G1 interpolation of generally unrestricted cubic Bézier curves
Computer Aided Geometric Design - Special issue: Topics in CAGD
Local smooth surface interpolation: a classification
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
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
Local surface interpolation with Bézier patches
Computer Aided Geometric Design
Existence conditions for Coons patches interpolating geodesic boundary curves
Computer Aided Geometric Design
Construction and smoothing of triangular Coons patches with geodesic boundary curves
Computer Aided Geometric Design
Construction of rational surface patches bounded by lines of curvature
Computer Aided Geometric Design
Constructing PDE-based surfaces bounded by geodesics or lines of curvature
Computers & Mathematics with Applications
Rotation-minimizing osculating frames
Computer Aided Geometric Design
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Given four polynomial or rational Bezier curves defining a curvilinear rectangle, we consider the problem of constructing polynomial or rational tensor-product Bezier patches bounded by these curves, such that they are geodesics of the constructed surface. The existence conditions and interpolation scheme, developed in a general context in earlier studies, are adapted herein to ensure that the geodesic-bounded surface patches are compatible with the usual polynomial/rational representation schemes of CAD systems. Precise conditions for four Bezier curves to constitute geodesic boundaries of a polynomial or rational surface patch are identified, and an interpolation scheme for the construction of such surfaces is presented when these conditions are satisfied. The method is illustrated with several computed examples.