In this paper we show that there is an upper bound on the volume of a hyperbolic knot in the 3-sphere with canonical genus g. This bound can in fact be chosen to be linear in g. In other words, if Seifert's algorithm builds a surface with small genus for a hyperbolic knot, then the complement of the knot cannot have large

Minimum distance computations on complex geometry commonly employ hierarchies of bounding volumes that are pruned through establishment of upper and lower bounds. In this paper we describe a novel time coherence scheme which utilizes coherence on these bounds, rather than coherence derived from the geometry of the bounding volumes or from the geometry of the underlying model. This method is thu...

If a normalized Kähler-Ricci flow g(t), t ∈ [0,∞), on a compact Kähler manifold M , dimC M = n ≥ 3, with positive first Chern class satisfies g(t) ∈ 2πc1(M) and has curvature operator uniformly bounded in Ln-norm, the curvature operator will also be uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a Kähler-Ricci soliton.

A bounding volume hierarchy is a common method for making ray tracing based rendering more efficient. Constructing good hierarchies, however, is a difficult problem as the number of hierarchies grows exponentially with the number of scene objects. In this paper, we attempted to apply stochastic search to techniques to solve the problem of automatic generation of bounding volume hierarchy. We ha...

This paper is an excerpt from Chapter 1 of my PhD thesis [Hav04], written to introduce my publications about bounding volume hierachies [Aga02, Arg04, Hav04BG]. 1 Computational geometry and geometric data structures Computational geometry is the area of algorithms research that deals with computations on geometric objects. Examples of such objects are points, lines and polygons in the plane—whi...

Bounding volume hierarchies (BVH) are a commonly used method for speeding up ray tracing. Even though the memory footprint of a BVH is relatively low compared to other acceleration data structures, they still can consume a large amount of memory for complex scenes and exceed the memory bounds of the host system. This can lead to a tremendous performance decrease on the order of several magnitud...

An image based model reconstruction system is described. Real images of a rigid object acquired under a simple but controlled environment are used to recover the three dimensional geometry and the surface appearance. Based on a multi-image calibration method, an algorithm to extract the rotation axis of a turn-table has been developed. Furthermore, this can be extended to estimate robustly the ...

A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The τ-function of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are characterized. Illustrative examples of exact solutions of Whitham hierarchies are derived and applications to conformal maps dynamics are indicated.

Active contour models have proven to be a promising approach for data driven object tracking without knowledge about the problem domain and the object. Problems arise in case of fast moving objects and in natural scenes with heterogeneous background. In these cases, a prediction step is an essential part of the tracking mechanism. In this paper we describe a new approach for modelling the conto...