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An interpolatory subdivision algorithm for surfaces over arbitrary triangulations
In this paper, an interpolatory subdivision algorithm for surfaces over ar-bitrary triangulations is introduced and its convergence properties over nonuni-form triangulations studied. The so called Butterfly Scheme (interpolatory) is a special case of this algorithm. In our analysis of the algorithm over uniform triangulations, a matrix approach is employed and the idea, of "Cross Differ-ence of Directional Divided Difference" analysis is presented. This method is a generalization of the technique used by Dyn, Gregory and Levin etc. to analyse univariate subdivision algorithms. While for nonuniform data, an extraordi-nary point analysis is introduced and the local subdivision matrix analysis is presented. It is proved that the algorithm produces smooth surfaces over ar-bitrary triangular networks provided the shape parameters are kept within an appropriate range
Implementation of MPEG-4s Subdivision Surfaces Tools
This work is about the implementation of a MPEG-4 decoder for subdivision surfaces, which are powerful 3D paradigms allowing to compactly represent piecewise smooth surfaces. This study will take place in the framework of MPEG-4 AFX, the extension of the MPEG-4 standard including the subdivision surfaces. This document will introduce, with some details, the theory of subdivision surfaces in the two forms present in MPEG-4: plain and detailed/ wavelet subdivision surfaces. It will particularly concentrate on wavelet subdivision surfaces, which permit progressive 3D mesh compression
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A 10-point interpolatory recursive subdivision algorithm for the generation of parametric surfaces
In this paper, an interpolatory subdivision algorithm for surfaces over arbitrary triangulations is introduced and its properties over uniform triangulations studied. The Butterfly Scheme, which is introduced by Dyn, Gregory and Levin is a special case of this algorithm. In our analysis, the matrix approach is employed and the idea of "Cross Difference of Directional Divided Difference" analysis is presented. This method is a generalization of the technique used by Dyn, Gregory and Levin etc. to analyse univariate subdivision algorithms. It is proved that the algorithm produces smooth surfaces provided the shape parameters are kept within an appropriate range
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Uniform subdivision algorithms for curves and surfaces
A convergence analysis for studying the continuity and differentiability of limit curves generated by uniform subdivision algorithms is presented. The analysis is based on the study of corresponding difference and divided difference algorithms. The alternative process of "integrating" the algorithms is considered. A specific example of a 4-point interpolatory curve algorithm is described and its generalization to a surface algorithm defined over a subdivision of a regular triangular partition is illustrated
On subdivision invariant actions for random surfaces
We consider a subdivision invariant action for dynamically triangulated
random surfaces that was recently proposed (R.V. Ambartzumian et. al., Phys.
Lett. B 275 (1992) 99) and show that it is unphysical: The grand canonical
partition function is infinite for all values of the coupling constants. We
conjecture that adding the area action to the action of Ambartzumian et. al.
leads to a well-behaved theory.Comment: 7 pages, Latex, RH-08-92 and YITP/U-92-3
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