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Combinatorial Triangles Polygonalizaton
To handle irregular solids, such as the ellipsoid, sphere, and torus intersection shown at right, and cells defined in terms of solid bodies, we have implemented an algorithm1 based on the intersection of triangles in two or more polygonalized objects. The algorithm subdivides triangles that intersect triangles in the other object so that intersections occur only along the edges of triangles. Triangles that do not satisfy the cell description are discarded. The methods starts with objects polygonalized as triangles with strict conventions for the ordering of the triangles and vertices. The algorithm is used for most cases of solid body geometry. If the cell description can be converted to unions of groups of bodies, the algorithm is applied separately to each group.
The method can consume a large amount of time and have problems with complicated cell descriptions. A number of settings, discussed below, can be used to limit the application of the method and thus the overall time spent processing a model for 3D display. Sometimes a more approximate representation made by another method may be preferable to long polygonalization times; in other cases a user may give precedence to a better 3D appearance.
A special case—TRIPOLYB—results when the planes of a part form a PHEDRON shape. This case is discussed in more detail in the section on conversion of surface to solid body geometry.
1. Philip M Hubbard, “Constructive Solid Geometry forTriangulated Polyhedra”, Brown University Report CS-90-07 (1990).
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