Surface simplification preserving a solid volume
AssigneeInternational Business Machines Corporation
InventorAndre Pierre Gueziec
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Abstract
Computer systems may be used to generate and display objects represented by triangles defined by coordinates of vertices. The present invention generates coordinates of a simplified vertex based upon coordinates of vertices adjacent to a first vertex and to a second vertex that define an edge of the triangles. First, a set of triangles that are adjacent to the edge is identified, Second, a first volume associated with the set of triangles is calculated. Finally, the coordinates of the simplified vertex are calculated such that a second volume associated with the simplified vertex corresponds to the first volume.
Claims20
In a computer system wherein objects are represented by triangles defined by coordinates of vertices, a method for generating coordinates of a simplified vertex based upon coordinates of vertices adjacent to a first vertex and to a second vertex that define an edge of said triangles, the method comprising the steps of:
- identifying a set of triangles that are adjacent to said edge;
- generating a set of tetrahedra corresponding to said set of triangles, wherein each tetrahedron in the set of tetrahedra is defined by three vertices of a corresponding triangle and a common point shared by all tetrahedra in the set of tetrahedra;
- calculating a first volume associated with said set of tetrahedra;
- and
- determining coordinates of said simplified vertex such that a second volume associated with said simplified vertex corresponds to said first volume.
A program storage device for use in a computer system wherein objects are represented by triangles defined by coordinates of vertices, the program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps for generating coordinates of a simplified vertex based upon coordinates of vertices adjacent to a first vertex and to a second vertex that define an edge of said triangles, the method steps comprising:
- identifying a set of triangles that are adjacent to said edge;
- generating a set of tetrahedra corresponding to said set of triangles, wherein each tetrahedron in the set of tetrahedra is defined by three vertices of a corresponding triangle and a common point shared by all tetrahedra in the set of tetrahedra;
- calculating a first volume associated with said set of tetrahedra;
- and
- determining coordinates of said simplified vertex such that a second volume associated with said simplified vertex corresponds to said first volume.
Dependencies are inferred from the claim text.