A matrix approach to the analysis of recursively generated B-spline surfaces
Computer-Aided Design
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Computer Aided Geometric Design
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: case studies
Computer Aided Geometric Design
On C2 triangle/quad subdivision
ACM Transactions on Graphics (TOG)
C2 subdivision over triangulations with one extraordinary point
Computer Aided Geometric Design
Jet subdivision schemes on the k-regular complex
Computer Aided Geometric Design
Concentric tessellation maps and curvature continuous guided surfaces
Computer Aided Geometric Design
Loop subdivision with curvature control
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Computing curvature bounds for bounded curvature subdivision
Computer Aided Geometric Design
ACM SIGGRAPH 2009 papers
Finite Curvature Continuous Polar Patchworks
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
An introduction to guided and polar surfacing
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
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Following [Karciauskas, K., Peters, J., 2007. Concentric tessellation maps and curvature continuous guided surfaces. Computer Aided Geometric Design 24 (2) 99-111], we analyze surfaces arising as an infinite sequence of guided C^2 surface rings. However, here we focus on constructions of a too low degree to be curvature continuous also at the extraordinary point. To characterize shape and smoothness of such surfaces, we track a sequence of quadratic functions anchored in a fixed coordinate system. These 'anchored osculating quadratics' are easily computed in terms of determinants of surface derivatives. Convergence of the sequence of quadratics certifies curvature continuity. Otherwise, the range of the curvatures of the limit quadratics gives a measure of deviation from curvature continuity.