A new paradigm for rigid body simulation is presented and analyzed. Current techniques for rigid body simulation run slowly on scenes with many bodies in close proximity. Each time two bodies collide or make or break a static contact, the simulator must interrupt the numerical integration of velocities and accelerations. Even for simple scenes, the number of discontinuities per frame time can rise to the millions. An efficient optimization-based animation (OBA) algorithm is presented which can simulate scenes with many convex threedimensional bodies settling into stacks and other “crowded” arrangements. This algorithm simulates Newtonian (second order) physics and Coulomb friction, and it uses quadratic programming (QP) to calculate new positions, momenta, and accelerations strictly at frame times. The extremely small integration steps inherent to traditional simulation techniques are avoided. Contact points are synchronized at the end of each frame. Resolving contacts with friction is known to be a difficult problem. Analytic force calculation can have ambiguous or non-existing solutions. Purely impulsive techniques avoid these ambiguous cases, but still require an excessive and computationally expensive number of updates in the case of

Penetration depth (PD) is a distance metric that is used to describe the extent of overlap between two intersecting objects. Most of the prior work in PD computation has been restricted to translational PD, which is defined as the minimal translational motion that one of the overlapping objects must undergo in order to make the two objects disjoint. In this paper, we extend the notion of PD to take into account both translational and rotational motion to separate the intersecting objects, namely generalized PD. When an object undergoes rigid transformation, some point on the object traces the longest trajectory. The generalized PD between two overlapping objects is defined as the minimum of the longest trajectories of one object under all possible rigid transformations to separate the overlapping objects. We present three new results to compute generalized PD between polyhedral models. First, we show that for two overlapping convex polytopes, the generalized PD is same as the translational PD. Second, when the complement of one of the objects is convex, we pose the generalized PD computation as a variant of the convex containment problem and compute an upper bound using optimization techniques. Finally, when both the objects are non-convex, we treat them as a combination of the above two cases, and present an algorithm that computes a lower and an upper bound on generalized PD. We highlight the performance of our algorithms on different models that undergo rigid motion in the 6-dimensional configuration space. Moreover, we utilize our algorithm for complete motion planning of polygonal robots undergoing translational and rotational motion in a plane. In particular, we use generalized PD computation for checking path non-existence.

Boolean operations, Minkowski sum evaluation, configuration space computation, and motion planning are fundamental problems in solid modeling and robotics. Their applications include computer-aided design, numerically-controlled machining, tolerance verification, packing, assembly planning, and dynamic simulation. Prior algorithms for solving these problems can be classified into exact and approximate approaches. The exact approaches are difficult to implement and are prone to robustness problems. Current approximate approaches may not solve these problems accurately. Our work aims to bridge this gap between exact and approximate approaches. We present a sampling-based approach to solve these geometric problems. Our approach

Mosaics are widely used for surface decoration to produce appealing visual effects. We present a method for synthesizing digital surface mosaics with irregularly shaped tiles, which are a type of tiles often used for mosaics design. Our method employs both continuous optimization and combinatorial optimization to improve tile arrangement. In the continuous optimization step, we iteratively partition the base surface into approximate Voronoi regions of the tiles and optimize the positions and orientations of the tiles to achieve a tight fit. Combination optimization performs tile permutation and replacement to further increase surface coverage and diversify tile selection. The alternative applications of these two optimization steps lead to rich combination of tiles and high surface coverage. We demonstrate the effectiveness of our solution with extensive experiments and comparisons.

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This work deals with the problem of minimize the waste of space that occurs on a placement of a set of bi-dimensional items inside a bi-dimensional container with fixed dimensions. This problem is approached with an heuristic based on Simulated Annealing (SA), which is in-spired on the physic-chemical process that takes place during the recrystallization of a metal. Traditional “external penalization” techniques are avoided through the application of no–fit polygons, that represents collision-free areas for each items before its placement. That gives to the proposed process a more universal character, as external penalization is based on empiric parameters of great influence on the optimization performance. The SA controls: the rotation and the placement. For each non–placed items

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In this paper, we highlight our past experiences on fast penetration depth computation and its applications in different areas such as physically-based animation, 6DOF haptic rendering and robot motion planning.

Current techniques for rigid body simulation run slowly on scenes with many bodies in close proximity. Each time two bodies collide or make or break a static contact, the simulator must interrupt the numerical integration of velocities and accelerations. Even for simple scenes, the number of discontinuities per frame time can rise to the millions. An efficient optimization-based animation (OBA) algorithm is presented which can simulate scenes with many convex three-dimensional bodies settling into stacks and other “crowded” arrangements. This algorithm simulates Newtonian (second order) physics and Coulomb friction, and it uses quadratic programming (QP) to calculate new positions, momenta and accelerations strictly at frame times. Contact points are synchronized at the end of each frame. The extremely small integration steps inherent to traditional simulation techniques are avoided. Non-convex bodies are simulated as unions of convex bodies. Links and joints are simulated successfully with bi-directional constraints. A hybrid of OBA and retroactive detection (RD) has been implemented as well. A review of existing work finds no other packages that can simulate similarly complex scenes in a practical amount of time.