Computer Aided Geometric Design - Special issue: Topics in CAGD
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Computer Aided Geometric Design
Interpolating nets of curves by smooth subdivision surfaces
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Combined subdivision schemes for the design of surfaces satisfying boundary conditions
Computer Aided Geometric Design
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Stationary Subdivision
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Geometric Modelling, Dagstuhl, Germany, 1996
Polynomial generation and quasi-interlpolation in stationary non-uniform subdivision
Computer Aided Geometric Design
Analysis and application of subdivision surfaces
Analysis and application of subdivision surfaces
On C2 triangle/quad subdivision
ACM Transactions on Graphics (TOG)
C2 subdivision over triangulations with one extraordinary point
Computer Aided Geometric Design
Polynomial-based non-uniform interpolatory subdivision with features control
Journal of Computational and Applied Mathematics
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We survey a number of related methods, which have been published by the author and collaborators, in the field of subdivision schemes for curves and surfaces. The theory presented in these works relies mainly on the notion of polynomial reproduction, i.e. the ability of a scheme to reproduce all polynomials up to a certain degree as limit functions. We demonstrate that the study of polynomial reproduction is central to smoothness analysis and to approximation. In particular, we show how to exploit polynomial reproduction in the context of piecewise-uniform stationary subdivision. The applications include boundary treatments for subdivision surfaces, interpolation of curves by surfaces, subdivision stencils around extraordinary vertices (construction of C2 schemes), as well as schemes that involve different kinds of grids (triangular / quadrilateral).