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

Physics-based modelling, simulation, placement and learning for musculo-skeletal animations.

In character production for Visual Effects, the realism of deformations and flesh dynamics is a vital ingredient of the final rendered moving images shown on screen. This work is a collection of projects completed at the hosting company MPC London focused on the main components needed for the animation of musculo-skeletal systems: primitives modeling, physically accurate simulation, interactive placement. Complementary projects are also presented, including the procedural modeling of wrinkles and a machine learning approach for deformable objects based on Deep Neural Networks. Primitives modeling aims at proposing an approach to generating muscle geometry complete with tendons and fibers from superficial patches sketched on the character skin mesh. The method utilizes the physics of inflatable surfaces and produces meshes ready to be tetrahedralized, that is without compenetrations. A framework for the simulation of muscles, fascia and fat tissues based on the Finite Elements Method (FEM) is presented, together with the theoretical foundations of fiber-based materials with activations and their fitting in the Implicit Euler integration. The FEM solver is then simplified in or- der to achieve interactive rates to show the potential of interactive muscle placement on the skeleton to facilitate the creation of intersection-free primitives using collision detection and resolution. Alongside physics simulation for biological tissues, the thesis explores an approach that extends the Implicit Skinning technique with wrinkles based on convolution surfaces by exploiting the gradients of the combination of bones fields. Finally, this work discusses a possible approach to the learning of physics-based deformable objects based on deep neural networks which makes use of geodesic disks convolutional layers