An unique motivation for algebraic geometry used to be to appreciate curves and surfaces in 3 dimensions. fresh theoretical and technological advances in parts reminiscent of robotics, computing device 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 vanguard of analysis. One specific problem is to mix appropriate equipment from algebraic geometry with confirmed options from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane preparations) to boost instruments for treating curved items. 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 through I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which accumulated top specialists during this rising box. The learn and expository articles within the quantity are meant to supply an outline of nonlinear computational geometry. because the subject consists of computational geometry, algebraic geometry, and geometric modeling, the amount has contributions from all of those parts. by means of addressing a huge diversity of matters from only theoretical and algorithmic difficulties, to implementation and useful purposes this quantity conveys the spirit of the IMA workshop.

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