The mathematical foundation of free form surface representations and constructions is an emerging field covering many interesting research problems and numerous important applications. This book contains selected presentations from the CAGD Conference at Oberwolfach, with new developments of mathematical methods and efficient algorithms for the representation of curves and surfaces. The contributions focus on the following topics: rational splines, scattered data interpolation, multivariate splines, interpolating with geometric constraints, algorithms for graphic representations.
A Rational Cubic Spline with Tension (J.A. Gregory, M. Sarfraz).
Constructing Piecewise Rational Curves with Frenet Frame Continuity (T.N.T.
Goodman). Good Approximation of Circles by Curvature-Continuous Bezier Curves
(T. Dokken et al.). Fairing Bezier Curves with Constraints (H. Nowacki, D.
Liu and X. Lu). Symmetric Triangular Algorithms for Curves (H.-P. Seidel).
Blossoming and Knot Insertion Algorithms for B-Spline Curves (R.N. Goldman).
Analytic Properties of Plane Offset Curves (R.T. Farouki, C.A. Neff).
Algebraic Properties of Plane Offset Curves (R.T. Farouki, C.A. Neff). Using
Parameters to Increase Smoothness of Curves and Surfaces Generated by
Subdivision (N. Dyn, D. Levin, C.A. Micchelli). Finite Quadric Segments with
Four Conic Boundary Curves (G. Geise, U. Langbecker). GC 1 Continuity
Conditions between Two Adjacent Rational Bezier Surface Patches (D. Liu).
Necessary and Sufficient Conditions for Tangent Plane Continuity of Bezier
Surfaces (T.D. DeRose). Explicit Continuity Conditions for Adjacent Bezier
Surface Patches (W.L.F. Degen). Local Smooth Surface Interpolation: a
Classification (J. Peters). G-splines (K. Hollig, H. Mogerle). G n-1
-Functional Splines for Interpolation and Approximation of Curves, Surfaces
and Solids (J. Li, J. Hoschek, E. Hartmann). Cyclides in Computer Aided
Geometric Design (M.J. Pratt). On Cyclides in Geometric Modeling (W. Boehm).
A Marching Method for Parametric Surface / Surface Intersection (R.E.
Barnhill, S.N. Kersey). Surfaces over Dirichlet Tessellations (G. Farin).
Cubic Spline Fitting using Data Dependent Triangulations (E. Quak, L.L.
Schumaker). Interpolation of Scattered Data on Closed Surfaces (T.A. Foley et
al.). Modified Multiquadric Methods for Scattered Data Interpolation over a
Sphere (H. Pottmann, M. Eck). Surfaces Defined on Surfaces (R.E. Barnhill,
H.S. Ou). Contouring a Bivariate Quadratic Polynomial over a Triangle (A.J.
Worsey, G. Farin). Visibility of Surfaces via Differential Geometry (R.
Walter).
