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Discrete Coons patches. (English) Zbl 0997.65033

Summary: We investigate surfaces which interpolate given boundary curves. We show that the discrete bilinearly blended Coons patch can be defined as the solution of a linear system. With the goal of producing better shape than the Coons patch, this idea is generalized, resulting in a new method based on a blend of variational principles. We show that no single blend of variational principles can produce “good” shape for all boundary curve geometries. We also discuss triangular Coons patches and point out the connections to the rectangular case.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D05 Numerical interpolation
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