Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
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
Modelling surfaces from planar irregular meshes
Computer Aided Geometric Design
C2 free-form surfaces of degree (3,5)
Computer Aided Geometric Design
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
Second order smoothness over extraordinary vertices
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Modified subdivision surfaces with continuous curvature
ACM SIGGRAPH 2006 Papers
Concentric tessellation maps and curvature continuous guided surfaces
Computer Aided Geometric Design
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Guided C2 spline surfaces with V-shaped tessellation
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Finite Curvature Continuous Polar Patchworks
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Efficient substitutes for subdivision surfaces
ACM SIGGRAPH 2009 Courses
Guided C2 spline surfaces with V-shaped tessellation
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
C2 splines covering polar configurations
Computer-Aided Design
Triangular bubble spline surfaces
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
Constraints on curve networks suitable for G2 interpolation
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Curve networks compatible with G2 surfacing
Computer Aided Geometric Design
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
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We separate the conceptual design and the representation of high quality surfaces by prescribing local shape via guide surfaces and then sampling these guides with a finite number of tensor-product patches. The paper develops a family of algorithms that allow trading polynomial degree for smoothness near the extraordinary points where more or fewer than four tensor-product patches meet. A key contribution are rules for a capping of a multi-sided hole by a small number of polynomial patches. The construction of highest quality creates first a G^1 cap of patches of degree (6,6) and then perturbs it to yield an exact G^2 cap of degree (8,8). Since this perturbation is so small that its effect is typically not perceptible even in curvature display, the unperturbed surface of degree (6,6) is an excellent alternative. Reducing the degree of the rings to (5,5), respectively (4,4), by choice of a different parameterization, increases the number of G^1 transition curves within the cap but does not alter the shape appreciably.