Carlos Ureña

Simulation of shallow-water systems using graphics processing units

This paper addresses the speedup of the numerical solution of shallow-water systems in 2D domains by using modern graphics processing units (GPUs). A first order well-balanced finite volume numerical scheme for 2D shallow-water systems is considered. The potential data parallelism of this method is identified and the scheme is efficiently implemented on GPUs for one-layer shallow-water systems. Numerical experiments performed on several GPUs show the high efficiency of the GPU solver in comparison with a highly optimized implementation of a CPU solver.

An area-preserving parametrization for spherical rectangles

We present an area‐preserving parametrization for spherical rectangles which is an analytical function with domain in the unit rectangle [0, 1]2 and range in a region included in the unit‐radius sphere. The parametrization preserves areas up to a constant factor and is thus very useful in the context of rendering as it allows to map random sample point sets in [0, 1]2 onto the spherical rectangle. This allows for easily incorporating stratified, quasi‐Monte Carlo or other sampling strategies in algorithms that compute scattering from planar rectangular emitters.

Improved Irradance Computation by Importance Sampling

In this paper we consider the task of refining a low-resolution radiosity solution by using final gather. This final gather can be done by using Monte-Carlo methods. We show how to built an adequate probability density function (pdf) such that the involved variance is greatly reduced and thus we can reduce the number of samples to take, keeping the error. The proposed pdf uses information gathered during the computation of low-resolution radiosity. This data includes an approximation to the distribution of irradiance landing on a patch and coming from other patches. Once this distribution is (approximately) known, we can use it to built an importance-based pdf for final gather, such that just a few tens of samples can be taken to accurately compute irradiance.

Computation of Irradiance from Triangles by Adaptive Sampling

We introduce an algorithm for sample positioning in a planar triangle, which can be used to make numerical integration of an arbitrary function defined on it. This algorithm has some interesting properties which make it suitable for applications in the context of realistic rendering. We use an adaptive triangle partitioning procedure, driven by an appropriate measure of the error. The underlying variance is shown to be bounded, and in fact it can be controlled, so that it approaches the minimum possible value. We show results obtained when applying the method to irradiance computation, in the context of final‐gather algorithms. We also describe a C++ class which offers all required functionality, and we made available its source code.

Area-Preserving Parameterizations for Spherical Ellipses

We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area‐preserving mappings from the unit square [0,1]2 to a spherical ellipse (i.e. the projection of the disk onto the unit sphere). These mappings allow for low‐variance stratified sampling of direct illumination from disk‐shaped light sources. We discuss how to efficiently incorporate our methods into a production renderer and demonstrate the quality of our maps, showing significantly lower variance than previous work.

A FORMALIZATION AND CLASSIFICATION OF GLOBAL ILLUMINATION METHODS

Abstract This report presents a classification of global illumination methods, focusing on the numerical algorithms used. The methods are grouped in several categories, and described by using a common theoretical formalism, which indicates the similarities and differences between them. This formalism is based on the notion of integral and projection operators, and Markov Chains. The Global Illumination problem and its solutions are presented based on these mathematical devices. A key element in this presentation is the inclusion of the notion of an observer as a projection operator which yields a finite representation of an image from the radiance function.

Application of Vector Quantization Algorithms to Protein Classification and Secondary Structure Computation

In this paper a feature-map based system for protein classification according to circular dichroism spectra is described. The training algorithm has been developed from Kohonen LVQ (Learning Vector Quantization) optimized to get maximum efficiency. As a result, proteins with different secondary structure are clearly separated through a completely unsupervised training process. The algorithm is able to extract features from a high-dimensional vector (CD spectra) and map it to a 2-dimensional network. A new tool has been developed to test LVQ performance, which can be used to fine tune some of LVQ algorithm parameters. Secondary structure for unknown proteins can also be computed, giving better results than classical methods. A 3D solid representation has been introduced to represent 3D feature maps.

Overestimation and Underestimation Biases in Photon Mapping with Non-Constant Kernels.

This paper presents an analysis of the overestimation bias in common used filtering kernels in the context of photon mapping density estimation. We use the joint distribution of order statistics to calculate the expected value of the estimators of irradiance, and show that the estimator provided by the cone filter is not consistent unless the slope is one (yielding the triangular kernel), and that the Epanechnikov and Silverman kernels are consistent. The Gaussian filter has two different estimation biases: the original normalization constant α underestimates radiance by 46.9 percent, and the use of the kth nearest photon reduces this underestimation slightly. We also show that a new normalization constant for the Gaussian filter together with discarding the contribution of the kth nearest photon in the Gaussian and cone filter estimators produces new, consistent estimators. The specialized differential filter also benefits from the new estimate.

Description and Solution of an Unreported Intrinsic Bias in Photon Mapping Density Estimation with Constant Kernel

This paper presents an analysis of the irradiance estimator often used in photon mapping algorithms and concludes that the classical approach with a constant kernel overestimates the correct value. We propose a new estimator that solves this problem and provide both theoretical and empirical studies to verify it.

Interactive global illumination for quasi-static scenes

This paper describes an approach to obtain interactive recalculation of global illumination for scenes with small moving objects (with respect to the complete geometry), on a standard PC, using density estimation techniques