MICADO: Models of Interactive Constraints for the Assembling of 1D Deformable Objects

This paper introduces a set of Lagrangian constraints, allowing most needed interaction and combinations of one-dimensional deformable elements for creating complex structures. The proposed tools can potentially be used with a large set of available 1D-models. All constraints formulation are compatible with linear, displacement-based, integration schemes. The proposed constraints allow for real-time complex structure simulation, and also novel interactions between simulated objects. Various examples are provided, illustrating the benefit of the proposed numerical tools

The application of three-dimensional mass-spring structures in the real-time simulation of sheet materials for computer generated imagery

Despite the resources devoted to computer graphics technology over the last 40 years, there is still a need to increase the realism with which flexible materials are simulated. However, to date reported methods are restricted in their application by their use of two-dimensional structures and implicit integration methods that lend themselves to modelling cloth-like sheets but not stiffer, thicker materials in which bending moments play a significant role. This thesis presents a real-time, computationally efficient environment for simulations of sheet materials. The approach described differs from other techniques principally through its novel use of multilayer sheet structures. In addition to more accurately modelling bending moment effects, it also allows the effects of increased temperature within the environment to be simulated. Limitations of this approach include the increased difficulties of calibrating a realistic and stable simulation compared to implicit based methods. A series of experiments are conducted to establish the effectiveness of the technique, evaluating the suitability of different integration methods, sheet structures, and simulation parameters, before conducting a Human Computer Interaction (HCI) based evaluation to establish the effectiveness with which the technique can produce credible simulations. These results are also compared against a system that utilises an established method for sheet simulation and a hybrid solution that combines the use of 3D (i.e. multilayer) lattice structures with the recognised sheet simulation approach. The results suggest that the use of a three-dimensional structure does provide a level of enhanced realism when simulating stiff laminar materials although the best overall results were achieved through the use of the hybrid model

Planning Framework for Robotic Pizza Dough Stretching with a Rolling Pin

Stretching a pizza dough with a rolling pin is a nonprehensile manipulation. Since the object is deformable, force closure cannot be established, and the manipulation is carried out in a nonprehensile way. The framework of this pizza dough stretching application that is explained in this chapter consists of four sub-procedures: (i) recognition of the pizza dough on a plate, (ii) planning the necessary steps to shape the pizza dough to the desired form, (iii) path generation for a rolling pin to execute the output of the pizza dough planner, and (iv) inverse kinematics for the bi-manual robot to grasp and control the rolling pin properly. Using the deformable object model described in Chap. 3, each sub-procedure of the proposed framework is explained sequentially

A biomechanics-based articulation model for medical applications

Computer Graphics came into the medical world especially after the arrival of 3D medical imaging. Computer Graphics techniques are already integrated in the diagnosis procedure by means of the visual tridimensional analysis of computer tomography, magnetic resonance and even ultrasound data. The representations they provide, nevertheless, are static pictures of the patients' body, lacking in functional information. We believe that the next step in computer assisted diagnosis and surgery planning depends on the development of functional 3D models of human body. It is in this context that we propose a model of articulations based on biomechanics. Such model is able to simulate the joint functionality in order to allow for a number of medical applications. It was developed focusing on the following requirements: it must be at the same time simple enough to be implemented on computer, and realistic enough to allow for medical applications; it must be visual in order for applications to be able to explore the joint in a 3D simulation environment. Then, we propose to combine kinematical motion for the parts that can be considered as rigid, such as bones, and physical simulation of the soft tissues. We also deal with the interaction between the different elements of the joint, and for that we propose a specific contact management model. Our kinematical skeleton is based on anatomy. Special considerations have been taken to include anatomical features like axis displacements, range of motion control, and joints coupling. Once a 3D model of the skeleton is built, it can be simulated by data coming from motion capture or can be specified by a specialist, a clinician for instance. Our deformation model is an extension of the classical mass-spring systems. A spherical volume is considered around mass points, and mechanical properties of real materials can be used to parameterize the model. Viscoelasticity, anisotropy and non-linearity of the tissues are simulated. We particularly proposed a method to configure the mass-spring matrix such that the objects behave according to a predefined Young's modulus. A contact management model is also proposed to deal with the geometric interactions between the elements inside the joint. After having tested several approaches, we proposed a new method for collision detection which measures in constant time the signed distance to the closest point for each point of two meshes subject to collide. We also proposed a method for collision response which acts directly on the surfaces geometry, in a way that the physical behavior relies on the propagation of reaction forces produced inside the tissue. Finally, we proposed a 3D model of a joint combining the three elements: anatomical skeleton motion, biomechanical soft tissues deformation, and contact management. On the top of that we built a virtual hip joint and implemented a set of medical applications prototypes. Such applications allow for assessment of stress distribution on the articular surfaces, range of motion estimation based on ligament constraint, ligament elasticity estimation from clinically measured range of motion, and pre- and post-operative evaluation of stress distribution. Although our model provides physicians with a number of useful variables for diagnosis and surgery planning, it should be improved for effective clinical use. Validation has been done partially. However, a global clinical validation is necessary. Patient specific data are still difficult to obtain, especially individualized mechanical properties of tissues. The characterization of material properties in our soft tissues model can also be improved by including control over the shear modulus

