The purpose of this thesis is to develop and demonstrate a physically based rigid body simulation with a focus on simplifications to achieve real-time performance. This thesis aims to demonstrate that by improving the efficiency with simplified calculations of possible bottlenecks of a real-time rigid body simulation, the accuracy can be improved. A prototype simulation framework is implemented to evaluate the simplifications. Finally, various real-time rendering features are implemented to achieve a realistic look, and also to imitate the game-like environment where real-time rigid body simulations are mostly utilized. A series of demonstration experiments are used to show that our simulator does, in fact, achieve real-time performance, while maintaining satisfactory accuracy. A direct comparison of this prototype with a commercially available simulator verifies that the simplified approach improves the efficiency and does not damage the accuracy under our test conditions. Integration of rendering elements like advanced shading, shadowing, depth of field and motion blur into our real-time framework also enhanced the perception of simulation outcomes.

This thesis examines the design and implementation of an extensible objectoriented physics engine framework. The design and implementation consolidates concepts from the wide literature in the field and clearly documents the procedures and methods. Two primary dynamic behaviors are explored: rigid body dynamics and articulated dynamics. A generalized collision response model is built for rigid bodies and articulated structures which can be adapted to other types of behaviors. The framework is designed around the use of interfaces for modularity and easy extensibility. It supports both a standalone physics engine and a supplement to a distributed immersive rendering environment. We present our results as a number of scenarios that demonstrate the viability of the framework. These scenarios include rigid bodies and articulated structures in free-fall, collision with dynamic and static bodies, resting contact, and friction. We show that we can effectively combine different dynamics into one cohesive structure. We also explain how we can efficiently extend current behaviors to develop new ones, such as altering rigid bodies to produce different collision responses or flocking behavior. Additionally, we demonstrate these scenarios in both the standalone and the immersive environment.

This thesis examines the design and implementation of an extensible objectoriented physics engine framework. The design and implementation consolidates concepts from the wide literature in the field and clearly documents the procedures and methods. Two primary dynamic behaviors are explored: rigid body dynamics and articulated dynamics. A generalized collision response model is built for rigid bodies and articulated structures which can be adapted to other types of behaviors. The framework is designed around the use of interfaces for modularity and easy extensibility. It supports both a standalone physics engine and a supplement to a distributed immersive rendering environment. We present our results as a number of scenarios that demonstrate the viability of the framework. These scenarios include rigid bodies and articulated structures in free-fall, collision with dynamic and static bodies, resting contact, and friction. We show that we can effectively combine different dynamics into one cohesive structure. We also explain how we can efficiently extend current behaviors to develop new ones, such as altering rigid bodies to produce different collision responses or flocking behavior. Additionally, we demonstrate these scenarios in both the standalone and the immersive environment.

The purpose of this thesis was to create a computational wrist model that predicts carpal bone motion in order to investigate the complex kinematics of the human wrist. The tuning of this model was primarily based on in vitro, kinematic measurements of the carpal bones obtained from the same cadaver arm as the geometry for the model was generated. A rigid body spring model of the wrist was built using the kinematic simulation software RecurDynTM 6.1. Surface models of the eight carpal bones, the bases of the five metacarpal bones, and the distal parts of the ulna and radius, all obtained from computed tomography (CT) scans of a cadaver upper limb, were utilized as the geometry for this model. Elastic contact conditions between the rigid bodies modeled the influence of the cartilage layers, and ligamentous structures were constructed using nonlinear, tension-only spring elements. Motion of the wrist was simulated by applying forces to the tendons of the five main wrist muscles modeled. Three wrist motions were simulated: extension, ulnar deviation and radial deviation. The model was mainly tuned by comparing the simulated displacement and orientation of the carpal bones with previously obtained CT-scans of the same cadaver arm in deviated (45 deg ulnar and 15 deg radial), and extended (57 deg) wrist positions. Simulation results for the scaphoid, lunate, capitate, hamate and triquetrum are presented here and provide credible prediction of carpal bone movement. The impact of certain model parameters on simulation results has been investigated by performing sensitivity analyses, and their severity has been documented. The results of the first simulations indicate that this model may assist in future wrist kinematics investigations. However, further optimization and validation are required to define and guarantee the reliability of this model. It is suggested that this rigid body spring model may be part of an interacting framework between in vitro and in vivo investigations, as well as other computational models, in order to improve and complement each biomechanical investigation method. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2007-08-30 16:30:32.543

