Geometric surface patches without twist constraints
Computer Aided Geometric Design
Bicubic patches for approximating non-rectangular control-point meshes
Computer Aided Geometric Design
Automatic smoothing with geometric surface patches
Computer Aided Geometric Design
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Curvature continuous triangular interpolants
Mathematical methods in computer aided geometric design
On the G1 continuity of piecewise Be´zier surfaces: a review with new results
Computer-Aided Design - Special Issue: Be´zier Techniques
Smoothing polyhedra using implicit algebraic splines
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
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
Degenerate polynomial patches of degree 4 and 5 used for geometrically smooth interpolation in R3
Computer Aided Geometric Design
Triangular G1 interpolation by 4-splitting domain triangles
Computer Aided Geometric Design
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Simple local interpolation of surfaces using normal vectors
Computer Aided Geometric Design
Hierarchical triangular splines
ACM Transactions on Graphics (TOG)
Approximate continuity for parametric Bézier patches
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Point-normal interpolation schemes reproducing spheres, cylinders and cones
Computer Aided Geometric Design
Generating Sharp Features on Non-regular Triangular Meshes
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Detail preserving deformation of B-spline surfaces with volume constraint
Computer Aided Geometric Design
On surface reconstruction: A priority driven approach
Computer-Aided Design
Simple local interpolation of surfaces using normal vectors
Computer Aided Geometric Design
Multi-degree reduction of triangular Bézier surfaces with boundary constraints
Computer-Aided Design
Surface interpolation of meshes by geometric subdivision
Computer-Aided Design
Smooth image surface approximation by piecewise cubic polynomials
CIARP'07 Proceedings of the Congress on pattern recognition 12th Iberoamerican conference on Progress in pattern recognition, image analysis and applications
G2 B-spline interpolation to a closed mesh
Computer-Aided Design
A C1 globally interpolatory spline of arbitrary topology
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
The technology of stereo photography and virtual reality in research of virtual museum
Edutainment'06 Proceedings of the First international conference on Technologies for E-Learning and Digital Entertainment
Curvature tensor computation by piecewise surface interpolation
Computer-Aided Design
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Triangular Bézier patches are an important tool for defining smooth surfaces over arbitrary triangular meshes. The previously introduced 4-split method interpolates the vertices of a 2-manifold triangle mesh by a set of tangent plane continuous triangular Bézier patches of degree five. The resulting surface has an explicit closed form representation and is defined locally. In this paper, we introduce a new method for visually smooth interpolation of arbitrary triangle meshes based on a regular 4-split of the domain triangles. Ensuring tangent plane continuity of the surface is not enough for producing an overall fair shape. Interpolation of irregular control-polygons, be that in 1D or in 2D, often yields unwanted undulations. Note that this undulation problem is not particular to parametric interpolation, but also occurs with interpolatory subdivision surfaces. Our new method avoids unwanted undulations by relaxing the constraint of the first derivatives at the input mesh vertices: The tangent directions of the boundary curves at the mesh vertices are now completely free. Irregular triangulations can be handled much better in the sense that unwanted undulations due to flat triangles in the mesh are now avoided.