Tiow Seng Tan

Decomposing polygon meshes for interactive applications

This paper discusses an efficient and effective framework to decompose polygon meshes into components. This is useful in various interactive graphics applications, such as, mesh editing, establishing correspondence between objects for morphing, computation of bounding volume hierarchy for collision detection and ray tracing. In this paper, we formalize the notion of a component as a sub-volume of an object with homogeneous geometric and topological features. Next, we describe the proposed framework, which adapts the idea of edge contraction and space sweeping to decompose an object automatically. Finally, we demonstrate an application of this framework to improve bounding volume hierarchies constructed by state-of-theart collision detection systems such as RAPID and QuickCD.

Model simplification using vertex-clustering

This paper presents a practical technique to automaticallycompute approximations of polygonal representations of3D objects. It is based on a previously developed modelsimplification technique which applies vertex-clustering.Major advantages of the vertex-clustering technique are itslow computational cost and high data reduction rate, andthus suitable for use in interactive applications. This paperadvances the technique with careful consideration ofapproximation quality and smoothness in transitionsbetween different levels of simplification, whilemaintaining its efficiency and efb%iveness. Its majorcontributions include: accuracy in grading vertices forindication of their visual importance, robustness inclustering for better preservation of important fimtures andconsistencies between levels of simplification, thick-lineswith dynamic normals to maximize visual fidelity, andexploitation of object and image space relationship forlevels-of-simplificationdetermination.

Jump flooding in GPU with applications to Voronoi diagram and distance transform

This paper studies jump flooding as an algorithmic paradigm in the general purpose computation with GPU. As an example application of jump flooding, the paper discusses a constant time algorithm on GPU to compute an approximation to the Voronoi diagram of a given set of seeds in a 2D grid. The errors due to the differences between the approximation and the actual Voronoi diagram are hardly noticeable to the naked eye in all our experiments. The same approach can also compute in constant time an approximation to the distance transform of a set of seeds in a 2D grid. In practice, such constant time algorithm is useful to many interactive applications involving, for example, rendering and image processing. Besides the experimental evidences, this paper also confirms quantitatively the effectiveness of jump flooding by analyzing the occurrences of errors. The analysis is a showcase of insights to the jump flooding paradigm, and may be of independent interests to other applications of jump flooding.

Parallel Banding Algorithm to compute exact distance transform with the GPU

We propose a Parallel Banding Algorithm (PBA) on the GPU to compute the exact Euclidean Distance Transform (EDT) for a binary image in 2D and higher dimensions. Partitioning the image into small bands to process and then merging them concurrently, PBA computes the exact EDT with optimal linear total work, high level of parallelism and a good memory access pattern. This work is the first attempt to exploit the enormous power of the GPU in computing the exact EDT, while prior works are only on approximation. Compared to these other algorithms in our experiments, our exact algorithm is still a few times faster in 2D and 3D for most input sizes. We illustrate the use of our algorithm in applications such as computing the Euclidean skeleton using the integer medial axis transform, performing morphological operations of 3D volumetric data, and constructing 2D weighted centroidal Voronoi diagrams.

Anti-aliasing and continuity with trapezoidal shadow maps

This paper proposes a new shadow map technique termed trapezoidal shadow maps to calculate high quality shadows in real-time applications. To address the resolution problem of the standard shadow map approach, our technique approximates the eyes frustum as seen from the light with a trapezoid to warp it onto a shadow map. Such a trapezoidal approximation, which may first seem straightforward, is carefully designed to achieve the goal of good shadow quality for objects from near to far, and to address the continuity problem that is found in all existing shadow map approaches. The continuity problem occurs mainly when the shadow map quality changes significantly from frame to frame due to the motion of the eye or the light. This results in flickering of shadows. On the whole, our proposed approach is simple to implement without using complex data structures and it maps well to graphics hardware as shown in our experiments with large virtual scenes of hundreds of thousands to over a million of triangles.

An O ( n 2 log n ) time algorithm for the minmax angle triangulation

It is shown that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time

Edge insertion for optimal triangulations

O(n^2 \log n)

Preprocessing occlusion for real-time selective refinement

and space

A quadratic time algorithm for the minmax length triangulation

O(n)

Generating an /spl omega/-tile set for texture synthesis

. The algorithm is fairly easy to implement and is based on the edge-insertion scheme that iteratively improves an arbitrary initial triangulation. It can be extended to the case where edges are prescribed, and, within the same time- and space-bounds, it can lexicographically minimize the sorted angle vector if the point set is in general position. Experimental results on the efficiency of the algorithm and the quality of the triangulations obtained are included.