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# Computing a Set of Triangular Plates Which Represent a Potential Surface of a Scalar Function Defined at the Vertices of a Three Dimensional Cartesian Mesh

IP.com Disclosure Number: IPCOM000084119D
Original Publication Date: 1975-Sep-01
Included in the Prior Art Database: 2005-Mar-02
Document File: 5 page(s) / 74K

IBM

## Related People

Schreiber, DE: AUTHOR

## Abstract

This is a method of computing the vertices and planar polyhedra, triangles, of solid surfaces defined in terms of a scalar function whose value is specified at the mesh points of a three-dimensional Cartesian mesh, and of organizing these vertices and triangles in such a manner as to be suitable for eliminating the hidden lines and surfaces from the rendering of the bodies which the potential surfaces bound. The steps of the method are as follows: I. Computing the vertices of the potential surface and the triangle faces which make up the surface; II. Eliminating redundantly computed vertices to condense the vertex list, and computing the distinct objects which make up the total surface; III. Computing the rendering of the potential surface; and IV.

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Computing a Set of Triangular Plates Which Represent a Potential Surface of a Scalar Function Defined at the Vertices of a Three Dimensional Cartesian Mesh

This is a method of computing the vertices and planar polyhedra, triangles, of solid surfaces defined in terms of a scalar function whose value is specified at the mesh points of a three-dimensional Cartesian mesh, and of organizing these vertices and triangles in such a manner as to be suitable for eliminating the hidden lines and surfaces from the rendering of the bodies which the potential surfaces bound. The steps of the method are as follows: I. Computing the vertices of the potential surface and the triangle faces which make up the surface; II. Eliminating redundantly computed vertices to condense the vertex list, and computing the distinct objects which make up the total surface; III. Computing the rendering of the potential surface; and IV. Eliminating the hidden lines and plotting the rendering on a computer controlled plotting device, or displaying it on a computer controlled interactive graphical device.

A different view of the potential surface obtained by executing all four phases of the program can be obtained by reexecuting only Phases III and IV of the computation. A different location from which to view the scene need only be specified. METHOD FOR PERFORMING PHASE I OF THE COMPUTATION AND DISPLAY OF A POTENTIAL SURFACE.

The Cartesian mesh of Fig. 1 for which a potential surface is to be computed comprises three sets of orthogonal planes. The number of planes in each of the sets is an integer greater than one. Thus there are L planes in the set of planes parallel to the Y-Z plane, M planes in the set of planes parallel to the Z-X plane, and N planes in the set of planes parallel to the X-Y plane. In Fig. 1, for example, L equals 4, M equals 6, and N equals 5.

The value of the function for which a potential surface is to be computed and rendered must be specified at all of the points of the Cartesian mesh. For a given mesh specified by three sets of orthogonal planes, each set individually containing L, M and N mesh planes, the value of the function to be rendered must be specified at all the mesh points (or, vertices of the Cartesian mesh). Also, the value of the function for which a potential surface is desired must be specified.

A single cell of the mesh is processed in the following manner: 1) Compute the coordinates of vertices of the potential surface. 2) Use these points on the potential surface as vertices of the triangular plates which make up the potential surface.

The vertices of the potential surface are computed in the following manner. The functional values at the mesh points of the cell are tested in pairs. The two functional values to be tested are specified at points lying on a common mesh line. If one of the mesh point's functional value is greater than or equal to the potential surface value and the other's functional value is less than the pot...