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Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obviou...
An Introduction
Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. S...
The book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The original motiva...
This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangu...
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Combinatorics and Algorithms
3. A randomized preprocessing procedure using [formula] time and storage, for any [epsilon] > 0, that builds a structure supporting O(log n)-time quer...
Abstract: "The zone theorem for an arrangement of n hyperplanes in d-dimensional real space says that the total number of faces bounding the cells int...
Topology, Combinatorics, and Algorithms
Arrangements of curves in the plane are fundamental to many problems in computational and combinatorial geometry (e.g. motion planning, algebraic cell...
A Technique to Cope with Degenerate Cases in Geometric Algorithms
Algorithms and Applications
Abstract: "A set of n weighted points in general position in R[superscript d] defines a unique regular triangulation. This paper proves that if the po...
Abstract: "We prove that for any set S of n points in the plane and [formula] triangles spanned by the points of S there exists a point (not necessari...
Abstract: "A plane geometric graph C in R℗ conforms to another such graph G if each edge of G is the union of some edges of C. It is provedthat for ...
Abstract: "This paper introduces the concept of an α-shape of a finite set of points with real weights in R[superscript d]. It is a polytope uniquely...
Abstract: "We show that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time 0(n[superscript 2] ...
Tight Bounds on the Number of Faces
Abstract: "Efficient algorithms are described for computing topological, combinatorial, and metric properties of the union of finitely many balls in R...
Abstract: "A general and direct method for computing the betti numbers of the homology groups of a finite simplicial complex is given. For subcomplexe...
Abstract: "We show that a triangulation of a set of n points in the plane that minimizes the maximum edge length can be computed in time O(n℗). The ...
Abstract: "Frequently, the data produced in scientific computing applications is in its abstract form a finite point set in space, and it issometimes ...
Abstract: "This paper proves an [formula] upper bound on the number of incidences between m points and n hyperplanes in four dimensions, assuming all ...
Abstract: "The shape of a protein is important for its functions. This includes the location and size of identifiable regions in its complement space....
Abstract: "Given a subspace X [subset] R[superscript d] and a finite set S [subset] R[superscript d], we introduce the Delaunay simplicial complex, D[...
Abstract: "We study the maintenance of a simplicial grid or complex under changing density requirements. The proposed method works in any fixed dimens...
Abstract: "Any arbitrary polyhedron P [subset of] R[superscript d] can be written as algebraic sum of simple terms, each an integer multiple of the in...