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We present a novel and fast algorithm to compute penetration depth (PD) between two polyhedral models for physically-based animation. Given two overlapping polyhedra, it computes the minimal translation distance to separate them using a combination of object-space and image-space techniques. The algorithm computes pairwise Minkowski sums of decomposed convex pieces and performs a closest point query using rasterization hardware. It uses bounding volume hierarchies, object-space and image-space culling algorithms to further accelerate the computation and refines the estimated PD in a hierarchical manner. We demonstrate its application to contact response computation and a time-stepping method for dynamic simulation.
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Rigid-body dynamics with unilateral contact is a good approximation for a wide range of everyday phenomena, from the operation of car brakes to walking to rock slides. It is also of vital importance for simulating robots, virtual reality, and realistic animation. However, correctly modeling rigid-body dynamics with friction is difficult due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law. This is particularly crucial for handling situations with large coefficients of friction, which can result in paradoxical results known at least since Painlevé [C. R. Acad. Sci. Paris, 121 (1895), pp. 112-115]. This single example has been a counterexample and cause of controversy ever since, and only recently have there been rigorous mathematical results that show the existence of solutions to his example. The new mathematical developments in rigid-body dynamics have come from several sources: "sweeping processes" and the measure differential inclusions of Moreau in the 1970s and 1980s, the variational inequality approaches of Duvaut and J.-L. Lions in the 1970s, and the use of complementarity problems to formulate frictional contact problems by Lο̈tstedt in the early 1980s. However, it wasn't until much more recently that these tools were finally able to produce rigorous results about rigid-body dynamics with Coulomb friction and impulses.
Contenido: Introducción; Propiedades de los fluidos; Estática de los fluidos; Fluidos en movimiento; Variación de presión en fluidos en movimiento; Principio de la cantidad de movimiento; Principio de energía; Análisis dimensional y similitud; Resistencia de superficie; Flujo en conductos; Arrastre y sustentación; Flujo compresible; Mediciones de flujo, Turbomaquinaria; Flujo variado en canales abiertos.
The traditional high-level algorithms for rigid body simulation work well for moderate numbers of bodies but scale poorly to systems of hundreds or more moving, interacting bodies. The problem is unnecessary synchronization implicit in these methods. Jefferson 's timewarp algorithm [22] is a technique for alleviating this problem in parallel discrete event simulation. Rigid body dynamics, though a continuous process, exhibits many aspects of a discrete one. With modification, the timewarp algorithm can be used in a uniprocessor rigid body simulator to give substantial performance improvements for simulations with large numbers of bodies. This paper describes the limitations of the traditional high-level simulation algorithms, introduces Jefferson's algorithm, and extends and optimizes it for the rigid body case. It addresses issues particular to rigid body simulation, such as collision detection and contact group management, and describes how to incorporate these into the timewarp framework. Quantitative experimental results indicate that the timewarp algorithm offers significant performance improvements over traditional high-level rigid body simulation algorithms, when applied to systems with hundreds of bodies. It also helps pave the way to parallel implementations, as the paper discusses.
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