By Horst Nowacki, Justus Heimann, Elefterios Melissaratos, Sven-Holm Zimmermann (auth.), Prof. Dr. Josef Hoschek, Prof. Dr. Panagiotis D. Kaklis (eds.)
Fairing and form keeping of Curves - reviews in CurveFairing - Co-Convexivity retaining Curve Interpolation - form protecting Interpolation by way of Planar Curves - form maintaining Interpolation through Curves in 3 Dimensions - A coparative research 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 holding of Curves and Surfaces form conserving interpolation with variable measure polynomial splines Fairing of Surfaces practical elements of equity - floor layout in accordance with brightness depth or isophotes-theory and perform - reasonable floor mixing, an summary of commercial difficulties - Multivariate Splines with Convex-B-Patch keep an eye on Nets are Convex form keeping of Surfaces Parametrizing Wing Surfaces utilizing Partial Differential Equations - Algorithms for convexity conserving interpolation of scattered information - summary schemes for sensible shape-preserving interpolation - Tensor Product Spline Interpolation topic to Piecewise Bilinear reduce and higher Bounds - development of Surfaces by means of form maintaining 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 conserving Interpolation - Benchmark strategies within the Aerea of form - restricted Approximation
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For w = 0 on all segments this gives the usual cubic spline. As w -+ 00 on a particular segment [ti, ti+1) , the curve will converge to the linear segment I i Ii+1. It is assumed that there are no consecutive collinear data and so choosing the 'weights' w large enough will ensure that the scheme is 1. c. p. 4 Rational G2 Our final scheme was originated by Goodman [4) and implemented and extended by Goodman and Unsworth [6), [7). Whereas the previously described schemes required solving a global system of equations with, in general, a unique solution, this scheme does not solve any equations but specifies the curve explicitly.
OOSm was used. In all the figures the solid line is the original curve and the dashed line is the faired curve. In figures 7-10 the effect of using the different methods may be seen. ' .... , ' .. ' .... ' .... ~' . : ~ ~' t\ /; >,,~ . :: ::' : . '.. ' , ... ~ ~. ",! -.. ~ _...... __ .... j Figure I I :Curvature for Conv _; • ............ , .. , .... . ~~ . ~,u ~ <>~ "' ,~~. __ • __ . ~~ . _____ . __ . • _ • • _ • . • r_ •• _•••••••••• . . . v ..... ............... , .. ...... • •• • •• •• ~ i=\ /......
Sapidis, N. : Convexity-Preserving Interpolatory Parametric Splines of Non-Uniform Degree. Computer Aided Geometric Design 12 (1995), 1-26.  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. , Armstrong Technology Centre, Davy Bank Wallsend TYNE and WEAR NE28 6UY UK Abstract A comparative study of two methods for the automatic fairing of B-Splines curves is made.
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.)