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Decomposition Algorithms in Geometry

In: Algebraic Geometry and its Applications

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  • Bernard Chazelle
  • Leonidas Palios

Abstract

Decomposing complex shapes into simpler components has always been a focus of attention in computational geometry. The reason is obvious: most geometric algorithms perform more efficiently and are easier to implement and debug if the objects have simple shapes. For example, mesh-generation is a standard staple of the finite-element method; partitioning polygons or polyhedra into convex pieces or simplices is a typical preprocessing step in automated design, robotics, and pattern recognition. In computer graphics, decompositions of two-dimensional scenes are used in contour filling, hit detection, clipping and windowing; polyhedra are decomposed into smaller parts to perform hidden surface removal and ray-tracing.

Suggested Citation

  • Bernard Chazelle & Leonidas Palios, 1994. "Decomposition Algorithms in Geometry," Springer Books, in: Chandrajit L. Bajaj (ed.), Algebraic Geometry and its Applications, chapter 27, pages 419-447, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2628-4_27
    DOI: 10.1007/978-1-4612-2628-4_27
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