Space-filling curves can be used to organise points in the plane into bounding-box hierarchies (such as R-trees). We develop measures of the bounding-box quality of space-filling curves that express how effective different space-filling curves are for this purpose. We give general lower bounds on the bounding-box quality measures and on locality according to Gotsman and Lindenbaum for a large c...

Bounding boxes are used in many applications for simplification of point sets or complex shapes. For example, in computer graphics, bounding boxes are used to maintain hierarchical data structures for fast rendering of a scene or for collision detection. Additional applications include those in shape analysis and shape simplification, or in statistics, for storing and performing range-search qu...

In this paper the problem of minimum cost communication network design is considered where the costs are piecewise linear concave. Several methods are compared: Simulated Annealing method, a heuristic based on the method proposed by Minoux, and a lagrangian method based on lower bounding procedure.

Polyomino Venn (or polyVenn) diagrams are Venn diagrams whose curves are the perimeters of polyominoes drawn on the integer lattice. Minimum area polyVenn diagrams are those in which each of the 2n intersection regions, in a diagram of n polyominoes, consists of exactly one unit square. We construct minimum area polyVenn diagrams in bounding rectangles of size 2r×2c whenever r, c ≥ 2. Our const...

We present different approaches for accelerating the process of continuous collision detection for deformable triangle meshes. The main focus is upon the collision detection for simulated virtual clothing, especially for situations involving a high number of contact points between the triangle meshes, such as multi-layered garments. We show how the culling efficiency of bounding volume hierarch...

The bounding-box of a geometric shape in 2D is the rectangle with the smallest area in a given orientation (usually upright) that complete contains the shape. The best-fit bounding-box is the smallest bounding-box among all the possible orientations for the same shape. In the context of document image analysis, the shapes can be characters (individual components) or paragraphs (component groups...