Bicubic patches for approximating non-rectangular control-point meshes
Computer Aided Geometric Design
G1 interpolation of generally unrestricted cubic Bézier curves
Computer Aided Geometric Design - Special issue: Topics in CAGD
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Filling polygonal holes with rectangular patches
Theory and practice of geometric modeling
Generalized B-spline surfaces of arbitrary topology
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A G1 triangular spline surface of arbitrary topological type
Computer Aided Geometric Design
SIAM Journal on Numerical Analysis
Computer Aided Geometric Design
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
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
C2 free-form surfaces of degree (3,5)
Computer Aided Geometric Design
Design of solids with free-form surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Approximate continuity for parametric Bézier patches
Proceedings of the 2007 ACM symposium on Solid and physical modeling
On the complexity of smooth spline surfaces from quad meshes
Computer Aided Geometric Design
Triangular bubble spline surfaces
Computer-Aided Design
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We present a piecewise bi-cubic parametric G1 spline surface interpolating the vertices of any irregular quad mesh of arbitrary topological type. While tensor product surfaces need a chess boarder parameterization they are not well suited to model surfaces of arbitrary topology without introducing singularities. Our spline surface consists of tensor product patches, but they can be assembled with G1-continuity to model any non-tensor-product configuration. At common patch vertices an arbitrary number of patches can meet. The parametric domain is built by 4-splitting one unit square for each input quadrangular face. This key idea of our method enables to define a very low degree surface, that interpolates the input vertices and results from an explicit and local procedure : no global linear system has to be solved.