Book ChapterDOI
Cubic recursive division with bounded curvature
Malcolm A. Sabin
- pp 411-414
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This paper describes a formulation which gives bounded non-zero curvature and close to curvature continuity and although it was claimed at the conference that this formulation was C2, this is not (quite) true.Abstract:
Previous cubic recursive division schemes have had either zero or unbounded curvature at the singular points. This paper describes a formulation which gives bounded non-zero curvature and close to curvature continuity. Although it was claimed at the conference that this formulation was C2, this is not (quite) true.read more
Citations
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Book
Subdivision Methods for Geometric Design: A Constructive Approach
Joe Warren,Henrik Weimer +1 more
TL;DR: Rich in theory, analysis, and practical information, this book is the complete resource for subdivision methods, providing all that is needed to understand how subdivision works its magic, and how to make that magic work.
Proceedings ArticleDOI
Non-uniform recursive subdivision surfaces
TL;DR: Rules are developed that generalize non-uniform tensor product Bspline surfaces to arbitrary topologies, which allows the natural introduction of features such as cusps, creases, and darts, while elsewhere maintaining the same order of continuity as their uniform counterparts.
Geometric Modeling Based on Polygonal Meshes
Leif Kobbelt,Stephan Bischoff,Mario Botsch,Kolja Kähler,Christian Rössl,Robert Schneider,Jens Vorsatz +6 more
TL;DR: This course discusses the whole geometry processing pipeline based on triangle meshes, and introduces general concepts of surface representations and point out the advantageous properties of triangle meshes in order to present efficient data structures for their implementation.
Proceedings ArticleDOI
Interpolating nets of curves by smooth subdivision surfaces
TL;DR: The algorithm is simple and easy to implement, and is based on a variant of the famous Catmull-Clark subdivision scheme, which can exactly interpolate a net of curves given in any parametric representation.
Journal ArticleDOI
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
TL;DR: In this paper, a subdivision framework for adding extraordinary vertices to NURBSs of arbitrarily high degree is presented, and the surfaces can represent any odd degree nurbs patch exactly.
References
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Journal ArticleDOI
Recursively generated B-spline surfaces on arbitrary topological meshes
Ed Catmull,J. Clark +1 more
TL;DR: The method is presented as a generalization of a recursive bicubic B-spline patch subdivision algorithm, which generates surfaces that approximate points lying-on a mesh of arbitrary topology except at a small number of points, called extraordinary points.
Journal ArticleDOI
Behaviour of recursive division surfaces near extraordinary points
D. Doo,Malcolm A. Sabin +1 more
TL;DR: In this article, the behaviour of the limits surface defined by a recursive division construction can be analyzed in terms of the eigenvalues of a set of matrices, and suggestions for the further improvement of the method are made.
Journal ArticleDOI
Design of an n -sided surface patch from Hermite boundary data
D. J. T. Storry,Alan Ball +1 more
TL;DR: It is demonstrated that a B-spline subdivision patch can be fitted into a general n-sided area of a bicubic surface with at least tangent plane continuity on the boundary.
Dissertation
B-spline surfaces over an irregular topology by recursive subdivision
TL;DR: The technique of recursive subdivision can be visualised, loosely, as successively chopping off the corners of a polyhedron to make it beelineless pointed as mentioned in this paper, and repeated application of the subdivision results in progressively finer meshes tending in the limit to a surface.