Geometric continuous patch complexes
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
Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIAM Journal on Numerical Analysis
The NURBS book
Fitting smooth surfaces to dense polygon meshes
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Stability Conditions for Free Form Surfaces
CGI '98 Proceedings of the Computer Graphics International 1998
G1 continuity conditions of adjacent NURBS surfaces
Computer Aided Geometric Design
Adaptive patch-based mesh fitting for reverse engineering
Computer-Aided Design
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Recently, there have been improvements on reconstruction of smooth B-spline surfaces of arbitrary topological type, but the most important problem of smoothly stitching B-spline surface patches (the continuity problem of B-spline surface patches) in surface reconstruction has not been solved in an effective way. Therefore, the motivation of this paper is to study how to better improve and control the continuity between adjacent B-spline surfaces.In this paper, we present a local scheme of constructing convergent G1 smooth bicubic B-spline surface patches with single interior knots over a given arbitrary quad partition of a polygonal model. Unlike previous work which only produces (non-controllable) toleranced G1 smooth B-spline surfaces, our algorithm generates convergent G1 smooth B-spline surfaces, which means the continuity of the B-spline surfaces tends to G1 smoothness as the number of control points increases. The most important feature of our algorithm is, in the meaning of convergent approximation order, the ability to control the continuity of B-spline surfaces within the given tolerance and capture the geometric details presented by the given data points.