\(C^{1}\) modeling with A-patches from rational trivariate functions. (English) Zbl 0971.68170
Summary: We approximate a manifold triangulation in \(R^{3}\) using smooth implicit algebraic surface patches, which we call A-patches. Here each A-patch is a real iso-contour of a trivariate rational function defined within a tetrahedron. The rational trivariate function provides increased degrees of freedom so that the number of surface patches needed for free-form shape modeling is significantly reduced compared to earlier similar approaches. Furthermore, the surface patches have quadratic precision, that is they exactly recover quadratic surfaces. We give conditions under which a \(C^{1}\) smooth and single sheeted surface patch is isolated from the multiple sheets.
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
Software:
PrismReferences:
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