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On Generating Topologically Correct Isosurfaces from Uniform Samples
Natarajan, Balas K.
HPL9176
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Abstract: A function f(x,y,z) of three variables may be visualized by examining its isosurfaces f(s,y,z) = t for various values of t. To display these isosurfaces on a graphics device it is desirable to approximate them with piecewise polygonal surfaces that are (1) geometrically good approximations, (1) topologically correct, and (3) consist of a small number of polygons. By topologically correct we mean that the connectivity of the constructed surface matches that of the true isosurfaceany two points in the given sample are connected by a path that does not pierce the constructed surface, if and only if they are connected by a path that does not pierce the true isosurface. / We are interested in functions specified as the piecewise trilinear interpolant of a uniform mesh of sample points. For such functions: the "marching cubes" algorithm of Cline et al. (1988) constructs a piecewise polygonal approximation to the isosurface, satisfying conditions (1) and (3) above, but not condition (2), i.e., the topology of the constructed surface may be incorrect; the "dividing cubes" algorithm of Cline et al. (1988) constructs a piecewise polygonal approximation to the isosurface satisfying conditions (1) and (2) above, but not condition (3), i.e., the constructed surface may not consist of a small number of polygons; here, we present an efficient algorithm that constructs a piecewise polygonal approximation to the isosurface satisfying all three conditions, i.e., the constructed surface is geometrically a good approximation, topologically correct, and consists of a small number of polygons.
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