Bicubic patches for approximating non-rectangular control-point meshes
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
Explicit error bounds for spline interpolation on a uniform partition
Journal of Approximation Theory
Triangular G1 interpolation by 4-splitting domain triangles
Computer Aided Geometric Design
Approximate continuity for parametric Bézier patches
Proceedings of the 2007 ACM symposium on Solid and physical modeling
High-order approximation of implicit surfaces by G1 triangular spline surfaces
Computer-Aided Design
Local and singularity-free G 1 triangular spline surfaces using a minimum degree scheme
Computing - Geometric Modelling, Dagstuhl 2008
Curvature estimation for meshes based on vertex normal triangles
Computer-Aided Design
G1 Bézier surface generation from given boundary curve network with T-junction
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Constructing G1 Bézier surfaces over a boundary curve network with T-junctions
Computer-Aided Design
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A piecewise quintic interpolation scheme with approximate G1 continuity is presented. For a given triangular mesh of arbitrary topology, one quintic triangular Bézier patch is constructed for each data triangle. Although the resulting surface has G1 continuity at the data vertices, we only require approximate G1 continuity along the patch boundaries so as to lower the patch degree. To reduce the normal discontinuity along boundaries, neighbouring patches are adjusted to have identical normals at the middle point of their common boundary. In most cases, the surfaces generated by this scheme have the same level of visual smoothness compared to an existing sextic G1 continuous interpolation scheme. Further, using the new boundary construction method presented in this paper, better shape quality is observed for sparse data sets than the surfaces of the original G1 continuous scheme, upon which the new scheme is based.