By Ioannis Z Emiris,Frank Sottile,Thorsten Theobald

An unique motivation for algebraic geometry was once to appreciate curves and surfaces in 3 dimensions. fresh theoretical and technological advances in parts akin to robotics, machine 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 acceptable equipment from algebraic geometry with confirmed concepts from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane preparations) to enhance instruments for treating curved items. those examine 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 study and expository articles within the quantity are meant to supply an summary of nonlinear computational geometry. because the subject comprises computational geometry, algebraic geometry, and geometric modeling, the quantity has contributions from all of those components. through addressing a vast variety of matters from simply theoretical and algorithmic difficulties, to implementation and useful functions this quantity conveys the spirit of the IMA workshop.

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