Geometric Data Structures for Computer Graphics
Data structures and tools from computational geometry help to solve problems in computer graphics; these methods have been widely adopted by the computer graphics community yielding elegant and efficient algorithms. This book focuses on algorithms and data structures that have proven to be versatile, efficient, fundamental, and easy to implement. The book familiarizes students, as well as practitioners in the field of computer graphics, with a wide range of data structures. The authors describe each data structure in detail, highlight fundamental properties, and present algorithms based on the data structure. A number of recent representative and useful algorithms from computer graphics are described in detail, illuminating the utilization of the data structure in a creative way.
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Orthogonal Windowing and Stabbing Queries
Bounding Volume Hierarchies
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Additionally algebraic algorithm approximation assume axis-parallel binary decomposition bounding volume BSP tree cell CGAL circumcenter collision detection Computational Geometry Computer Graphics construction convex hull corresponding d-dimensional data structure DCEL defined definition Delaunay triangulation delete denote distance field dynamic efficient endpoints Equation evaluation exact example Figure floating-point arithmetic floating-point number function Geom geometric algorithm Geometric Computation given Guibas IEEE implemented input interpolation search intersection interval tree kd-tree Klein leaf Lemma line segments logn matrix mod q nearest neighbor node objects octree orientation test Overmars perturbation plane point cloud polygons precision predicates problem Proc proximity graph quadtree range tree recursive relative error representation represents RightChild robust root scheme Section segment tree set of points Shewchuk simple space sphere split stabbing query static stored surface Theorem training set triangle vector vertex vertices Voronoi diagram WeakDelete operation x-coordinates Zachmann