The area covered by a three-dimensional bounding box after projection onto the screen is relevant for view-dependent algorithms in real-time and photorealistic rendering. We describe a fast method to compute the accurate two-dimensional area of a three-dimensional oriented bounding box, and show how it can be computed equally fast or faster than its approximation with a two-dimensional bounding...

Noah Stein, Pablo Parrilo, and Asu Ozdaglar pointed out an error on page 10, lines 13-14 of our paper “Computing Correlated Equilibria in Multi-Player Games” (Journal of the ACM, 2008). The incorrect phrase is “...which contradicts our assumption that the violating y is within the current ellipsoid”. This conclusion would be valid for the bounding ellipsoid used for the original dual program (D...

1. Quick Review of Elliptic Curves 2 2. Elliptic Curves over C 4 3. Elliptic Curves over Local Fields 6 4. Elliptic Curves over Number Fields 12 5. Elliptic Curves with Complex Multiplication 15 6. Descent 22 7. Elliptic Units 27 8. Euler Systems 37 9. Bounding Ideal Class Groups 43 10. The Theorem of Coates and Wiles 47 11. Iwasawa Theory and the “Main Conjecture” 50 12. Computing the Selmer G...

In the animation of deformable objects, collision detection is crucial for the performance. Contrary to volumetric bodies, the accuracy requirements for the collision treatment of textiles are particularly strict because any overlapping is visible. Therefore, we apply methods specifically designed for deformable surfaces that speed up the collision detection. In this paper the efficiency of bou...

Recently, Guibas et al. 10 studied deformable necklaces – flexible chains of balls, called beads, in which only adjacent balls can intersect. In this paper, we investigate the problem of covering a necklace by cylinders. We consider several problems under different optimization criteria. We show that optimal cylindrical cover of a necklace with n beads in R by k cylinders can be computed in pol...

We propose a novel adaptive pipeline for continuous collision detection in cloth simulation. The pipeline consists of four components: bounding volume hierarchy (BVH) update, BVH traversal, a skipping frame session, and elementary test processing. The skipping frame session is activated adaptively for skipping both BVH update and BVH traversal during the process of collision detection. The prop...

Aiming at developing a simple and efficient collision detection method to support the wandering in equipment deploy scene in land reclamation area of mining dump. This paper presents an efficient algorithm for collision detection in the waste dump land reclamation equipment deploy scene using a bounding volume nestification which consists of an oriented bounding boxes (OBBs) enhanced with axial...

We study the practicability and performance of different classes of bounding volume hierarchies for self collision detection in complex human hair styles with authentic geometrical properties. In particular, we focus on topology based hierarchies which allow for fast update schemes as well as conventional spatially adapted hierarchies. In this context, we introduce a parameterized k-DOP approac...

Lin and Chang gave a generating function of convex polyominoes with an m+1 by n + 1 minimal bounding rectangle. Gessel showed that their result implies that the number of such polyominoes is m+ n+mn m+ n ( 2m+ 2n 2m ) − 2mn m+ n ( m+ n m )2 . We show that this result can be derived from some binomial coefficients identities related to the generating function of Jacobi polynomials. Some (binomia...