DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF WATERLOO SEMINAR ACTIVITIES THEORY SEMINAR - Wednesday, August 19, 1998 Alfredo Viola, Instituto de Computacion, Universidad de la Republica, Montevideo, Uruguay, will speak ``On Combinatorial Aspects of Linear Probing Hashing''. TIME: 3:30-4:30 p.m. ROOM: DC 1304 ABSTRACT We present moment analyses and characterizations of limit distributions for the construction cost of hash tables under the linear probing strategy. For full tables, the construction cost has expectation 3/2 O(n ) , the standard deviation is of the same order, and a limit law of the Airy type holds. For sparse tables with a fixed filling ratio strictly smaller than 1, the construction cost has expectation O(n), standard deviation O(square root of n), and a limit law of the Gaussian type holds. We conclude with a brief presentation of combinatorial relations with other problems leading to Airy phenomena (such as graph connectivity, tree inversions, tree path length, or area under excursions). This is joint work with Philippe Flajolet and Patricio Poblete. ------------------------------------------------------------------- Advanced Image Synthesis Spring 1998 What: CS788 students are required to give formal public presentations describing and summarizing their projects and the related theory. Presentations will be 20 minutes in length, with 10 minutes for questions and discussion. Anyone with an interest is invited to attend. Please note that the talks will be presented on two separate dates, August 21st and August 27th. When: Aug 21, 1998 1:30---2:00 Where: DC 1304 Who: Carsten Whimster Interactive Global Illumination Hardware rendering, augmented with shadows, can be used to accelerate the last two bounces of a light path tracing global illumination algorithm. An implementation of this algorithm was performed, using a scattering of a few hundred infinitesimal area sources and the shadow volume reconstruction algorithm. When: Aug 27, 1998 1:00---3:30 Where: DC 1304 Who: (1:00) Ian Stewart Acceleration of General Implicit Surface Raycasting The interval Newton method can be used to robustly find all roots along a ray through arithmetically computable functions, which can be used to render general implicit surfaces. Unfortunately, naive interval analysis is relatively slow. Fortunately, there are ways to greatly speed up the process that do not sacrifice robustness. (1:30) Jan Kautz Interactive Rendering with Arbitrary Reflectances Bidirectional reflectance distributions are general models of surface reflectance. They can be decomposed into sums of separable functions by finding the SVD of a sampled matrix representation of the BRDF. This compressed representation of the BRDF lets us use hardware texture mapping, compositing, and accumulation operations to reconstruct the reflectance. (2:00) Caroline Kierstead Simulation of Reflectance due to Subsurface Scattering Many important real materials, such as skin, leaves, and painted surfaces, are composed of multiple layers of semitranslucent materials, each of which scatters, absorbs, and reflects light. A Monte Carlo simulator was built to estimate the bidirectional reflectance distributions from such surfaces. This was compared with the analytic, first-bounce solution. (2:30) Shalini Aggarwal Rendering and Modelling with A-Patches A-patches are implicit surfaces based on Bezier tetrahedra that are guaranteed to contain a single-sheeted algebraic surface patch where all line segments between one vertex/face pair intersect the patch exactly once. Under such conditions the patches can be quickly and robustly rendered using a scalar root solver. A-patches were analyzed with blossoming techniques, and used to fit surfaces to parametric scattered data. (3:00) Eric Hall Texture Mapping Pasted Surfaces Pasted surfaces can be used to adaptively and efficiently add detail to a spline surface. However, due to the lack of a global surface parameterization, texture maps on these surfaces can exhibit discontinuities. Various techniques were explored to obtain a suitable continuous global parameterization. For More Information: http://www.cgl.uwaterloo.ca/~mmccool/cs788/