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 new method for computing shadows from semitransparent objects like hair. Extending the concept of opacity shadow maps, the deep opacity map method uses a depth map to obtain a per pixel distribution of opacity layers. This approach totally eliminates the layering artifacts of opacity shadow maps and requires much fewer layers to achieve high quality shadow computation. We provide qualitative comparisons to opacity shadow maps and give performance results. Our algorithm is easy to implement, fast, and memory efficient, enabling us to generate high quality hair self-shadows in real-time using consumer graphics hardware on a standard PC.

Deep Opacity Maps

We propose a particle-based technique for simulating incompressible fluid that includes adaptive refinement of particle sampling. Each particle represents a mass of fluid in its local region. Particles are split into several particles for finer sampling in regions of complex flow. In regions of smooth flow, neighboring particles can be merged. Depth below the surface and Reynolds number are exploited as our criteria for determining whether splitting or merging should take place. For the fluid dynamics calculations, we use the hybrid FLIP method, which is computationally simple and efficient. Since the fluid is incompressible, each particle has a volume proportional to its mass. A kernel function, whose effective range is based on this volume, is used for transferring and updating the particle’s physical properties such as mass and velocity. Our adaptive particle-based simulation is demonstrated in several scenarios that show its effectiveness in capturing fine detail of the flow, where needed, while efficiently sampling regions where less detail is required.

Adaptive particles for incompressible fluid simulation

Despite the visual importance of hair and the attention paid to hair modeling in the graphics research, modeling realistic hair still remains a very challenging task that can be performed by very few artists. In this paper we present hair meshes, a new method for modeling hair that aims to bring hair modeling as close as possible to modeling polygonal surfaces. This new approach provides artists with direct control of the overall shape of the hair, giving them the ability to model the exact hair shape they desire. We use the hair mesh structure for modeling the hair volume with topological constraints that allow us to automatically and uniquely trace the path of individual hair strands through this volume. We also define a set of topological operations for creating hair meshes that maintain these constraints. Furthermore, we provide a method for hiding the volumetric structure of the hair mesh from the end user, thus allowing artists to concentrate on manipulating the outer surface of the hair as a polygonal surface. We explain and show examples of how hair meshes can be used to generate individual hair strands for a wide variety of realistic hair styles.

Hair meshes

An important part of solid modeling systems based on curved primitives is the representation and manipulation of algebraic plane curves with rational coefficients and points with algebraic coordinates. These objects are often approximated by floating-point numbers and spline curves, which are easy to manipulate, but are subject to accuracy and robustness problems. Exact computation can eliminate these numerical robustness problems, but efficient exact methods have not been available. Moreover, it is widely believe that exact arithmetic is impractical for manipulating curved primitives. In this paper, we present an efficient approach for exact manipulation of algebraic points and non-singular curves in the plane. We describe the underlying representations and discuss techniques for making exact computations more efficient through two algorithms and the use of floating-point speedups. Specifically, we describe algorithms for curve–curve intersections and curve topology. We also discuss various issues related to their implementation in a library, MAPC. We demonstrate their performance on a number of applications including curve topology evaluation, computing arrangements of curves and boundary evaluation of low degree algebraic solids.

Efficient and exact manipulation of algebraic points and curves

We propose a method for applying genetic algorithms to create 3D terrain data sets. Existing procedural algorithms for generation of terrain have several shortcomings. The most popular approach, fractal-based terrain generation, is efficient, but is difficult for a user to control. Other methods tend to require too much user input. In this paper, we provide an alternative method of terrain generation that uses a two-pass genetic algorithm approach to produce a variety of terrain types using only intuitive user inputs. We allow a user to specify a rough sketch of terrain region boundaries, and we refine these boundaries using a genetic algorithm. We then couple this with a database of given terrain data to generate an artificial terrain, which we optimize using a second genetic algorithm.

John Keyser

Papers

Deep Opacity Maps

Adaptive particles for incompressible fluid simulation

Hair meshes

Efficient and exact manipulation of algebraic points and curves

Terrain generation using genetic algorithms