July 2002
Intermediate to advanced
576 pages
15h 37m
English
Content preview from Pyramid Algorithms
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8.7 Toric Bezier Patches
Toric Bezier patches are pyramid patches defined by special indexing sets and special barycentric coordinate functions. These indexing sets and barycentric coordinate functions are chosen to overcome some of the deficiencies we have observed in arbitrary P-patches and in general C-patches.
Blossoming the pyramid algorithm does not provide the dual functionals for arbitrary pyramid patches. C-patches overcome this deficiency by blossoming the multitier evaluation algorithm, but C-patches have two other serious shortcomings. First, as we observed in the previous section, the boundary of a C-patch is not easy to determine. More serious, but perhaps more subtle, we do not even know what the boundary control points are for ...
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