculation process of the calculation apparatus for drawing of this invention. It is explanatory drawing which shows typically the connection relation of the reference vertex in the resultant force calculation process of the drawing calculation apparatus of this invention, and the four side vertex adjacent to this reference vertex. It is explanatory drawing which shows typically the connection relation of the edge part of the three-dimensional target object in the calculation apparatus for drawing of this invention. It is a flowchart which shows the normal vector calculation process of the calculation apparatus for drawing of this invention. It is explanatory drawing which shows typically the connection relation of the reference vertex in the normal vector calculation process of the calculation apparatus for drawing of this invention, and the four side vertex adjacent to this reference vertex. It is explanatory drawing which shows typically the connection relation of the edge part of the three-dimensional target object in the calculation apparatus for drawing of this invention.

Explanation of symbols

100 Image processing apparatus 101 CPU
DESCRIPTION OF SYMBOLS 102 Signal processor 103 Matrix arithmetic processor 104 Image drawing processor 105 Auxiliary storage means 106 RAM
DESCRIPTION OF SYMBOLS 107 Input interface circuit 108 Input means 109 Audio | voice output interface circuit 110 Audio | voice D / A converter 111 Pre-main amplifier 112 Image output interface circuit 113 Image | video D / A converter 120 Audio | voice output means 130 Display means 200 Recording medium 201 Computer program

Claims (9)

A drawing calculation device for performing calculations necessary for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data,
A matrix processor that performs matrix-related operations;
Means for extracting one reference vertex of an arbitrary polygon and a plurality of neighboring vertices adjacent to the reference vertex as mass points;
Means for obtaining the coordinates of the reference vertex and each side vertex extracted as a mass point from polygon data;
Means for calculating , using a matrix arithmetic processor, a first matrix whose elements are the difference between the coordinates of the obtained reference vertex and the coordinates of each neighboring vertex;
The difference between the coordinates of the reference vertex and the coordinates of each side vertex is divided by the vector size from the reference vertex to each side vertex, and further multiplied by the distance between the reference vertex and each side vertex. Means for calculating two matrices using a matrix arithmetic processor ;
Means for calculating a third matrix obtained by multiplying the calculated difference between the first matrix and the second matrix by a constant using a matrix arithmetic processor ;
Matrix calculation is performed for the calculation required for drawing with the fourth matrix having the sum of the elements related to each of the neighboring vertices as the combined force of the forces from the plurality of neighboring vertices with respect to the reference vertex. A drawing computing device comprising: means for performing processing using a processor . The first matrix is represented by the following formula (A):
The second matrix is represented by the following formula (B):
The drawing calculation apparatus according to claim 1, wherein the third matrix is represented by the following formula (C).

