THE INSTITUTE OF MATHEMATICS
AND ITS APPLICATIONS

Mathematics of Surfaces VI

Editor: Glen Mullineux, University of Bath
Proceedings of a sixth conference on "Mathematics of Surfaces" held at Brunel University in September 1994.

The Sixth IMA Mathematics of Surfaces Conference was held at Brunel University in early September 1994. Over the three days, papers were presented covering a wide range of research into the area. Some papers were invited and others contributed. The conference and these proceedings are dedicated to the memory of Dr. John Gregory who had died suddenly the previous year. John, who had been a reader in the Mathematics Department at Brunel University, had been the editor of the proceedings for the first of this series of conferences. He had researched for many years in the area of free-form surfaces and gained an international reputation. He was popular with all who knew him and will be sadly missed. The conference was attended by a number of John's former research students as well as people who had known or collaborated with him over the years. The first two papers at the conference reviewed John's contribution to the mathematics of surfaces and they are preceded in these proceedings by a list of his publications.

Contents

• Publications of Dr. John Gregory
• John Gregory's Research: From Computational Error Bounds through Gregory's Square to Convex Combinations by R.E. Barnhill
• The Work of John Gregory, Rational Spline Interpolation, Subdivision Algorithms and C2 Polygonal Patches by N. Dyn
• Dupin Cyclides and Supercyclides by M.J. Pratt
• A Practical Implementation of Vertex Blend Surfaces using an n-Sided Patch by D. Plowman and P. Charrot
• The Sub-Parabolic Lines of a Surface by R. Morris
• Geodesic Paths for General Surfaces Generated by Solid Modellers by D.J. Robinson and C.G. Armstrong
• Free-Form Surface Matching for Surface Inspection by E.M. Bispo and R.B. Fisher
• Surface Fitting by Exploiting Data Distribution by I.J. Anderson and J.C. Mason
• The Types of Triangular Bézier Surfaces by W.L.F. Degen
• Polyhedral Metrics in Surface Reconstruction by L. Alboul and R. van Damme
• Linear Approximation of Trimmed Surfaces by R. Klein
• Cubic Algebraic Surface Interpolation of Three Points with Prescribed Normals by A.E. Middleditch and E.E. Dimas
• Robust Implementation of Geometric Algorithms Using Exact Arithmetic by S. Fortune and C.J. van Wyk
• Validity Determination for MAT Surface Representation by C.M. Hoffmann and P.J. Vermeer
• Physics-Based NURBS Swung Surfaces by H. Qin and D. Terzopoulos
• Numerical Aspects of Stability Investigations on Surfaces by St. Hahmann and H. Hagen
• Pre-Wavelets on Scattered Knots and from Radial Function Spaces: A Review by M.D. Buhmann
• Towards a Classification of Curve and Surface Algorithms Using Invariance by H.E. Bez
• Loop Detection via Homotopy Continuation by G. Lukács
• Polynomial and Rational Pythagorean-Hodograph Curves Reconciled by R.T. Farouki and H. Pottmann
• A Geometric Newton Method for Interference Processing of Rational Curves and Surfaces in Homogeneous Space by K. Matsumura, A. Yamada and F. Yamaguchi
• An Arbitrary Rectangular Patch Network Scheme for Free-Form Surface Modelling by J. Zhou and V.K.H. Lau
• Best Fit Surface Curvature at Vertices of Topologically Irregular Curve Networks by T. Várady and T. Hermann
• G1-Interpolation of Rectangular Unrestricted Cubic Curve Meshes Using Biquintic Bézier Patches by X. Ye and H. Nowacki
• Hybrid B-Spline Interpolants by M. Walker
• C2 Surfaces Built from Zero Sets of the 7-Direction Box Spline by J. Peters
• Matching NURBS Surfaces G1 and G2 by L.J. Nachman
• Transfinite Surface Interpolation by M. Sabin
• Simplex Splines, Polar Simplex Splines and Triangular B-Splines by H.-P. Seidel

• Numerical Computations of Medial Surface Vertices by D.J. Sheehy, C.G. Armstrong and D.J. Robinson