By Ioannis Z. Emiris, Frank Sottile, Thorsten Theobald
An unique motivation for algebraic geometry was once to appreciate curves and surfaces in 3 dimensions. contemporary theoretical and technological advances in parts equivalent to robotics, desktop imaginative and prescient, computer-aided geometric layout and molecular biology, including the elevated availability of computational assets, have introduced those unique questions once again into the leading edge of analysis. One specific problem is to mix appropriate tools from algebraic geometry with confirmed concepts from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane preparations) to advance instruments for treating curved gadgets. those study efforts should be summarized lower than the time period nonlinear computational geometry. This quantity grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized via I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which accrued top specialists during this rising box. The study and expository articles within the quantity are meant to supply an summary of nonlinear computational geometry. because the subject contains computational geometry, algebraic geometry, and geometric modeling, the quantity has contributions from all of those components. by means of addressing a extensive diversity of concerns from in basic terms theoretical and algorithmic difficulties, to implementation and functional purposes this quantity conveys the spirit of the IMA workshop.