Eulerian on Lagrangian Cloth Simulation

This thesis introduces a novel Eulerian-on-Lagrangian (EoL) approach for simulating cloth. This approach allows for the simulation of traditionally difficult cloth scenarios, such as draping and sliding cloth over sharp features like the edge of a table. A traditional Lagrangian approach models a cloth as a series of connected nodes. These nodes are free to move in 3d space, but have difficulty with sliding over hard edges. The cloth cannot always bend smoothly around these edges, as motion can only occur at existing nodes. An EoL approach adds additional flexibility to a Lagrangian approach by constructing special Eulerian on Lagrangian nodes (EoL Nodes), where cloth material can pass through a fixed point. On contact with the edge of a box, EoL nodes are introduced directly on the edge. These nodes allow the cloth to bend exactly at the edge, and pass smoothly over the area while sliding. Using this ‘Eulerian-on-Lagrangian’ discretization, a set of rules for introducing and constraining EoL Nodes, and an adaptive remesher, This simulator allows cloth to move in a sliding motion over sharp edges. The current implementation is limited to cloth collision with static boxes, but the method presented can be expanded to include contact with more complicated meshes and dynamic rigid bodies

Novel Degrees of Freedom, Constraints, and Stiffness Formulation for Physically Based Animation

I identify and improve upon three distinct components of physically simulated systems with the aim of increasing both robustness and efficiency for the application of computer graphics: A) the degrees of freedom of a system; B) the constraints put on that system; C) and the stiffness that derives from force differentiation and in turn enables implicit integration techniques. These three components come up in many implementations of physics-based simulation in computer animation. From a combination of these components, I explore four novel ideas implemented and experimented on over the course of my graduate degree. Eulerian-on-Lagrangian Cloth Simulation resolves a longstanding problem of simulating contact-mediated interaction of cloth and sharp geometric features by exploring a combination of all three of our components. Bilateral Staggered Projections for Joints explores the constrained degrees of freedom of articulated rigid bodies in a reduced state to extend the popular Staggered Projects technique into a novel formulation for rapid evaluation of frictional articulated dynamics. Condensation Jacobian with Adaptivity looks at using reduction methods to improve the efficiency of soft body deformations by allowing larger time step in dynamics simulations. Finally, Ldot: Boosting Deformation Performance with Cholesky Extrapolation explores the inner workings of sparse direct solvers to introduce a Cholesky factorization that is linearly extrapolated in time, which can improve the performance when encapsulated inside an iterative nonlinear solver

Learning an Intrinsic Garment Space for Interactive Authoring of Garment Animation

Authoring dynamic garment shapes for character animation on body motion is one of the fundamental steps in the CG industry. Established workflows are either time and labor consuming (i.e., manual editing on dense frames with controllers), or lack keyframe-level control (i.e., physically-based simulation). Not surprisingly, garment authoring remains a bottleneck in many production pipelines. Instead, we present a deep-learning-based approach for semi-automatic authoring of garment animation, wherein the user provides the desired garment shape in a selection of keyframes, while our system infers a latent representation for its motion-independent intrinsic parameters (e.g., gravity, cloth materials, etc.). Given new character motions, the latent representation allows to automatically generate a plausible garment animation at interactive rates. Having factored out character motion, the learned intrinsic garment space enables smooth transition between keyframes on a new motion sequence. Technically, we learn an intrinsic garment space with an motion-driven autoencoder network, where the encoder maps the garment shapes to the intrinsic space under the condition of body motions, while the decoder acts as a differentiable simulator to generate garment shapes according to changes in character body motion and intrinsic parameters. We evaluate our approach qualitatively and quantitatively on common garment types. Experiments demonstrate our system can significantly improve current garment authoring workflows via an interactive user interface. Compared with the standard CG pipeline, our system significantly reduces the ratio of required keyframes from 20% to 1 -- 2%

Motion Guided Deep Dynamic 3D Garments

Realistic dynamic garments on animated characters have many AR/VR applications. While authoring such dynamic garment geometry is still a challenging task, data-driven simulation provides an attractive alternative, especially if it can be controlled simply using the motion of the underlying character. In this work, we focus on motion guided dynamic 3D garments, especially for loose garments. In a data-driven setup, we first learn a generative space of plausible garment geometries. Then, we learn a mapping to this space to capture the motion dependent dynamic deformations, conditioned on the previous state of the garment as well as its relative position with respect to the underlying body. Technically, we model garment dynamics, driven using the input character motion, by predicting per-frame local displacements in a canonical state of the garment that is enriched with frame-dependent skinning weights to bring the garment to the global space. We resolve any remaining per-frame collisions by predicting residual local displacements. The resultant garment geometry is used as history to enable iterative rollout prediction. We demonstrate plausible generalization to unseen body shapes and motion inputs, and show improvements over multiple state-of-the-art alternatives.Comment: 11 page

Spatially Adaptive Cloth Regression with Implicit Neural Representations

The accurate representation of fine-detailed cloth wrinkles poses significant challenges in computer graphics. The inherently non-uniform structure of cloth wrinkles mandates the employment of intricate discretization strategies, which are frequently characterized by high computational demands and complex methodologies. Addressing this, the research introduced in this paper elucidates a novel anisotropic cloth regression technique that capitalizes on the potential of implicit neural representations of surfaces. Our first core contribution is an innovative mesh-free sampling approach, crafted to reduce the reliance on traditional mesh structures, thereby offering greater flexibility and accuracy in capturing fine cloth details. Our second contribution is a novel adversarial training scheme, which is designed meticulously to strike a harmonious balance between the sampling and simulation objectives. The adversarial approach ensures that the wrinkles are represented with high fidelity, while also maintaining computational efficiency. Our results showcase through various cloth-object interaction scenarios that our method, given the same memory constraints, consistently surpasses traditional discrete representations, particularly when modelling highly-detailed localized wrinkles.Comment: 16 pages, 13 figure

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