Fast and exact continuous collision detection with Bernstein sign classification

We present fast algorithms to perform accurate CCD queries between triangulated models. Our formulation uses properties of the Bernstein basis and Bézier curves and reduces the problem to evaluating signs of polynomials. We present a geometrically exact CCD algorithm based on the exact geometric computation paradigm to perform reliable Boolean collision queries. Our algorithm is more than an order of magnitude faster than prior exact algorithms. We evaluate its performance for cloth and FEM simulations on CPUs and GPUs, and highlight the benefits

Tetrahedral Image-to-Mesh Conversion Software for Anatomic Modeling of Arteriovenous Malformations

We describe a new implementation of an adaptive multi-tissue tetrahedral mesh generator targeting anatomic modeling of Arteriovenous Malformation (AVM) for surgical simulations. Our method, initially constructs an adaptive Body-Centered Cubic (BCC) mesh of high quality elements. Then, it deforms the mesh surfaces to their corresponding physical image boundaries, hence, improving the mesh fidelity and smoothness. Our deformation scheme, which builds upon the ITK toolkit, is based on the concept of energy minimization, and relies on a multi-material point-based registration. It uses non-connectivity patterns to implicitly control the number of the extracted feature points needed for the registration, and thus, adjusts the trade-off between the achieved mesh fidelity and the deformation speed. While many medical imaging applications require robust mesh generation, there are few codes available to the public. We compare our implementation with two similar open-source image-to-mesh conversion codes: (1) Cleaver from US, and (2) CGAL from EU. Our evaluation is based on five isotropic/anisotropic segmented images, and relies on metrics like geometric & topologic fidelity, mesh quality, gradation and smoothness. The implementation we describe is open- source and it will be available within: (i) the 3D Slicer package for visualization and image analysis from Harvard Medical School, and (ii) an interactive simulator for neurosurgical procedures involving vasculature using SOFA, a framework for real-time medical simulation developed by INRIA

Interactive Thin Elastic Materials

Despite great strides in past years are being made to generate motions of elastic 1 materials such as cloth and biological skin in virtual world, unfortunately, the computational cost of realistic high-resolution simulations currently precludes their use in interactive applications. Thin elastic materials such as cloth and biological skin often exhibit complex nonlinear elastic behaviors. However, modeling elastic nonlinearity can be computationally expensive and numerically unstable, imposing significant challenges for their use in interactive applications. This paper presents a novel simulation framework for simulating realistic material behaviours with interactive frame rate. Central to the framework is the use of a constraint-based multi-resolution solver for efficient and robust modelling of the material nonlinearity. We extend a strain limiting method to work on deformation gradients of triangulated surface models in three dimensional space with a novel data structure. The simulation framework utilises an iterative nonlinear Gauss-Seidel procedure and a multilevel hierarchy structure to achieve computational speed ups. As material non-linearity are generated by enforcing strain limiting constraints at a multilevel hierarchy, our simulation system can rapidly accelerate the convergence of the large constraint system with simultaneous enforcement of boundary conditions. The simplicity and efficiency of the framework makes simulations of highly realistic thin elastic materials substantially fast and is applicable of simulations for interactive applications

A Framework for Dynamic Terrain with Application in Off-road Ground Vehicle Simulations

