A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Surface interpolation on irregular networks with normal conditions
Computer Aided Geometric Design
The NURBS book
Curve interpolation in recursively generated B-spline surfaces over arbitrary topology
Computer Aided Geometric Design
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Interpolating nets of curves by smooth subdivision surfaces
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Combined subdivision schemes for the design of surfaces satisfying boundary conditions
Computer Aided Geometric Design
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Recursive subdivision of polygonal complexes and its applications in computer-aided geometric design
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Dynamic Catmull-Clark Subdivision Surfaces
IEEE Transactions on Visualization and Computer Graphics
Lofting curve networks using subdivision surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Generating subdivision surfaces from profile curves
Computer-Aided Design
Loop subdivision surfaces interpolating B-spline curves
Computer-Aided Design
Cross-sectional design with curvature constraints
Computer-Aided Design
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In a recent paper (Ma and Wang, 2009), it was found that the limit curve corresponding to a regular edge path of a Loop subdivision surface reduces to a uniform cubic B-spline curve (CBSC) under a degeneration condition. One can thus define a Loop subdivision surface interpolating a set of input CBSCs with various topological structures that can be mapped to regular edge paths of the underlying surface. This paper presents a new solution for defining a Loop subdivision surface interpolating an arbitrary number of CBSCs meeting at an extraordinary point. The solution is based on the concept of a polygonal complex method previously used for Catmull-Clark surface interpolation and is built upon an extended set of constraints of the control vertices under which local edge paths meeting at an extraordinary point reduces to a set of endpoint interpolating CBSCs. As a result, the local subdivision rules near an extraordinary point can be modified such that the resulting Loop subdivision surface exactly interpolates a set of input endpoint interpolating CBSCs meeting at the extraordinary point. If the given endpoint interpolating CBSCs have a common tangent plane at the meeting point, the resulting Loop surface will be G^1 continuous. The proposed method of curve interpolation provides an important alternative solution in curve-based subdivision surface design.