Conditions for a Smooth Junction Between Three Quasi-Rectangular Patches
In the context of the representation of C2 three-dimensional surfaces by vector-valued biparametric piecewise polynomials, necessary conditions are obtained for three such surfaces to meet with C2 continuity along their common parameter lines, with particular attention to the smoothness at the common vertex. The conditions can not be met by pure bicubic splines, but can be met by increasing the polynomial order to six in the three patches surrounding the common vertex. By way of illustration, a spherical octant is represented by just three patches.
KeywordsSingular Point Common Vertex Common Boundary Sculpture Surface Rectangular Patch
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