Efficient Deformations Using Custom Coordinate Systems

Physics-based deformable object simulations have been playing an increasingly important role in 3D computer graphics. They have been adopted for humanoid character animations as well as special effects such as fire and explosion. However, simulations of large, complex systems can consume large amounts of computation and mostly remain offline, which prohibits their use for interactive applications.We present several highly efficient schemes for deformable object simulation using custom spatial coordinate systems. Our choices span the spectrum of subspace to full space and both Lagrangian and Eulerian viewpoints.Subspace methods achieve massive speedups over their “full space” counterparts by drastically reducing the degrees of freedom involved in the simulation. A long standing difficulty in subspace simulation is incorporating various non-linearities. They introduce expensive computational bottlenecks and quite often cause novel deformations that are outside the span of the subspace.We address these issues in articulated deformable body simulations from a Lagrangian viewpoint. We remove the computational bottleneck of articulated self-contact handling by deploying a pose-space cubature scheme, a generalization of the standard “cubature” approximation. To handle novel deformations caused by arbitrary external collisions, we introduce a generic approach called subspace condensation, which activates full space simulation on the fly when an out-of-basis event is encountered. Our proposed frameworkefficiently incorporates various non-linearities and allows subspace methods to be used in cases where they previously would not have been considered.Deformable solids can interact not only with each other, but also with fluids. Wedesign a new full space method that achieves a two-way coupling between deformable solids and an incompressible fluid where the underlying geometric representation is entirely Eulerian. No-slip boundary conditions are automatically satisfied by imposing a global divergence-free condition. We are able to simulate multiple solids undergoing complex, frictional contact while simultaneously interacting with a fluid. The complexity of the scenarios we are able to simulate surpasses those that we have seen from any previous method

Quotient-Space Motion Planning

International audienceA motion planning algorithm computes the motion of a robot by computing a path through its configuration space. To improve the runtime of motion planning algorithms, we propose to nest robots in each other, creating a nested quotient-space decomposition of the configuration space. Based on this decomposition we define a new roadmap-based motion planning algorithm called the Quotient-space roadMap Planner (QMP). The algorithm starts growing a graph on the lowest dimensional quotient space, switches to the next quotient space once a valid path has been found, and keeps updating the graphs on each quotient space simultaneously until a valid path in the configuration space has been found. We show that this algorithm is probabilistically complete and outperforms a set of state-of-the-art algorithms implemented in the open motion planning library (OMPL)

Automatic generation of dynamic skin deformation for animated characters

© 2018 by the authors. Since non-automatic rigging requires heavy human involvements, and various automatic rigging algorithms are less efficient in terms of computational efficiency, especially for current curve-based skin deformation methods, identifying the iso-parametric curves and creating the animation skeleton requires tedious and time-consuming manual work. Although several automatic rigging methods have been developed, but they do not aim at curve-based models. To tackle this issue, this paper proposes a new rigging algorithm for automatic generation of dynamic skin deformation to quickly identify iso-parametric curves and create an animation skeleton in a few milliseconds, which can be seamlessly used in curve-based skin deformation methods to make the rigging process fast enough for highly efficient computer animation applications

Analysis of friction coupling and the Painlevé paradox in multibody systems

Multibody models are useful to describe the macroscopic motion of the elements of physical systems. Modeling contact in such systems can be challenging, especially if friction at the contact interface is taken into account. Furthermore, the dynamics equations of multibody systems with contacts and Coulomb friction may become ill-posed due to friction coupling, as in the Painlevé paradox, where a solution for system dynamics may not be found. Here, the dynamics problem is considered following a general approach so that friction phenomena, such as dynamic jamming, can be analyzed. The effect of the contact forces on the velocity field of the system is the cornerstone of the proposed formulation, which is used to analyze friction coupling in multibody systems with a single contact. In addition, we introduce a new representation of the so-called generalized friction cone, a quadratic form defined in the contact velocity space. The geometry of this cone can be used to determine the critical cases where the solvability of the system dynamic equations can be compromised. Moreover, it allows for assessing friction coupling at the contact interface, and obtaining the values of the friction coefficient that can make the dynamics formulation inconsistent. Finally, the classical Painlevé example of a single rod and the multibody model of an articulated arm are used to illustrate how the proposed cone can detect the cases where the dynamic equations have no solution, or multiple solutions.Postprint (author's final draft

Animation, Simulation, and Control of Soft Characters using Layered Representations and Simplified Physics-based Methods

Realistic behavior of computer generated characters is key to bringing virtual environments, computer games, and other interactive applications to life. The plausibility of a virtual scene is strongly influenced by the way objects move around and interact with each other. Traditionally, actions are limited to motion capture driven or pre-scripted motion of the characters. Physics enhance the sense of realism: physical simulation is required to make objects act as expected in real life. To make gaming and virtual environments truly immersive,it is crucial to simulate the response of characters to collisions and to produce secondary effects such as skin wrinkling and muscle bulging. Unfortunately, existing techniques cannot generally achieve these effects in real time, do not address the coupled response of a character's skeleton and skin to collisions nor do they support artistic control. In this dissertation, I present interactive algorithms that enable physical simulation of deformable characters with high surface detail and support for intuitive deformation control. I propose a novel unified framework for real-time modeling of soft objects with skeletal deformations and surface deformation due to contact, and their interplay for object surfaces with up to tens of thousands of degrees of freedom.I make use of layered models to reduce computational complexity. I introduce dynamic deformation textures, which map three dimensional deformations in the deformable skin layer to a two dimensional domain for extremely efficient parallel computation of the dynamic elasticity equations and optimized hierarchical collision detection. I also enhance layered models with responsive contact handling, to support the interplay between skeletal motion and surface contact and the resulting two-way coupling effects. Finally, I present dynamic morph targets, which enable intuitive control of dynamic skin deformations at run-time by simply sculpting pose-specific surface shapes. The resulting framework enables real-time and directable simulation of soft articulated characters with frictional contact response, capturing the interplay between skeletal dynamics and complex,non-linear skin deformations