Polyhedral Subdivision for Free-Form Algebraic Surfaces
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چکیده
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 within Σ to approximate P. An A-patch is a smooth and functional algebraic surface (zero-contour of a trivariate polynomial) in Bernstein-Bézier (BB) form defined within each tetrahedron of Σ.
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