Open AccessJournal Article
A computational basis for conic arcs and boolean operations on conic polygons
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In this paper, an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arc that immediately leads to a realization of regularized boolean operations on conic polygons.Abstract:
We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately leads to a realization of regularized boolean operations on conic polygons. A conic polygon, or polygon for short, is anything that can be obtained from linear or conic halfspaces (= the set of points where a linear or quadratic function is non-negative) by regularized boolean operations. The algorithm and its implementation are complete (they can handle all cases), exact (they give the mathematically correct result), and efficient (they can handle inputs with several hundred primitives).read more
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References
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Generic Programming
TL;DR: It is argued that generically programmed software component libraries have important advantages for achieving software productivity and reliability.
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Efficient isolation of polynomial's real roots
TL;DR: A generic algorithm is presented, which enables one to describe all the known algorithms based on Descartes' rule of sign and the bisection strategy in a unified framework and is optimal in terms of memory usage and as fast as both Collins and Akritas' algorithm and Krandick's variant, independently of the input polynomial.