Journal ArticleDOI
Family of shape preserving fractal-like bézier curves
TLDR
This work extends the Overveld scheme toth degree curves, and deduce the condition for curvature continuity and convex hull property, and finds the conditions for positive preserving fractal-like Bézier curves in the proposed subdivision matrices.Abstract:
Subdivision schemes generate self-similar curves and surfaces for which it has a familiar connection between fractal curves and surfaces generated by iterated function systems (IFS). Overveld [Comp...read more
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Journal Article
Fractal Image Compression
TL;DR: A brief review of basic fractal image compression algorithm, adaptive partitioning methods, complexity reduction methods, alternative choice of affine transformation and so on are discussed.
References
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Journal ArticleDOI
A survey of curve and surface methods in CAGD
TL;DR: It is suggested that B6zier curves should be considered as a single type of curve, but the design of these curves should not be confused with other types of curves, which are known to have different properties.
Journal ArticleDOI
A 4-point interpolatory subdivision scheme for curve design
TL;DR: A 4-point interpolatory subdivision scheme with a tension parameter is analysed and it is shown that for a certain range of the tension parameter the resulting curve is C^1.
Journal ArticleDOI
The Bernstein polynomial basis: A centennial retrospective
TL;DR: One hundred years after the introduction of the Bernstein polynomial basis, this survey surveys the historical development and current state of theory, algorithms, and applications associated with this remarkable method of representing polynomials over finite domains.
Journal ArticleDOI
Subdivision schemes in geometric modelling
Nira Dyn,David Levin +1 more
TL;DR: Different representations of subdivision schemes, and several tools for the analysis of convergence, smoothness and approximation order are discussed, followed by explanatory examples.
Journal ArticleDOI
Analysis of uniform binary subdivision schemes for curve design
TL;DR: In this article, the convergence of the control polygons to aC° curve is analyzed in terms of the convergence to zero of a derived scheme for the differences of the differences.
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