The dissertation develops a framework for the visualization of dynamic terrains for use in interactive real-time 3D systems. Terrain visualization techniques may be classified as either static or dynamic. Static terrain solutions simulate rigid surface types exclusively; whereas dynamic solutions can also represent non-rigid surfaces. Systems that employ a static terrain approach lack realism due to their rigid nature. Disregarding the accurate representation of terrain surface interaction is rationalized because of the inherent difficulties associated with providing runtime dynamism. Nonetheless, dynamic terrain systems are a more correct solution because they allow the terrain database to be modified at run-time for the purpose of deforming the surface. Many established techniques in terrain visualization rely on invalid assumptions and weak computational models that hinder the use of dynamic terrain. Moreover, many existing techniques do not exploit the capabilities offered by current computer hardware. In this research, we present a component framework for terrain visualization that is useful in research, entertainment, and simulation systems. In addition, we present a novel method for deforming the terrain that can be used in real-time, interactive systems. The development of a component framework unifies disparate works under a single architecture. The high-level nature of the framework makes it flexible and adaptable for developing a variety of systems, independent of the static or dynamic nature of the solution. Currently, there are only a handful of documented deformation techniques and, in particular, none make explicit use of graphics hardware. The approach developed by this research offloads extra work to the graphics processing unit; in an effort to alleviate the overhead associated with deforming the terrain. Off-road ground vehicle simulation is used as an application domain to demonstrate the practical nature of the framework and the deformation technique. In order to realistically simulate terrain surface interactivity with the vehicle, the solution balances visual fidelity and speed. Accurately depicting terrain surface interactivity in off-road ground vehicle simulations improves visual realism; thereby, increasing the significance and worth of the application. Systems in academia, government, and commercial institutes can make use of the research findings to achieve the real-time display of interactive terrain surfaces

Efficient computation of discrete Voronoi diagram and homotopy-preserving simplified medial axis of a 3d polyhedron

The Voronoi diagram is a fundamental geometric data structure and has been well studied in computational geometry and related areas. A Voronoi diagram defined using the Euclidean distance metric is also closely related to the Blum medial axis, a well known skeletal representation. Voronoi diagrams and medial axes have been shown useful for many 3D computations and operations, including proximity queries, motion planning, mesh generation, finite element analysis, and shape analysis. However, their application to complex 3D polyhedral and deformable models has been limited. This is due to the difficulty of computing exact Voronoi diagrams in an efficient and reliable manner. In this dissertation, we bridge this gap by presenting efficient algorithms to compute discrete Voronoi diagrams and simplified medial axes of 3D polyhedral models with geometric and topological guarantees. We apply these algorithms to complex 3D models and use them to perform interactive proximity queries, motion planning and skeletal computations. We present three new results. First, we describe an algorithm to compute 3D distance fields of geometric models by using a linear factorization of Euclidean distance vectors. This formulation maps directly to the linearly interpolating graphics rasterization hardware and enables us to compute distance fields of complex 3D models at interactive rates. We also use clamping and culling algorithms based on properties of Voronoi diagrams to accelerate this computation. We introduce surface distance maps, which are a compact distance vector field representation based on a mesh parameterization of triangulated two-manifolds, and use them to perform proximity computations. Our second main result is an adaptive sampling algorithm to compute an approximate Voronoi diagram that is homotopy equivalent to the exact Voronoi diagram and preserves topological features. We use this algorithm to compute a homotopy-preserving simplified medial axis of complex 3D models. Our third result is a unified approach to perform different proximity queries among multiple deformable models using second order discrete Voronoi diagrams. We introduce a new query called N-body distance query and show that different proximity queries, including collision detection, separation distance and penetration depth can be performed based on Nbody distance query. We compute the second order discrete Voronoi diagram using graphics hardware and use distance bounds to overcome the sampling errors and perform conservative computations. We have applied these queries to various deformable simulations and observed up to an order of magnitude improvement over prior algorithms

Fast Simulation of Mass-Spring Systems

We describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. This scheme provides a fast solution for classical linear (Hookean) springs. We express the widely used implicit Euler method as an energy minimization problem and introduce spring directions as auxiliary unknown variables. The system is globally linear in the node positions, and the non-linear terms involving the directions are strictly local. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. Our method converges to the same final result as would be obtained by solving the standard form of implicit Euler using Newton’s method. Although the asymptotic convergence of Newton’s method is faster than ours, the initial ratio of work to error reduction with our method is much faster than Newton’s. For real-time visual applications, where speed and stability are more important than precision, we obtain visually acceptable results at a total cost per timestep that is only a fraction of that required for a single Newton iteration. When higher accuracy is required, our algorithm can be used to compute a good starting point for subsequent Newton’s iteration

