Computer Aided Geometric Design
Modeling surfaces of arbitrary topology using manifolds
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Modelling surfaces from planar irregular meshes
Computer Aided Geometric Design
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
C2 free-form surfaces of degree (3,5)
Computer Aided Geometric Design
Improved Triangular Subdivision Schemes
CGI '98 Proceedings of the Computer Graphics International 1998
A simple manifold-based construction of surfaces of arbitrary smoothness
ACM SIGGRAPH 2004 Papers
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
On C2 triangle/quad subdivision
ACM Transactions on Graphics (TOG)
Second order smoothness over extraordinary vertices
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
C2 subdivision over triangulations with one extraordinary point
Computer Aided Geometric Design
Modified subdivision surfaces with continuous curvature
ACM SIGGRAPH 2006 Papers
Jet subdivision schemes on the k-regular complex
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
Concentric tessellation maps and curvature continuous guided surfaces
Computer Aided Geometric Design
ACM Transactions on Graphics (TOG)
On the curvature of guided surfaces
Computer Aided Geometric Design
Pairs of bi-cubic surface constructions supporting polar connectivity
Computer Aided Geometric Design
Computer Aided Geometric Design
ACM SIGGRAPH 2009 papers
Gn blending multiple surfaces in polar coordinates
Computer-Aided Design
Metric-aware processing of spherical imagery
ACM SIGGRAPH Asia 2010 papers
G2 B-spline interpolation to a closed mesh
Computer-Aided Design
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
A new interpolation subdivision scheme for triangle/quad mesh
Graphical Models
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We describe a subdivision scheme that acts on control nodes that each carry a vector of values. Each vector defines partial derivatives, referred to as jets in the following and subdivision computes new jets from old jets. By default, the jets are automatically initialized from a design mesh. While the approach applies more generally, we consider here only a restricted class of design meshes, consisting of extraordinary nodes surrounded by triangles and otherwise quadrilaterals with interior nodes of valence four. This polar mesh structure is appropriate for surfaces with the combinatorial structure of objects of revolution and for high valences. The resulting surfaces are curvature continuous with good curvature distribution near extraordinary points. Near extraordinary points the surfaces are piecewise polynomial of degree (6, 5), away they are standard bicubic splines.