By Horst Nowacki, Justus Heimann, Elefterios Melissaratos, Sven-Holm Zimmermann (auth.), Prof. Dr. Josef Hoschek, Prof. Dr. Panagiotis D. Kaklis (eds.)
Fairing and form holding of Curves - reviews in CurveFairing - Co-Convexivity holding Curve Interpolation - form conserving Interpolation by way of Planar Curves - form keeping Interpolation through 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 maintaining of Curves and Surfaces form protecting interpolation with variable measure polynomial splines Fairing of Surfaces sensible facets of equity - floor layout according to brightness depth or isophotes-theory and perform - reasonable floor mixing, an summary of commercial difficulties - Multivariate Splines with Convex-B-Patch keep watch over Nets are Convex form conserving of Surfaces Parametrizing Wing Surfaces utilizing Partial Differential Equations - Algorithms for convexity holding interpolation of scattered info - summary schemes for practical shape-preserving interpolation - Tensor Product Spline Interpolation topic to Piecewise Bilinear decrease and top Bounds - building of Surfaces through form holding Approximation of Contour Data-B-Spline Approximation with strength constraints - Curvature approximation with software to floor modelling - Scattered information Approximation with Triangular B-Splines Benchmarks Benchmarking within the zone of Planar form maintaining Interpolation - Benchmark methods within the Aerea of form - limited Approximation
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Extra resources for Advanced Course on FAIRSHAPE
In  is considered the following torsion condition for an interplation scheme, where we write Li = IHI - Ii, i = 0, ... , N - 1. ° ° For 1 :=:; i :=:; N - 2, if [Li- 1 , Li, LHl] > (resp. < 0, = 0), then the torsion of r is> (resp. < 0, = 0) on (ti' ti+l). We note that the case '= 0' requires that when Ii-I, .. ,IH2 are coplanar, then the curve r on [ti, ti+l] lies in the same plane. In  they only require this to be satisfied up to a given tolerance. LHd < 0, then the torsion of the curve r changes sign at l;.
X,>'y), >. > 0. x,y), all >. > 0, imply invariance under all linear transformations. If, in addition, we impose invariance under all shifts, then we have invariance under all affine transformations. Many schemes are affine invariant but this may not be appropriate in all situations as we now illustrate. Suppose that a scheme is comonotone in a direction v and is also rotation invariant. It is then clearly comonotone in all directions. IH 1. " IN. If a scheme is 1. m. p. in some direction and rotation invariant, then it is also 1.
Properties of Splines in Tension. J. Approx. Theory 17 (1976), 86-96.  Sapidis, N. , Kaklis, P. : A Hybrid Method for Shape-Preserving Interpolation with Curvature-Continuous Quintic Splines. Compo Suppl. 10 (1995). : On Global GC 2 Convexity Preserving Interpolation of Planar Curves by Piecewise Bezier Polynomials. In T. Lyche and L. L. ): Mathematical Methods in CAGD, Academic Press (1989), 539-548.  Schweikert, D. : Interpolatory Tension Splines with Automatic Selection of Tension Factors.
Advanced Course on FAIRSHAPE by Horst Nowacki, Justus Heimann, Elefterios Melissaratos, Sven-Holm Zimmermann (auth.), Prof. Dr. Josef Hoschek, Prof. Dr. Panagiotis D. Kaklis (eds.)