There is a growing need to be able to accurately and efficiently search visual data sets, and in particular, 3D shape data sets. This paper proposes a novel technique, called Topology Matching, in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing Multiresolutional Reeb Graphs (MRGs). The MRG thus operates well as a search key for 3D shape data sets. In particular, the MRG represents the skeletal and topological structure of a 3D shape at various levels of resolution. The MRG is constructed using a continuous function on the 3D shape, which may preferably be a function of geodesic distance because this function is invariant to translation and rotation and is also robust against changes in connectivities caused by a mesh simplification or subdivision. The similarity calculation between 3D shapes is processed using a coarse-to-fine strategy while preserving the consistency of the graph structures, which results in establishing a correspondence between the parts of objects. The similarity calculation is fast and efficient because it is not necessary to determine the particular pose of a 3D shape, such as a rotation, in advance. Topology Matching is particularly useful for interactively searching for a 3D object because the results of the search fit human intuition well.

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Topology matching for fully automatic similarity estimation of 3D shapes

A morphable model for the synthesis of 3D faces

The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware a compelling platform for computationally demanding tasks in a wide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping general-purpose computation to graphics hardware. We begin with the technical motivations that underlie general-purpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping general-purpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in general-purpose application development on graphics hardware. This survey should be of particular interest to researchers who are interested in using the latest GPGPU applications in their systems of interest.

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A Survey of General-Purpose Computation on Graphics Hardware

A Survey of General-Purpose Computation on Graphics Hardware.

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany oneor two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

Modern computer algebra

We present a simple yet effective method for modeling of object decomposition under combustion. A separate simulation models the flame production and generates heat from a combustion process, which is used to trigger pyrolysis of the solid object. The decomposition is modeled using level set methods, and can handle complex topological changes. Even with a very simple flame model on a coarse grid, we can achieve a plausible decomposition of the burning object.

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Modeling Decomposing Objects under Combustion

The problem of accurate and robust implementation of geometric algorithms has received considerable attention for more than a decade. Despite much progress in computational geometry and geometric modeling, practical implementations of geometric algorithms are prone to error. Much of the difficulty arises from the fact that reasoning about geometry most naturally occurs in the domain of the real numbers, which can only be represented approximately on a digital computer. Many times, the correctness of geometric algorithms depends on correctly evaluating the signs of arithmetic expressions, and errors due to rounding or imprecise inputs can lead to grossly incorrect results or failure to run to completion.

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Reliable Geometric Computations with Algebraic Primitives and Predicates

This work presents an approach to effectively integrate into one unified modular fire simulation framework the major processes related to fire, namely: a burning process, chemical combustion, heat distribution, decomposition and deformation of burning solids, and rigid body simulation of the residue. Simulators for every stage are described, and the modular structure enables switching to different simulators if more accuracy or more interactivity is desired. A “Stable Fluids” based three gas system is used to model the combustion process, and the heat generated during the combustion is used to drive the flow of the hot air. Objects, if exposed to enough heat, ignite and start burning. The decomposition of the burning object is modeled as a level set method, driven by the pyrolysis process, where the burning object releases combustible gases. Secondary deformation effects, such as bending burning matches and crumpling burning paper, are modeled as a proxy based deformation. 
Physically based simulation, done at interactive rates, enables the user to efficiently test different setups, as well as interact and change the conditions during the simulation. The graphics card is used to generate additional frames for real-time visualization. 
This work further proposes a method for controlling and directing high resolution simulations. An interactive coarse resolution simulation is provided to the user as a “preview” to control and achieve the desired simulation behavior. A higher resolution “final” simulation that creates all the fine scale behavior is matched to the preview simulation such that the preview and final simulations behave in a similar manner. 
In this dissertation, we highlighted a gap within the CG community for the simulation of fire. There has not previously been a physically based yet interactive simulation for fire. This dissertation describes a unified simulation framework for physically based simulation of fire and burning. Our results show that our implementation can model fire, objects catching fire, burning objects, decomposition of burning objects, and additional secondary deformations. The results are plausible even at interactive frame rates, and controllable.

Interactive simulation of fire, burn and decomposition

The ACM Symposium on Solid and Physical Modeling is an annual international forum for the exchange of recent research on topics related to modeling of solids and their physical properties and realizations. The symposium encompasses modeling and computational topics related to design, analysis, and manufacturing, as well as to emerging applications in biomedical, geophysical, and other areas. Previous symposia in this series were held in Austin, Texas, 1991; Montreal, Canada, 1993; Salt Lake City, Utah, 1995; Atlanta, Georgia, 1997; Ann Arbor, Michigan in 1999 and 2001; Saarbrucken, Germany, 2002; Seattle, Washington, 2003; Genoa, Italy, 2004; Cambridge, Massachusetts, 2005; Cardiff, Wales, United Kingdom, 2006; Beijing, China, 2007; Stony Brook, New York, 2008; and in San Francisco, California, 2009. For additional information, visit www.solidmodeling.org, the home page of the Solid Modeling Association that oversees the symposia series.

The ACM Symposium on Solid and Physical Modeling was held in Haifa, Israel, on September 1-3, 2010. More than fifty submitted papers were reviewed by an international program committee, with five committee members reviewing each paper. From these submissions, 15 papers have been selected for plenary presentation and full-length publication in the proceedings. In addition, 11 papers have been selected for short presentation and six-page publication in the proceedings.

The symposium program also includes four keynote presentations invited from leading authorities in industry and academe.

Proceedings of the 14th ACM Symposium on Solid and Physical Modeling

This paper will present a way to use keyframing methods of particle motion to enhance the visual effects and user controllability of physically based particle systems. This will be done using an adaptive correction methodology. This will allow for three general types of keyframing: position to position, density to density, and boundary to boundary. While similar techniques have been explored in flocking behaviors and robotic motion planning, this paper implements them in conjunction with physically based systems and allows a comparison of particle based keyframing to those achieved using other methodologies. To illustrate the technique we will present two examples. The first morphs between two particle images. The second forces a smoke-like substance to change into various letters of the alphabet. While these are specific examples the techniques presented herein should apply to most any particle based system to achieve a diverse range of effects.

John Keyser

Papers

Modeling Decomposing Objects under Combustion

Reliable Geometric Computations with Algebraic Primitives and Predicates

Interactive simulation of fire, burn and decomposition

Proceedings of the 14th ACM Symposium on Solid and Physical Modeling

Keyframing Particles of Physically Based Systems