This dissertation describes several techniques to improve performance and controllability of large-scale rigid body simulations. We first describe a statistical simulation method that replaces certain stages of rigid body simulation with a statistically- based approximation. We begin by collecting statistical data regarding changes in linear and angular momentum for collisions of a given object. From the data, we extract a statistical ”signature” for the object, giving a compact representation of the object’s response to collision events. During object simulation, both the collision detection and the collision response calculations are replaced by simpler calculations based on the statistical signature. In addition, based on our statistical simulator, we develop a mixed rigid body simulator that combines an impulse-based with a statistically-based collision response method. This allows us to maintain high accuracy in important parts of the scene while achieving greater efficiency by simplifying less important parts of the simulation. The resulting system gives speedups of more than an order of magnitude on several large rigid body simulations while maintaining high accuracy in key places and capturing overall statistical behavior in other places. Also, we introduce two methods for directing pile behavior to form the desired shapes. To fill up the space inside the desired shapes and maintain the stability of the desired pile shapes, our methods analyze the configurations and status of all objects and properly select some candidates to have their degrees of freedom (DOFs) reduced. Our first method utilizes the idea of angles of repose to perform the analysis. According to the desired angle of repose, we create an additional spatial structure to track the piling status and select suitable objects to reduce their DOFs. In our second method, we adapt equilibrium analysis in a local scheme to find “stable” objects of the stacking structure. Then, we restrict their DOFs by adding constraints on them for stabilizing the structure. Overall, our directing methods generate a wider variety of piled structures than possible with strict physically-based simulation.

The aim of the research is the analysis and motion curve synthesis for cam-gear intermittent mechanisms. Based on the grooved-cam-controlled motion of rocker planet gear and motion superposition of the planet gear trains, cam-gear intermittent mechanisms transfer continuous rotation to intermittent rotation. Interpolation of non-parametric rational B-splines motion curve is first introduced in this thesis, and it provides better motion characteristics. Based on rigid body transformation, the analytical grooved cam profile can be determined, and the pressure angle and radius of curvature can be calculated. By applying vector operation, rigid body dynamic analysis is also performed. An application example for cam-gear intermittent mechanisms used in the paper delivery system of the die cutting and creasing machine is served to support the content of this research and to improve the kinematic and dynamic characteristics of the paper delivery system.

We present a solution to animating interactions between characters and thin, non-rigid bodies using a passive optical motion capture system. Prior work in human body motion capture can accurately recreate human motion but this work is not adequate because it does not allow for interactions with a non-rigid body. Prior work in face and cloth motion capture handles non-rigid planes but rope is better handled with a curved spline rather than a curved plane. The segmented motion is in the form of un-indexed motion capture data. After segmenting the motion of the thin, non-rigid body and the human character the separated motion capture data can be recreated individually. The recreated motion streams are then recombined using 3D modeling and animation software. The presented solution also improves techniques for recreating thin, non-rigid body motion from un-indexed motion capture data. Using the linear combination of two predicted marker positions our solution can accurately track motion capture markers through each frame of the motion capture data. This also allows our solution to invent marker positions when gaps are present in the motion capture data. Our improvements allow users to reconstruct the motion of both a human character and a thin, non-rigid body simultaneously from motion capture data gathered in a mixed motion capture session.

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For synthetic data generation with concave collision objects, two physics simu- lations techniques are investigated; convex decomposition of mesh models for globally concave collision results, used with the physics simulation library Bullet, and a GPU implemented rigid body solver using spherical decomposition and impulse based physics with a spatial sorting-based collision detection. Using the GPU solution for rigid body physics suggested in the thesis scenes con- taining large amounts of bodies results in a rigid body simulation up to 2 times faster than Bullet 2.83.

Two Poisson brackets are called compatible if any linear combination of these brackets is a Poisson bracket again. The set of non-zero linear combinations of two compatible Poisson brackets is called a Poisson pencil. A system is called bihamiltonian (with respect to a given pencil) if it is hamiltonian with respect to any bracket of the pencil. The property of being bihamiltonian is closely related to integrability. On the one hand, many integrable systems known from physics and geometry possess a bihamiltonian structure. On the other hand, if we have a bihamiltonian system, then the Casimir functions of the brackets of the pencil are commuting integrals of the system. We consider the situation when these integrals are enough for complete integrability. As it was shown by Bolsinov and Oshemkov, many properties of the system in this case can be deduced from the properties of the Poisson pencil itself, without explicit analysis of the integrals. Developing these ideas, we introduce a notion of linearization of a Poisson pencil. In terms of linearization, we give a criterion for non-degeneracy of a singular point and describe its type. These results are applied to solve the stability problem for a free multidimensional rigid body.