Surfaces with Arbitrary Topology
The surfaces that we have met so far are best suited for shapes that are the image of some part of the plane—of a rectangle in the case of B-spline or Bézier surfaces, of a triangulated region in the case of composite Bézier triangles. This limits the topology of these surfaces; for example, it is not possible to construct even a sphere without introducing degenerate patches while using a C1 map of a part of the plane. Even shapes that have the topology of a planar region may be too complex to model with one tensor product surface; just imagine modeling a glove that way. The complexity issue may be tackled using the approach of hierarchical B-spline surfaces as proposed by Forsey and Bartels [245]. But even ...
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