Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Smooth mesh interpolation with cubic patches
Computer-Aided Design
Local surface interpolation with Be´zier patches: errata and improvements
Computer Aided Geometric Design
Surface approximation using geometric Hermite patches
Surface approximation using geometric Hermite patches
A G1 triangular spline surface of arbitrary topological type
Computer Aided Geometric Design
Cubic precision Clough-Tocher interpolation
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Polynomial Surfaces Interpolating Arbitrary Triangulations
IEEE Transactions on Visualization and Computer Graphics
Parametric triangular Bézier surface interpolation with approximate continuity
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Bicubic G1 interpolation of irregular quad meshes using a 4-split
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
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In this paper, we present a piecewise cubic, parametric surface scheme to interpolate positions and normals on a triangulated data set. For each data triangle, we fit three triangular cubic patches in a Clough-Tocher like arrangement. However, while we construct the micro-patches to meet each other C1, we only require approximate G1 continuity across macro-patches boundaries. To control the normal discontinuity on the macro-patch boundaries, neighbouring patches are constructed to interpolate the position and normals at the ends of their common boundary, as well as to have equal normals at additional points on the boundary. The resulting scheme constructs patches with similar shape to the quartic Shirman-Séquin construction, and has better shape than Peters' G1 cubic scheme on near singular data.