The polygon is a rectangle,
The number of the side vertices is four. The drawing calculation device according to claim 1, wherein the number of the side vertices is four. A drawing calculation device for performing calculations necessary for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data,
The polygon is a rectangle,
Means for extracting two to four neighboring vertices adjacent to one reference vertex of an arbitrary rectangle;
Means for obtaining a position vector based on the coordinates of the four neighboring vertices when the extracted neighboring vertices is four ;
Means for obtaining a position vector based on the coordinates of the four side vertices, with the coordinates of the reference vertex set as the coordinates of the one side vertex when the number of extracted side vertices is 3,
Means for obtaining a position vector based on the coordinates of the four neighboring vertices, with the coordinates of the second neighboring vertex being the coordinates of the second neighboring vertex when the extracted number of neighboring vertices is two;
A quadrangle formed by the extracted four vertices , or one of the opposite vertices at the diagonal position of a virtual calculation rectangle formed by the extracted vertices and a reference vertex as a vertice. A drawing calculation apparatus comprising: means for performing calculation required for drawing, wherein a vector obtained by normalizing an outer product of two sets of vectors toward a side vertex is a normal vector of a reference vertex. Before performing the calculation required for drawing,
Means for extracting a plurality of triangles forming a surface of a three-dimensional object in which the plurality of polygons are triangles;
Means for converting a three-dimensional object whose surface is formed by a plurality of triangles into a three-dimensional object whose surface is formed by a plurality of quadrilaterals by deleting the long side of each extracted triangle. The drawing calculation apparatus according to claim 1, wherein the calculation apparatus is a drawing calculation apparatus. A computer program for causing a computer having a matrix operation processor for performing an operation relating to a matrix to perform calculations necessary for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data. ,
A procedure for causing a computer to extract a reference vertex of an arbitrary polygon position and a plurality of neighboring vertices adjacent to the reference vertex as mass points;
A procedure for causing a computer to obtain the coordinates of reference vertices and respective side vertices extracted as mass points from polygon data;
A procedure for causing a computer to calculate a first matrix having a difference between the coordinates of the obtained reference vertex and the coordinates of each of the neighboring vertices using a matrix processor ;
The computer divides the difference between the coordinates of the reference vertex and the coordinates of each side vertex by the size of the vector from the reference vertex to each side vertex, and further multiplied by the distance between the reference vertex and each side vertex. A procedure for calculating a second matrix to be calculated using a matrix arithmetic processor ;
A procedure for causing a computer to calculate a third matrix obtained by multiplying a difference between the calculated first matrix and second matrix by a constant using a matrix arithmetic processor ;
The computer performs a calculation required for drawing, with the fourth matrix having the sum of the elements related to each of the neighboring vertices among the calculated third matrix elements as the resultant force of the forces from the plurality of neighboring vertices. And a computer program for executing a procedure to be performed using a matrix arithmetic processor . A computer program for causing a computer to perform calculations necessary for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data,
The polygon is a rectangle,
A procedure for causing a computer to extract two to four neighboring vertices adjacent to one reference vertex of an arbitrary rectangle;
A procedure for causing a computer to obtain a position vector based on the coordinates of the four neighboring vertices when the extracted neighboring vertices is four ;
A procedure for causing the computer to obtain a position vector based on the coordinates of the four side vertices when the number of extracted side vertices is 3, using the coordinates of the reference vertex as the coordinates of the one side vertex,
A procedure for causing the computer to obtain a position vector based on the coordinates of the four side vertices, with the coordinates of the reference vertex being the coordinates of the second side vertex when the number of extracted side vertices is 2,
On the computer, the quadrangle formed by the extracted four vertices , or one of the vertices of the hypothetical computational rectangle formed by the extracted vertices and the reference vertex as the vertices. A computer program for executing a calculation required for drawing, wherein a vector obtained by normalizing an outer product of two sets of vectors from one to the other neighboring vertex is set as a normal vector of a reference vertex. A computer program that performs a calculation required for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose coordinates of vertexes are indicated by polygon data is recorded in a computer having a matrix calculation processor that performs matrix-related calculations. A computer-readable recording medium,
A procedure for causing a computer to extract a reference vertex of an arbitrary polygon position and a plurality of neighboring vertices adjacent to the reference vertex as mass points;
A procedure for causing a computer to obtain the coordinates of reference vertices and respective side vertices extracted as mass points from polygon data;
A procedure for causing a computer to calculate a first matrix having a difference between the coordinates of the obtained reference vertex and the coordinates of each of the neighboring vertices using a matrix processor ;
The computer divides the difference between the coordinates of the reference vertex and the coordinates of each side vertex by the size of the vector from the reference vertex to each side vertex, and further multiplied by the distance between the reference vertex and each side vertex. A procedure for calculating a second matrix to be calculated using a matrix arithmetic processor ;
A procedure for causing a computer to calculate a third matrix obtained by multiplying a difference between the calculated first matrix and second matrix by a constant using a matrix arithmetic processor ;
The computer performs a calculation required for drawing, with the fourth matrix having the sum of the elements related to each of the neighboring vertices among the calculated third matrix elements as the resultant force of the forces from the plurality of neighboring vertices. A computer-readable recording medium having recorded thereon a computer program for executing a procedure performed using a matrix arithmetic processor . A computer program for performing calculations necessary for drawing a three-dimensional object whose surface is formed by a plurality of polygons whose vertex coordinates are indicated by polygon data is recorded on the computer and can be read by the computer. A recording medium,
The polygon is a rectangle,
A procedure for causing a computer to extract two to four neighboring vertices adjacent to one reference vertex of an arbitrary rectangle;
A procedure for causing a computer to obtain a position vector based on the coordinates of the four neighboring vertices when the extracted neighboring vertices is four ;
A procedure for causing the computer to obtain a position vector based on the coordinates of the four side vertices when the number of extracted side vertices is 3, using the coordinates of the reference vertex as the coordinates of the one side vertex,
A procedure for causing the computer to obtain a position vector based on the coordinates of the four side vertices, with the coordinates of the reference vertex being the coordinates of the second side vertex when the number of extracted side vertices is 2,
On the computer, the quadrangle formed by the extracted four vertices , or one of the vertices of the hypothetical computational rectangle formed by the extracted vertices and the reference vertex as the vertices. A computer program is recorded that executes a calculation procedure required for drawing, with a vector obtained by normalizing the outer product of two sets of vectors from one to the other neighboring vertex as a normal vector of the reference vertex. A recording medium that can be read by a computer.

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