Computational Methods for Algebraic Spline Surfaces [electronic resource] : ESF Exploratory Workshop / by Tor Dokken, Bert J�ttler.

Approximate Parametrisation of Confidence Sets -- Challenges in Surface-Surface Intersections -- Computing the Topology of Three-Dimensional Algebraic Curves -- Distance Properties of ?-Points on Algebraic Curves -- Distance Separation Measures Between Parametric Curves and Surfaces Toward Intersection and Collision Detection Applications -- Elementary Theory of Del Pezzo Surfaces -- The Geometry of the Tangent Developable -- Numerical and Algebraic Properties of Bernstein Basis Resultant Matrices -- Polynomial C2 Spline Surfaces Guided by Rational Multisided Patches -- A Recursive Taylor Method for Algebraic Curves and Surfaces -- Self-Intersection Problems and Approximate Implicitization -- Singularities of Some Projective Rational Surfaces -- On the Shape Effect of a Control Point: Experimenting with NURBS Surfaces -- Third Order Invariants of Surfaces -- Universal Rational Parametrizations and Spline Curves on Toric Surfaces -- Panel Discussion.

The papers included in this volume provide an overview about the state-of-the-art in approximative implicitization and various related topics, including both the theoretical basis and the existing computational techniques. The novel idea of approximate implicitization has strengthened the existing link between Computer Aided Geometric Design and classical algebraic geometry. There is a growing interest from researchers and professionals both in CAGD and Algebraic Geometry, to meet and combine knowledge and ideas, in order to better solve industrial--type challenges, as well as to initiate new directions for basic research. This volume will support this exchange of ideas between the various communities.