Collision response analysis and fracture simulation of deformable objects for computer graphics

Computer Animation is a sub-field of computer graphics with an emphasis on the time-dependent description of interested events. It has been used in many disciplines such as entertainment, scientific visualization, industrial design, multimedia, etc. Modeling of deformable objects in a dynamic interaction and/or fracture process has been an active research topic in the past decade. The main objective of this thesis is to provide a new effective approach to address the dynamic interaction and fracture simulation. With respect to the dynamic interaction between deformable objects, this thesis proposes a new semi-explicit local collision response analysis (CRA) algorithm which is better than most of previous approaches in three aspects: computational efficiency, accuracy mid generality. The computational cost of the semi-explicit local CRA algorithm is guaranteed to be O('n') for each time step, which is especially desirable for the collision response analysis of complex systems. With the use of the Lagrange multiplier method, the send-explicit local CPA algorithm avoids shortcomings associated with the penalty method and provides an accurate description of detailed local deformation during a collision process. The generic geometric constraint and the Gauss-Seidel iteration for enforcing the loading constraint such as Coulomb friction law make the semi-explicit local CRA algorithm to be general enough to handle arbitrary oblique collisions. The experimental results indicate that the semi-explicit local CRA approach is capable of capturing all the key features during collision of deformable objects and matches closely with the theoretical solution of a classic collision problem in solid mechanics. In the fracture simulation, a new element-split method is proposed, which has a sounder mechanical basis than previous approaches in computer graphics and is more flexible to accommodate different material fracture criteria such that different failure patterns are obtained accordingly. Quantitative simulation results show that the element-split approach is consistent with the theoretical Mohr's circle analysis and the slip-line theory in plasticity, while qualitative results indicate its visual effectiveness

A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected] present a unified method to simulate deformable elastic bodies consisting of mixed-dimensional components represented with potentially non-manifold simplicial meshes. Building on well-known simplicial rod, shell, and solid models for elastic continua, we categorize and define a comprehensive palette expressing all possible constraints and elastic energies for stiff and flexible connections between the 1D, 2D, and 3D components of a single conforming simplicial mesh. This palette consists of three categories: point connections, in which simplices meet at a single vertex around which they may twist and bend; curve connections in which simplices share an edge around which they may rotate (bend) relative to one another; and surface connections, in which a shell is embedded on or into a solid. To define elastic behaviors across non-manifold point connections, we adapt and apply parallel transport concepts from elastic rods. To address discontinuous forces that would otherwise arise when large accumulated relative rotations wrap around in the space of angles, we develop an incremental angle-update strategy. Our method provides a conceptually simple, flexible, and highly expressive framework for designing complex elastic objects, by modeling the geometry with a single simplicial mesh and decorating its elements with appropriate physical models (rod, shell, solid) and connection types (point, curve, surface). We demonstrate a diverse set of possible interactions achievable with our method, through technical and application examples, including scenes featuring complex aquatic creatures, children's toys, and umbrellas.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (RGPIN-04360-2014

Real-time simulation and visualisation of cloth using edge-based adaptive meshes

Real-time rendering and the animation of realistic virtual environments and characters has progressed at a great pace, following advances in computer graphics hardware in the last decade. The role of cloth simulation is becoming ever more important in the quest to improve the realism of virtual environments. The real-time simulation of cloth and clothing is important for many applications such as virtual reality, crowd simulation, games and software for online clothes shopping. A large number of polygons are necessary to depict the highly exible nature of cloth with wrinkling and frequent changes in its curvature. In combination with the physical calculations which model the deformations, the effort required to simulate cloth in detail is very computationally expensive resulting in much diffculty for its realistic simulation at interactive frame rates. Real-time cloth simulations can lack quality and realism compared to their offline counterparts, since coarse meshes must often be employed for performance reasons. The focus of this thesis is to develop techniques to allow the real-time simulation of realistic cloth and clothing. Adaptive meshes have previously been developed to act as a bridge between low and high polygon meshes, aiming to adaptively exploit variations in the shape of the cloth. The mesh complexity is dynamically increased or refined to balance quality against computational cost during a simulation. A limitation of many approaches is they do not often consider the decimation or coarsening of previously refined areas, or otherwise are not fast enough for real-time applications. A novel edge-based adaptive mesh is developed for the fast incremental refinement and coarsening of a triangular mesh. A mass-spring network is integrated into the mesh permitting the real-time adaptive simulation of cloth, and techniques are developed for the simulation of clothing on an animated character

