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.

/pdf/topology-matching-for-fully-automatic-similarity-estimation-2pui3z62og.pdf

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.

/pdf/a-survey-of-general-purpose-computation-on-graphics-hardware-2phx1q9xxr.pdf

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

The behavior of Catmull-Rom curves heavily depends on the choice of parameter values at the control points. We analyze a class of parameterizations ranging from uniform to chordal parameterization and show that, within this class, curves with centripetal parameterization contain properties that no other curves in this family possess. Researchers have previously indicated that centripetal parameterization produces visually favorable curves compared to uniform and chordal parameterizations. However, the mathematical reasons behind this behavior have been ambiguous. In this paper we prove that, for cubic Catmull-Rom curves, centripetal parameterization is the only parameterization in this family that guarantees that the curves do not form cusps or self-intersections within curve segments. Furthermore, we provide a formulation that bounds the distance of the curve to the control polygon and explain how globally intersection-free Catmull-Rom curves can be generated using these properties.

/pdf/on-the-parameterization-of-catmull-rom-curves-4cytf0bvk3.pdf

On the parameterization of Catmull-Rom curves

In this paper we describe a method for simulating motion of realistically complex plants interactively. We use a precomputation stage to generate the plant structure, along with a set of simulation levels of detail. The levels of detail are made by continuously grouping branches starting from the tips of the branches and working toward the trunk. Grouped branches are simulated as single branches that have similar simulation characteristics to the original branches. During run-time, we traverse the plant and determine the allowable error in the simulation of branch motion. This allows us to choose the appropriate simulation level of detail and we provide smooth transitions from level to level. Our level of detail approach affects only the simulation parameters, allowing geometry to be handled independently. Using this method we can significantly improve simulation times for complex trees.

/pdf/simulation-levels-of-detail-for-plant-motion-rsyswkyoh2.pdf

Simulation levels of detail for plant motion

Efficient and accurate B-rep generation of low degree sculptured solids using arithmetic: II—computation

Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic

In this paper we describe a system, BOOLE, that generates the boundary representations (B-reps) of solids given as a CSG expression in the form of trimmed Bezier patches. The system makes use of techniques from computational geometry, numerical linear algebra and symbolic computation to generate the B-reps. Given two solids, the system first computes the intersection curve between the two solids using our surface intersection algorithm. Using the topological information of each solid, it computes various components within each solid generated by the intersection curve and their connectivity. The component classification step is performed by ray-shooting. Depending on the Boolean operation performed, appropriate components are put together to obtain the final solid. We also present techniques to parallelize this system on shared memory multiprocessor machines. The system has been successfully used to generate B-reps for a number of large industrial models including parts of a notional submarine storage and handling room (courtesy - Electric Boat Inc.) and Bradley fighting vehicle (courtesy - Army Research Labs). Each of these models is composed of over 8000 Boolean operations and is represented using over 50,000 trimmed Bezier patches. Our exact representation of the intersection curve and use of stable numerical algorithms facilitate an accurate boundary evaluation at every Boolean set operation and generation of topologically consistent solids.

John Keyser

Papers

On the parameterization of Catmull-Rom curves

Simulation levels of detail for plant motion

Efficient and accurate B-rep generation of low degree sculptured solids using arithmetic: II—computation

Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic

Boole: a boundary evaluation system for boolean combinations of sculptured solids