Collision Detection and Merging of Deformable B-Spline Surfaces in Virtual Reality Environment

This thesis presents a computational framework for representing, manipulating and merging rigid and deformable freeform objects in virtual reality (VR) environment. The core algorithms for collision detection, merging, and physics-based modeling used within this framework assume that all 3D deformable objects are B-spline surfaces. The interactive design tool can be represented as a B-spline surface, an implicit surface or a point, to allow the user a variety of rigid or deformable tools. The collision detection system utilizes the fact that the blending matrices used to discretize the B-spline surface are independent of the position of the control points and, therefore, can be pre-calculated. Complex B-spline surfaces can be generated by merging various B-spline surface patches using the B-spline surface patches merging algorithm presented in this thesis. Finally, the physics-based modeling system uses the mass-spring representation to determine the deformation and the reaction force values provided to the user. This helps to simulate realistic material behaviour of the model and assist the user in validating the design before performing extensive product detailing or finite element analysis using commercially available CAD software. The novelty of the proposed method stems from the pre-calculated blending matrices used to generate the points for graphical rendering, collision detection, merging of B-spline patches, and nodes for the mass spring system. This approach reduces computational time by avoiding the need to solve complex equations for blending functions of B-splines and perform the inversion of large matrices. This alternative approach to the mechanical concept design will also help to do away with the need to build prototypes for conceptualization and preliminary validation of the idea thereby reducing the time and cost of concept design phase and the wastage of resources

Multi-Surface Simplex Spine Segmentation for Spine Surgery Simulation and Planning

This research proposes to develop a knowledge-based multi-surface simplex deformable model for segmentation of healthy as well as pathological lumbar spine data. It aims to provide a more accurate and robust segmentation scheme for identification of intervertebral disc pathologies to assist with spine surgery planning. A robust technique that combines multi-surface and shape statistics-aware variants of the deformable simplex model is presented. Statistical shape variation within the dataset has been captured by application of principal component analysis and incorporated during the segmentation process to refine results. In the case where shape statistics hinder detection of the pathological region, user-assistance is allowed to disable the prior shape influence during deformation. Results have been validated against user-assisted expert segmentation

Enabling Motion Planning and Execution for Tasks Involving Deformation and Uncertainty

A number of outstanding problems in robotic motion and manipulation involve tasks where degrees of freedom (DoF), be they part of the robot, an object being manipulated, or the surrounding environment, cannot be accurately controlled by the actuators of the robot alone. Rather, they are also controlled by physical properties or interactions - contact, robot dynamics, actuator behavior - that are influenced by the actuators of the robot. In particular, we focus on two important areas of poorly controlled robotic manipulation: motion planning for deformable objects and in deformable environments; and manipulation with uncertainty. Many everyday tasks we wish robots to perform, such as cooking and cleaning, require the robot to manipulate deformable objects. The limitations of real robotic actuators and sensors result in uncertainty that we must address to reliably perform fine manipulation. Notably, both areas share a common principle: contact, which is usually prohibited in motion planners, is not only sometimes unavoidable, but often necessary to accurately complete the task at hand. We make four contributions that enable robot manipulation in these poorly controlled tasks: First, an efficient discretized representation of elastic deformable objects and cost function that assess a ``cost of deformation\u27 for a specific configuration of a deformable object that enables deformable object manipulation tasks to be performed without physical simulation. Second, a method using active learning and inverse-optimal control to build these discretized representations from expert demonstrations. Third, a motion planner and policy-based execution approach to manipulation with uncertainty which incorporates contact with the environment and compliance of the robot to generate motion policies which are then adapted during execution to reflect actual robot behavior. Fourth, work towards the development of an efficient path quality metric for paths executed with actuation uncertainty that can be used inside a motion planner or trajectory optimizer