Sudhir P. Mudur

Interval Methods for Processing Geometric Objects

In this approach, the parametric form is applied without the usual computational nightmare. The key is to view the parametric range as an interval, relying on subdivision algorithms.

Computation of global illumination in a participating medium by monte carlo simulation

This paper discusses techniques for the computation of global illumination in environments with a participating medium using a Monte Carlo simulation of the particle model of light. Efficient algorithms and data structures for tracking the particles inside the volume have been developed. The necessary equation for computing the illumination along any given direction has been derived for rendering a scene with a participating medium. A major issue in any Monte Carlo simulation is the uncertainty in the final simulation results. Various steps of the algorithm have been analysed to identify major sources of uncertainty. To reduce the uncertainty, suitable modifications to the simulation algorithm have been suggested using variance reduction methods of forced collision, absorption suppression and particle divergence. Some sample scenes showing the results of applying these methods are also included.

Adjoint equations and random walks for illumination computation

In this paper we introduce the potential equation that along with the rendering equation forms an adjoint system of equations and provides a mathematical frame work for all known approaches to illumination computation based on geometric optics. The potential equation is more natural for illumination computations that simulate light propagation starting from the light sources, such as progressive radiosity and particle tracing. Using the mathematical handles provided by this framework and the random-walk solution model, we present a number of importance sampling schemes for improving the computation of flux estimation. Of particular significance is the use of approximately computed potential for directing a majority of the random walks through regions of importance in the environment, thus reducing the variance in the estimates of luminous flux in these regions. Finally, results from a simple implementation are presented to demonstrate the high-efficiency improvements made possible by the use of these techniques.

Constraint-satisfying planar development of complex surfaces

Abstract Composite laminates are made of multiple layers of fibrous material, each layer being formed by laying tapes of various widths on subregions of the planar development of the surface. The tapes are laid only along a certain direction, thus requiring the cuts and overlaps of the planar development to lie along that direction. The paper presents algorithms that have been implemented to obtain planar developments (within acceptable tolerances) of complex surfaces with cuts and overlaps only in specified orientations. The algorithm is based on the novel approach of first obtaining an approximate planar development, and then reorienting the cracks and overlaps in the plane of development to satisfy the orientation constraint.

The Potential Equation and Importance in Illumination Computations

An equation adjoint to the luminance equation for describing the global illumination can be formulated using the notion of a surface potential to illuminate the region of interest. This adjoint equation which we shall call as the potential equation, is fundamental to the adjoint radiosity equation used to devise the importance driven radiosity algorithm. In this paper we first briefly derive the adjoint system of integral equations and then show that the adjoint linear equations used in the above algorithm are basically discrete formulations of the same. We also show that the importance entity of the linear equations is basically the potential function integrated over a patch. Further we prove that the linear operators in the two equations are indeed transposes of each other.

An Efficient Technique for Mining Usage Profiles Using Relational Fuzzy Subtractive Clustering

We propose an efficient technique for mining web usage profiles based on subtractive clustering that scales to large datasets. Unlike earlier clustering based techniques for the same purpose, our technique does not require user specification of any input parameter to obtain the desired clustering. Instead, we achieve this by searching in the cluster space for the best clustering of the given web usage data. To evaluate clustering quality, we have formulated a validity index for our algorithm. Our implementation of the proposed technique and the experiments with large real life datasets show that it indeed mines the desired usage profiles much faster than existing techniques.

The Brush-Trajectory Approach to Figure Specification: Some Algebraic Solutions

The brush-trajectory method, a very natural scheme for describing two-dimensional shapes used in graphic arts and typesetting applications, has been used in only a few systems largely ¢,wing to the computational complexity involved in transforming such descriptions into raster bit maps. This paper addresses the problem. For some specific brushes and trajectories we derive algebraic solutions for describing the resulting outlines. The result of dynamic transformations on the brush as it moves along the trajectory is also studied. A special closed, smooth, convex brush defined by a Jburth-order parametric equation is introduced to describe more complex shapes. An algorithmic solution to determining the outlines for an unconstrained brush is then presented. Finally, we present some ideas on a canonical brush and its use in solving the inverse problem, that is, determininl, the brushtrajectory description from given outlines.

Distributed Augmented Reality for Visualizing Collaborative Construction Tasks

Augmented reality is a visualization method in which virtual objects are aligned with the real world and the viewer can interact with the virtual objects in real time. In this paper, a new methodology called distributed augmented reality for visualizing collaborative construction tasks (DARCC) is proposed. Using this methodology, virtual models of construction equipment can be operated and viewed by several operators to interactively simulate construction activities on the construction site in augmented reality mode. The paper investigates the design issues of DARCC including tracking and registration, object modeling, engineering constraints, and interaction and communication methods. The DARCC methodology is implemented in a prototype system and tested in a case study about a bridge deck rehabilitation project.

Generation of continuous smooth curves resulting from operations on parametric surface patches

Abstract In recent years a number of techniques based on the subdivision principle have been suggested for detecting the curves resulting from the intersection of two parametrically defined surface patches. Silhouette curves of surfaces can also be detected using analogous techniques. Usually the output is a set of pixels or line segments which form the complete curve, though not necessarily in an ordered manner. This paper presents data structures for maintaining the result of subdivision, and algorithms for tracing the curves in a continuous fashion. Using a few iterations of the Newton-Raphson technique the curve points may be refined to any required precision. For each point on the curve the nonlinear equations are chosen by looking at the local topological nature of the curve so as to guarantee convergence of the Newton-Raphson technique in one or two iterations.

Computational techniques for processing parametric surfaces

This paper presents computational techniques using which subdivision algorithms may be devised for the processing (rendering, intersection detection, silhouette detection) of parametrically defined surfaces. These algorithms work by subdividing surface patches until they are simple enough for direct handling. For example, planar surface patches can be handled analytically. For interference it is necessary to box the surface as well. The computational techniques presented are essentially for efficient computation of surface properties needed by the processing tasks. The three properties considered are: (1) Euclidean bounds: this is done by working in extrema in x, y, and z over the patch; (2) planarity estimate: this test is defined in terms of the linearity of constituent curves; (3) Local visibility: which says whether a patch is totally visible, invisible, or partially visible from a given viewpoint. Rendering algorithms make use of this information. This too is done by working in extrema of the visibility function. All the techniques are based on the parametric form of the surface representation. The class of surfaces that can be handled by these techniques is very large, basically C2 continuous surfaces. A class of surfaces known as product surfaces is specially introduced as the above methods are extremely efficient for this class. Application of these methods to bicubic surfaces is also discussed.