By Pierre-Jean Laurent; Alain Le Mehaute

ISBN-10: 0124386601

ISBN-13: 9780124386600

There's a good deal of present curiosity in mathematical equipment for representing and manipulating complex curves and surfaces in a electronic desktop surroundings. This edited paintings is a set of either brief survey papers and lengthy study papers, addressing a couple of issues very important to improvement within the box. between those are 3-D reconstruction, skinny plate splines, geometric continuity, photograph compression, and radial capabilities. The survey papers specialize in a number of rather lively subareas of approximation concept, together with tomography, wavelets, limited approximation, multivariate splines, approximation of pictures, and floor compression

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**Extra resources for Curves and Surfaces**

**Example text**

0 show that non-intersecting hemispheres are recovered with less noise than the input data (there is one exception), and that intersecting spheres 48 Terrance E. Boult and Mark Lerner can be recovered better at larger angles. 58 radians. 15 separation. Figure 1. Spheres and Errors. Energy-Based Segmentation 49 The second experiment (Fig. 001] noise. The figure shows a side view of this surface (upper right). Seed surfaces are located with the random-walk technique and the segmenter recovers three non-intersecting surfaces.

Throughout this paper we assume that the function F is monotone increasing in each of its variables, so that reducing any individual ûrt-(T) results in a reduction of a(T). Some typical examples of such criteria (see [3] for details and references) include: 1) a(T) = J2tLi <*i(T)> w n e r e ai(T) is t n e length of the i-th edge; 2) α(Γ) = Σ ϋ ι αι{Τ), where α,·(Τ) is the area of the i-th triangular facet. §3. Locally Optimal Triangulations and Edge Swapping Suppose we are given data points as in Section 1 and an associated triangulation T.

Spheres and Errors. Energy-Based Segmentation 49 The second experiment (Fig. 001] noise. The figure shows a side view of this surface (upper right). Seed surfaces are located with the random-walk technique and the segmenter recovers three non-intersecting surfaces. These three recovered surfaces are shown (left and below the unsegmented data). Figure 2. Wave Surfaces. 05). 20. The figure shows a needle-plot of the unsegmented data (upper right), as well as the five sets of recovered data points.

### Curves and Surfaces by Pierre-Jean Laurent; Alain Le Mehaute

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