Coupling, Conservation, and Performance in Numerical Simulations

This thesis considers three aspects of the numerical simulations, which arecoupling, conservation, and performance. We conduct a project and addressone challenge from each of these aspects.We propose a novel penalty force to enforce contacts with accurate Coulombfriction. The force is compatible with fully-implicit time integration and theuse of optimization-based integration. In addition to processing collisionsbetween deformable objects, the force can be used to couple rigid bodies todeformable objects or the material point method. The force naturally leads tostable stacking without drift over time, even when solvers are not run toconvergence. The force leads to an asymmetrical system, and we provide apractical solution for handling these.Next we present a new technique for transferring momentum and velocity betweenparticles and MAC grids based on the Affine-Particle-In-Cell (APIC) frameworkpreviously developed for co-locatedgrids. We extend the original APIC paper and show thatthe proposed transfers preserve linear and angular momentum and also satisfyall of the original APIC properties.Early indications in the original APIC paper suggested that APIC might besuitable for simulating high Reynolds fluids due to favorable retention ofvortices, but these properties were not studied further. We use twodimensional Fourier analysis to investigate dissipation in the limit \dt=0.We investigate dissipation and vortex retention numerically to quantify theeffectiveness of APIC compared with other transfer algorithms.Finally we present an efficient solver for problems typically seen inmicrofluidic applications.Microfluidic ``lab on a chip'' devices are small devices that operate on smalllength scales on small volumes of fluid. Designs for microfluidic chips aregenerally composed of standardized and often repeated components connected bylong, thin, straight fluid channels. We propose a novel discretizationalgorithm for simulating the Stokes equations on geometry with these features,which produces sparse linear systems with many repeated matrix blocks. Thediscretization is formally third order accurate for velocity and second orderaccurate for pressure in the $L^\infty$ norm. We also propose a novel linearsystem solver based on cyclic reduction, reordered sparse Gaussian elimination,and operation caching that is designed to efficiently solve systems withrepeated matrix blocks

Physically Interacting With Four Dimensions

Thesis (Ph.D.) - Indiana University, Computer Sciences, 2009People have long been fascinated with understanding the fourth dimension. While making pictures of 4D objects by projecting them to 3D can help reveal basic geometric features, 3D graphics images by themselves are of limited value. For example, just as 2D shadows of 3D curves may have lines crossing one another in the shadow, 3D graphics projections of smooth 4D topological surfaces can be interrupted where one surface intersects another. The research presented here creates physically realistic models for simple interactions with objects and materials in a virtual 4D world. We provide methods for the construction, multimodal exploration, and interactive manipulation of a wide variety of 4D objects. One basic achievement of this research is to exploit the free motion of a computer-based haptic probe to support a continuous motion that follows the \emph{local continuity\/} of a 4D surface, allowing collision-free exploration in the 3D projection. In 3D, this interactive probe follows the full local continuity of the surface as though we were in fact \emph{physically touching\/} the actual static 4D object. Our next contribution is to support dynamic 4D objects that can move, deform, and collide with other objects as well as with themselves. By combining graphics, haptics, and collision-sensing physical modeling, we can thus enhance our 4D visualization experience. Since we cannot actually place interaction devices in 4D, we develop fluid methods for interacting with a 4D object in its 3D shadow image using adapted reduced-dimension 3D tools for manipulating objects embedded in 4D. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D interactive or haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the real-world experience accessible to human beings

Real-time Physics Based Simulation for 3D Computer Graphics

Restoration of realistic animation is a critical part in the area of computer graphics. The goal of this sort of simulation is to imitate the behavior of the transformation in real life to the greatest extent. Physics-based simulation provides a solid background and proficient theories that can be applied in the simulation. In this dissertation, I will present real-time simulations which are physics-based in the area of terrain deformation and ship oscillations. When ground vehicles navigate on soft terrains such as sand, snow and mud, they often leave distinctive tracks. The realistic simulation of such vehicle-terrain interaction is important for ground based visual simulations and many video games. However, the existing research in terrain deformation has not addressed this issue effectively. In this dissertation, I present a new terrain deformation algorithm for simulating vehicle-terrain interaction in real time. The algorithm is based on the classic terramechanics theories, and calculates terrain deformation according to the vehicle load, velocity, tire size, and soil concentration. As a result, this algorithm can simulate different vehicle tracks on different types of terrains with different vehicle properties. I demonstrate my algorithm by vehicle tracks on soft terrain. In the field of ship oscillation simulation, I propose a new method for simulating ship motions in waves. Although there have been plenty of previous work on physics based fluid-solid simulation, most of these methods are not suitable for real-time applications. In particular, few methods are designed specifically for simulating ship motion in waves. My method is based on physics theories of ship motion, but with necessary simplifications to ensure real-time performance. My results show that this method is well suited to simulate sophisticated ship motions in real time applications