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Spline approximation of surfaces of explicit type containing cracks. (Approximation spline de surfaces de type explicite comportant des failles.) (French) Zbl 0886.65008

The presence of fault lines in geological and geographical profiles suggests that the representation of piecewise differentiable surfaces is an important one in computer graphics. The authors present a general theoretical framework in terms of Sobolev spaces but for practical purposes concretely work with triangulations where the jumps are restricted to lie in edges of the triangulations and the approximation on the rest of the domain is not more than \(C^1\). On the interior of the elements of triangulation, splines exist that can be obtained from their minimal property and convergence is shown for refinement of the mesh. Pictures are given from a program developed along the lines exhibited (but whose details are not included) that show that the error bounds developed are valid but within these bounds the errors vary wildly, as is to be expected in this type of problem.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D10 Numerical smoothing, curve fitting
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References:

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