Piecewise surface flattening for non-distorted texture mapping
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
An Operator Calculus for Surface and Volume Modeling
IEEE Computer Graphics and Applications
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
Construction of Bézier surface patches with Bézier curves as geodesic boundaries
Computer-Aided Design
Construction of Bézier surface patches with Bézier curves as geodesic boundaries
Computer-Aided 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
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Given two pairs of regular space curves r"1(u), r"3(u) and r"2(v), r"4(v) that define a curvilinear rectangle, we consider the problem of constructing a C^2 surface patch R(u,v) for which these four boundary curves correspond to geodesics of the surface. The possibility of constructing such a surface patch is shown to depend on the given boundary curves satisfying two types of consistency constraints. The first constraint is global in nature, and is concerned with compatibility of the variation of the principal normals along the four curves with the normal to an oriented surface. The second constraint is a local differential condition, relating the curvatures and torsions of the curves meeting at each of the four patch corners to the angle between those curves. For curves satisfying these constraints, the surface patch is constructed using a bicubically-blended Coons interpolation process.