Ray Shooting, Depth Orders and Hidden Surface Removal
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Computational geometry is the part of theoretical computerscience that concerns itself with geometrical objects; itaims to define efficient algorithms for problems involvingpoints, lines, polygons, and so on. The field has gainedpopularity very rapidly during the last decade. This ispartly due to the many application areas of computationalgeometry and partly due to the beauty of the field itself.This monograph focuses on three problems that arise inthree-dimensional computational geometry. The first problemis the ray shooting problem: preprocess a set of polyhedrainto a data structure such tha...
Computational geometry is the part of theoretical computerscience that concerns itself with geometrical objects; itaims to define efficient algorithms for problems involvingpoints, lines, polygons, and so on. The field has gainedpopularity very rapidly during the last decade. This ispartly due to the many application areas of computationalgeometry and partly due to the beauty of the field itself.This monograph focuses on three problems that arise inthree-dimensional computational geometry. The first problemis the ray shooting problem: preprocess a set of polyhedrainto a data structure such that the first polyhedron that ishit by a query ray can be determined quickly. The secondproblem is that of computing depth orders: we want to sort aset of polyhedra such thatif one polyhedron is (partially)obscured by another polyhedron then it comes first in theorder. The third problem is the hidden surface removalproblem: given a set of polyhedra and a view point, computewhich parts of the polyhedra are visible from the viewpoint. These three problems involve issues that arefundamental to three-dimensional computational geometry.The book also contains a large introductory part discussingthe techniques used to tackle the problems. This part shouldinterest not only those who need the background for the restof the book but also anyone who wants to know more aboutsome recent techniques in computational geometry.
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