Cubic recursive division with bounded curvature
Curves and surfaces
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Geometric Modelling, Dagstuhl, Germany, 1996
Improved Triangular Subdivision Schemes
CGI '98 Proceedings of the Computer Graphics International 1998
Subdivision scheme tuning around extraordinary vertices
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
Ternary subdivision for quadrilateral meshes
Computer Aided Geometric Design
ACM Transactions on Graphics (TOG)
On the curvature of guided surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
Local energy-optimizing subdivision algorithms
Computer Aided Geometric Design
Pairs of bi-cubic surface constructions supporting polar connectivity
Computer Aided Geometric Design
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM SIGGRAPH 2009 papers
Tuning subdivision algorithms using constrained energy optimization
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Modeling smooth shape using subdivision on differential coordinates
Computer-Aided Design
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
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In this paper the problem of curvature behavior around extraordinary points of a Loop subdivision surface is addressed. A variant of Loop's algorithm with small stencils is used that generates surfaces with bounded curvature and prescribed elliptic or hyperbolic behavior. We present two different techniques that avoid the occurrence of hybrid configurations, so that an elliptic or hyperbolic shape can be guaranteed. The first technique uses a symmetric modification of the initial control-net to avoid hybrid shapes in the vicinity of an extraordinary point. To keep the difference between the original and the modified mesh as small as possible the changes are formulated as correction stencils and spread to a finite number of subdivision steps. The second technique is based on local optimization in the frequency domain. It provides more degrees of freedom and so more control over the global shape.