Index 343 pole (Voronoi center), 207, 236 power, 79 power diagram, 79, 241 quadratic Voronoi diagram, 87 Randomized Incremental Construction, 53 randomized incremental construction, 99 rational numbers, 119 rational univariate representation, 47 real numbers, 118 Reeb graph, 307 regular triangulation, 80, 241 regular value, 298 remeshing, 213 restricted Delaunay triangulation, 201 rounding mode, 120 saddle point, 223, 300 sample ε-sample, 202, 248 ψ-sample, 202 weak ε-sample, 203 weak ψ-sample, 203 scattered data interpolation, 182 seed triangle, 206 silhouette, 210 simplex, 279 d-dimensional, 279 oriented, 280 simplicial k-chain, 283 simplicial k-cycle, 284 simplicial collapse, 292 simplicial complex, 280 simplicial homology, 282 simply connected, 282 sliver tetrahedron, 235 smooth surface, 295 Snyder’s meshing algorithm, 191–196 space of spheres, 75 spherical diagrams, 84 split tree, 309 stable manifold, 244, 304 Sturm sequences, 4, 19, 47 subcomplex, 280 submanifold, 297 surface implicit, 182 smooth, 295 surface Delaunay ball, 201 surface extraction, 182 surface network, 306 Sylvester matrix formulation, 38 systems of equations zero-dimensional, 213 tangent space, 297 tangent vector, 297 topological ball property, 209, 228, 241 topological space, 278 traits, 25–28, 30, 32–34, 40, 314, 315 triangulation, 280 tubular neighborhood, 185, 202, 247 unstable manifold, 304 vertical decomposition, 42 visitor design pattern, 32 Voronoi diagram restricted, 238 Voronoi diagram, 72, 235 Voronoi hierarchy, 106 . point, 223, 300 sample ε-sample, 202, 248 ψ-sample, 202 weak ε-sample, 203 weak ψ-sample, 203 scattered data interpolation, 182 seed triangle, 206 silhouette, 210 simplex, 279 d-dimensional, 279 oriented,. triangle, 206 silhouette, 210 simplex, 279 d-dimensional, 279 oriented, 280 simplicial k-chain, 283 simplicial k-cycle, 284 simplicial collapse, 292 simplicial complex, 280 simplicial homology, 282 simply. Delaunay ball, 201 surface extraction, 182 surface network, 306 Sylvester matrix formulation, 38 systems of equations zero-dimensional, 213 tangent space, 297 tangent vector, 297 topological ball property,