Interactive display and visualization of large geometric and textured models is becoming a fundamental capability. There are numerous application areas, including games, movies, CAD, virtual prototyping, and scientific visualization. One of observations about geometric models used in interactive applications is that their model complexity continues to increase because of fundamental advances in 3D modeling, simulation, and data capture technologies. As computing power increases, users take advantage of the algorithmic advances and generate even more complex models and data sets. Therefore, there are many cases where we are required to visualize massive models that consist of hundreds of millions of triangles and, even, billions of triangles. However, interactive visualization and handling of such massive models still remains a challenge in computer graphics and visualization. In this monograph we discuss various techniques that enable interactive visualization of massive models. These techniques include visibility computation, simplification, levels-of-detail, and cache-coherent data management.We believe that the combinations of these techniques can make it possible to interactively visualize massive models in commodity hardware. Table of Contents: Introduction / Visibility / Simplification and Levels of Detail / Alternative Representations / Cache-Coherent Data Management / Conclusions / Bibliography

This book gives a broad overview of research on sound simulation driven by a variety of applications. Vibrating objects produce sound, which then propagates through a medium such as air or water before finally being heard by a listener. As a crucial sensory channel, sound plays a vital role in many applications. There is a well-established research community in acoustics that has studied the problems related to sound simulation for six decades. Some of the earliest work was motivated by the design of concert halls, theaters, or lecture rooms with good acoustic characteristics. These problems also have been investigated in other applications, including noise control and sound design for urban planning, building construction, and automotive applications. Moreover, plausible or realistic sound effects can improve the sense of presence in a virtual environment or a game. In these applications, sound can provide important clues such as source directionality and spatial size. The book first surveys various sound synthesis methods, including harmonic synthesis, texture synthesis, spectral analysis, and physics-based synthesis. Next, it provides an overview of sound propagation techniques, including wave-based methods, geometric-based methods, and hybrid methods. The book also summarizes various techniques for sound rendering. Finally, it surveys some recent trends, including the use of machine learning methods to accelerate sound simulation and the use of sound simulation techniques for other applications such as speech recognition, source localization, and computer-aided design.

This book surveys the state of the art in explainable and interpretable reinforcement learning (RL) as relevant for robotics. While RL in general has grown in popularity and been applied to increasingly complex problems, several challenges have impeded the real-world adoption of RL algorithms for robotics and related areas. These include difficulties in preventing safety constraints from being violated and the issues faced by systems operators who desire explainable policies and actions. Robotics applications present a unique set of considerations and result in a number of opportunities related to their physical, real-world sensory input and interactions. The authors consider classification techniques used in past surveys and papers and attempt to unify terminology across the field. The book provides an in-depth exploration of 12 attributes that can be used to classify explainable/interpretable techniques. These include whether the RL method is model-agnostic or model-specific, self-explainable or post-hoc, as well as additional analysis of the attributes of scope, when-produced, format, knowledge limits, explanation accuracy, audience, predictability, legibility, readability, and reactivity. The book is organized around a discussion of these methods broken down into 42 categories and subcategories, where each category can be classified according to some of the attributes. The authors close by identifying gaps in the current research and highlighting areas for future investigation.

We present a simple algorithm to compute the proper parametrization of a polynomial curve and reduce the problem of detecting cusps in a rational curve to that of a polynomial curve. Finally, we use the regular parametrizations to analyze for inflection points."

The problem of interference detection or contact determination between two or more objects in dynamic environment is fundamental in computer graphics, robotics, and virtual environments. Most of the earlier work is restricted to either polyhedral models or static environments. In this paper, we present efficient algorithms for contact determination and interference detection between geometric models undergoing rigid motion. The set of models include polyhedra and surfaces described by algebraic sets or piecewise algebraic functions. The algorithms make use of temporal and spatial coherence between successive instances and their running time is a function of the motion between successive instances. The main characteristics of these algorithms are their simplicity and efficiency. They have been implemented; their performance on many applications indicates their potential for real-time simulations. Contact determination, Collision detection, Visual simulations, Animation, Robotics, Geometric models, Coherence, Voronoi regions, Closest features and points.

The problem of computing the intersection of parametric and algebraic curves arises in many applications of computer graphics, geometric and solid modeling. Previous algorithms are based on techniques from Elimination theory or subdivision and iteration. The former is however, restricted to low degree curves. This is mainly due to issues of efficiency and numerical stability. In this paper we use Elimination theory and express the resultant of the equations of intersection as a matrix determinant. The matrix itself rather than its symbolic determinant, a polynomial, is used as representation. The algorithm for intersection corresponds to substituting the other equation to construct an equivalent matrix such that the intersection points can be extracted from the eigenvalues and eigenvectors of the latter. Moreover, the algebraic and geometric multiplicities of eigenvalues give us information about the intersection (multiplicity, tangential intersection etc.). As a result we are able to accurately compute high order intersections in most cases. The main advantage of this approach lies in its efficiency and robustness. Moreover, the numerical accuracy of these operations is well understood. For almost all cases we are able to compute accurate answers in 64 bit IEEE floating point arithmetic.