Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Degenerate polynomial patches of degree 4 and 5 used for geometrically smooth interpolation in R3
Computer Aided Geometric Design
A note on degenerate triangular Be´zier patches
Computer Aided Geometric Design
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Degenerate Be´zier patches with continuous curvature
Computer Aided Geometric Design
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Shape characterization of subdivision surfaces: basic principles
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)
Modified subdivision surfaces with continuous curvature
ACM SIGGRAPH 2006 Papers
Direct evaluation of NURBS curves and surfaces on the GPU
Proceedings of the 2007 ACM symposium on Solid and physical modeling
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
ACM Transactions on Graphics (TOG)
ACM SIGGRAPH 2009 papers
C2 splines covering polar configurations
Computer-Aided Design
An introduction to guided and polar surfacing
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
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Surface constructions of polynomial degree (3,3) come in four flavours that complement each other: one pair extends the subdivision paradigm, the other the NURBS patch approach to free-form modeling. The first pair, Catmull-Clark subdivision and Polar subdivision (Catmull, E., Clark, J., 1978. Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design 10, 350-355; Karciauskas, K., Peters, J., 2007. Bicubic polar subdivision. ACM Trans. Graph. 26 (4), 14) generalize bi-cubic subdivision: While Catmull-Clark subdivision is more suitable where few facets join, Polar subdivision nicely models regions where many facets join as when capping extruded features. We show how to easily combine (the meshes of) these two generalizations of bi-cubic spline subdivision. The second pair of surface constructions with a finite number of patches consists of PCCM (Peters, J., 2000. Patching Catmull-Clark meshes. In: SIGGRAPH '00, ACM, pp. 255-258) for layouts where Catmull-Clark would apply and a singularly parameterized NURBS patch for polar layout. A novel analysis shows the latter to yield a C^1 surface with bounded curvatures.