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 keeping of Curves - studies in CurveFairing - Co-Convexivity holding Curve Interpolation - form conserving Interpolation via Planar Curves - form conserving Interpolation via Curves in 3 Dimensions - A coparative learn of 2 curve fairing tools 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 protecting of Curves and Surfaces form keeping interpolation with variable measure polynomial splines Fairing of Surfaces sensible points of equity - floor layout in response to brightness depth or isophotes-theory and perform - reasonable floor mixing, an outline of business difficulties - Multivariate Splines with Convex-B-Patch keep watch over Nets are Convex form holding of Surfaces Parametrizing Wing Surfaces utilizing Partial Differential Equations - Algorithms for convexity retaining interpolation of scattered information - summary schemes for useful shape-preserving interpolation - Tensor Product Spline Interpolation topic to Piecewise Bilinear decrease and top 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 facts Approximation with Triangular B-Splines Benchmarks Benchmarking within the sector of Planar form conserving Interpolation - Benchmark strategies within the Aerea of form - limited Approximation
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Extra info for Advanced Course on FAIRSHAPE
Sample text
We say a curve r : [a, b) (resp. negatively) convex if for any a :::; 81 < 82 < 83 :::; b, -t R2 is positively We say r is locally positively (resp. negatively) convex at 8 in [a, b) if r is positively (resp. negatively) convex on some neighbourhood of 8. If r is not locally convex at 8 (with either sign), we say r has an inflection at 8. We say a scheme is local convexity preserving (1. c. ) if the following hold. For any 0 :::; i :::; j - 2 :::; N - 2, the polygonal arc Ii . . I j being positively (resp.
4] Goodman, T. N. , Ong, B. : Shape Preserving Interpolation by G 2 Space Curves. University of Dundee Report AA/964 (1996). [5] Kaklis, P. , Sapidis, N. : Convexity-Preserving Interpolatory Parametric Splines of Non-Uniform Degree. Computer Aided Geometric Design 12 (1995), 1-26. [6] Kaklis, P. , Karavelas, M. : Shape-Preserving Interpolation in R3. Submitted to Computer Aided Geometric Design. : Coils. To appear in Computer Aided Geometric Design. Authors Prof. Dr. T. Goodman University of Dundee Dept.
L. ): Mathematical Methods in CAGD, Academic Press (1989), 539-548. [14] Schweikert, D. : Interpolatory Tension Splines with Automatic Selection of Tension Factors. J. Math. Phys. 45 (1966), 312-317. Shape Preserving Interpolation by Curves In Three Dimensions Tim Goodman l , Boon-Hua Ong 2 1 2 University of Dundee Universiti Sains Malaysia Abstract: Requirements for shape preserving interpolation by space curves are discussed and earlier work is mentioned. Then we describe two new local schemes using rational cubics.
