Physically-based Editing Of Elastic Motion

Physically-based simulation of deformable objects can generate exquisite result-s, and has become pervasive in computer graphics. However, fine-tuning of an anima-tion often requires a time-consuming trial-and-error process to find the right simulation parameters. Editing an existing simulated sequence to meet user-specified constraints without making the resulting motion visually implausible is therefore crucial in practice.Shape interpolation methods provide fast and reasonable inbetweening of two giv-en geometric shapes, albeit without control over dynamical effects. Recently proposed physically-based interpolation methods provide more dynamics, however, significant us-er interaction is required, because one cannot prescribe only the positions of a portion of the object, which reduces control flexibility. Conversely, sequence editing methods try to find alterations of an input animation to satisfy user-specified constraints. This type of approach lends itself well to partial editing of an input sequence in space and time, which allows users to drag any vertex at any time of the input sequence to revise the animation. However, previous methods based on space-time constraints are typically compute-intensive because of their high-dimensional and nonlinear nature, or produce noticeable artifacts under large edits, and can not provide precise positional constraints. What’s more, most current methods assume a fixed elastic material during the optimiza-tion of control forces, which may not be appropriate for, or compatible with, the type of position constraints that the user imposes. Besides, collision handling is also an impor-tant and challenge problem for motion editing of elastic objects. In this thesis, we investigate space-time constraints, numerical optimization tech-niques, material optimization and QP problem for collision handling, propose several robust and efficient elastic motion editing approaches. Our contributions include:· We present an intuitive and interactive approach for motion editing through space- time constraints on positions. We formulate our motion editing as an optimiza-tion problem with dynamics constraints to enforce a physically plausible result. Through linearization around the input trajectory, we simplify this constrained optimal control problem into an unconstrained quadratic optimization, which we solve efficiently by using adjoint method with conjugate gradient solver.· We construct an efficient and robust subspace coordinates, and significantly im-prove the efficiency and robustness for large elastic motion editing. We adopt this subspace to diagonalize the equation of motion to simplify the space-time con-straints formulation. We build our novel subspace on geometric reduction and cu-bature, significantly speed up the reconstruction of 3D coordinates from subspace coordinates, and provide robustness to large deformation.· We present a new approach to space-time motion editing of elastic objects through material optimization, make it more easier to set the elastic material properly. It provides a unified framework for animation editing, elastic material design and reconstruction. Our solution provides much smaller control forces compared to previous works, and therefore promise more plausible results. We Optimize the elastic material in subspace to reduce the computational cost, and propose an iter-ative scheme to efficiently compute the optimal motion.· We introduce a novel approach for collision handling, which is robust, stable and efficient for large deformable objects with hundreds of thousands DOFs. Our QP solver significantly extends the traditional MPRGP solver to support more general constraints arising in collision handling, while a constraints decoupling scheme further improves the efficiency of this solver.