Marc Alexa We introduce the notion of harmonic triangulations: a harmonic triangulation simultaneously minimizes the Dirichlet energy of all piecewise linear functions. By a famous result of Rippa, Delaunay triangulations are the harmonic triangulations of planar point sets. We prove by explicit counterexample that in 3D a harmonic triangulation does not exist in general. However, […]

Thomas Buffet, Damien Rohmer, Loïc Barthe, Laurence Boissieux, Marie-Paule Cani We propose a robust method for untangling an arbitrary number of cloth layers, possibly exhibiting deep interpenetrations, to a collision-free state, ready for animation. Our method relies on an intermediate, implicit representation to solve the problem: the user selects a few garments stored in a […]

Teseo Schneider, Jérémie Dumas, Xifeng Gao, Mario Botsch, Daniele Panozzo, Denis Zorin We introduce an integrated meshing and finite element method pipeline enabling solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of […]

Bowen Yang, William Corse, Jiecong Lu, Joshuah Wolper, Chenfanfu Jiang We present a novel approach for animating incompressible fluids with Eulerian advection-projection solvers on the surface of a sphere by extending the recent work by Hill and Henderson [2016] with a staggered spherical grid discretization. By doing so, we avoid the infamous checkerboard null modes. […]

Mickeal Verschoor, Andrei C. Jalba Simulating (elastically) deformable models that can collide with each other and with the environment remains a challenging task. The resulting contact problems can be elegantly approached using Lagrange multipliers to represent the unknown magnitude of the response forces. Typical methods construct and solve a Linear Complementarity Problem (LCP) to obtain […]

Byungsoo Kim, Vinicius C. Azevedo, Nils Thuerey, Theodore Kim, Markus Gross, Barbara Solenthaler This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to the capability of deep learning architectures to […]

Ying Wang, Nicolas J. Weidner, Margaret A. Baxter, Yura Hwang, Danny Kaufman, Shinjiro Sueda It is well known that the dynamics of articulated rigid bodies can be solved in O(n) time using a recursive method, where n is the number of joints. However, when elasticity is added between the bodies (eg damped springs), with linearly […]

Ryan Goldade, Yipeng Wang, Mridul Aanjaneya, Christopher Batty While pressure forces are often the bottleneck in (near-)inviscid fluid simulations, viscosity can impose orders of magnitude greater computational costs at lower Reynolds numbers. We propose an implicit octree finite difference discretization that significantly accelerates the solution of the free surface viscosity equations using adaptive staggered grids, […]

Lawson Fulton, Vismay Modi, David Duvenaud, David I. W. Levin, