Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Constrained design of polynomial surfaces from geodesic curves
Computer-Aided Design
Cubic polynomial patches through geodesics
Computer-Aided Design
Surface reconstruction via geodesic interpolation
Computer-Aided Design
Existence conditions for Coons patches interpolating geodesic boundary curves
Computer Aided Geometric Design
Construction of Bézier surface patches with Bézier curves as geodesic boundaries
Computer-Aided Design
Constructing PDE-based surfaces bounded by geodesics or lines of curvature
Computers & Mathematics with Applications
| Hi-index | 0.00 |
Given three regular space curves r"1(t), r"2(t), r"3(t) for t@?[0,1] that define a curvilinear triangle, we consider the problem of constructing a triangular surface patch R(u"1,u"2,u"3) bounded by these three curves, such that they are geodesics of the constructed surface. Results from a prior study (Farouki et al., 2009a) concerned with tensor-product patches are adapted to identify constraints on the given curves for the existence of such geodesic-bounded triangular surface patches. For curves satisfying these conditions, the patch is constructed by means of a cubically-blended triangular Coons interpolation scheme. A formulation of thin-plate spline energy in terms of barycentric coordinates with respect to a general domain triangle is also derived, and used to optimize the smoothness of the geodesic-bounded triangular surface patches.