Jorge Stolfi

Primitives for the manipulation of general subdivisions and the computation of Voronoi

The following problem is discussed: given n points in the plane (the sites) and an arbitrary query point q, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the griven sites and then locating the query point inone of its regions. Two algorithms are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new sit on O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. the simplicity of both algorithms can be attributed to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings of graphs in two-dimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficients for building and modifying arbitrary diagrams.

Optimal point location in a monotone subdivision

Point location, often known in graphics as “hit detection,” is one of the fundamental problems of computational geometry. In a point location query we want to identify which of a given collection of geometric objects contains a particular point. Let

The image foresting transform: theory, algorithms, and applications

\mathcal{S}

A kinetic framework for computational geometry

denote a subdivision of the Euclidean plane into monotone regions by a straight-line graph of m edges. In this paper we exhibit a substantial refinement of the technique of Lee and Preparata [SIAM J. Comput., 6 (1977), pp. 594–606] for locating a point in

Epsilon geometry: building robust algorithms from imprecise computations

\mathcal{S}

Affine Arithmetic: Concepts and Applications

based on separating chains. The new data structure, called a layered dag, can be built in

A multiscale method for the reassembly of two-dimensional fragmented objects

O(m)

Reporting and Counting Intersections Between Two Sets of Line Segments

time, uses

Lines in space: Combinatorics and algorithms

O(m)

T-HOG: An effective gradient-based descriptor for single line text regions

storage, and makes possible point location in