Vertex-Rounding a Three-Dimensional Polyhedral Subdivision
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Polyhedral Subdivision for Free-Form Algebraic Surfaces
We present a robust algorithm to construct an “inner” simplicial hull Σ as a single step of subdivision of an input polyhedron P in three dimensional space. Similar to traditional subdivision schemes P becomes the ‘control net’ for free-form modeling while an inner surface triangulation T of Σ is a second level mesh. Free-Form C1 cubic A-patches and C2 quintic A-patches can then be constructed ...
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Let $G=(V(G),E(G))$ be a graph, $gamma_t(G)$. Let $ooir(G)$ be the total domination and OO-irredundance number of $G$, respectively. A total dominating set $S$ of $G$ is called a $textit{total perfect code}$ if every vertex in $V(G)$ is adjacent to exactly one vertex of $S$. In this paper, we show that if $G$ has a total perfect code, then $gamma_t(G)=ooir(G)$. As a consequence, ...
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