By Horst Nowacki, Justus Heimann, Elefterios Melissaratos, Sven-Holm Zimmermann (auth.), Prof. Dr. Josef Hoschek, Prof. Dr. Panagiotis D. Kaklis (eds.)

Inhalt
Fairing and form conserving of Curves - reviews in CurveFairing - Co-Convexivity maintaining Curve Interpolation - form maintaining Interpolation via Planar Curves - form keeping Interpolation through Curves in 3 Dimensions - A coparative learn of 2 curve fairing equipment in Tribon preliminary layout Fairing Curves and Surfaces Fairing of B-Spline Curves and Surfaces - Declarative Modeling of reasonable shapes: an extra method of curves and surfaces computations form conserving of Curves and Surfaces form conserving interpolation with variable measure polynomial splines Fairing of Surfaces useful features of equity - floor layout in accordance with brightness depth or isophotes-theory and perform - reasonable floor mixing, an outline of business difficulties - Multivariate Splines with Convex-B-Patch regulate Nets are Convex form retaining of Surfaces Parametrizing Wing Surfaces utilizing Partial Differential Equations - Algorithms for convexity keeping interpolation of scattered info - summary schemes for practical shape-preserving interpolation - Tensor Product Spline Interpolation topic to Piecewise Bilinear decrease and higher Bounds - development of Surfaces by means of form keeping Approximation of Contour Data-B-Spline Approximation with power constraints - Curvature approximation with software to floor modelling - Scattered info Approximation with Triangular B-Splines Benchmarks Benchmarking within the zone of Planar form maintaining Interpolation - Benchmark tactics within the Aerea of form - limited Approximation

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An alternative approach is now under investigation with the help of Miss L. Sampoli. In this approach the above non-linear torsion conditions are replaced by sufficient linear conditions and then L)li _li)2 + ~)Ti - Ti)2 is minimised subject to the linearised shape preserving conditions. The resulting curve can then be interrogated and, if necessary, the values li, Ti modified and the process repeated. This iterative procedure is performed automatically by the algorithm. 1, for the user to modify the curve by varying certain parameters.

O. : Fairing Spatial B-Spline Curves. 2. , Hadenfeld J. : Local Energy Fairing of B-Splines Curves. In G. Farin, H. Hagen, and H. ): Computing, Supplementum 10, Springer (1995), 203-212 3. , Automatic Fairing Algorithm for B-Spline Curves, Computer Aided Design, Vol. 22, pp. 121-129, 1990Design, Vol. 22, pp. 121-129,1990 4. Lines Techinical Brief, KCS Fairing Curves and Surfaces Fairing of B-Spline Curves and Surfaces Jan Hadenfeld Technische Hochschule Darmstadt Abstract: We want to give an overview on our methods for fairing B-spline curves [7) and surfaces [16).

The corresponding definition to convexity for a space curve r : [a, b] --+ R3 would be that for any a :=:; 81 < 82 < 83 < 84 :=:; b, [r(82) - r(81), r(83) - r(82), r(84) - r(83)] ~ ° (resp. :=:; 0). Such a curve is called an ascending (resp. descending) coil by Labenski and Piper [7J. Clearly an ascending (resp. descending) coil has non-negative (resp. non-positive) torsion. This definition suggests the following coil condition. ° For any :=:; i :=:; j-3 :=:; N -3, the polygonal arc Ii'" Ij being an ascending (resp.

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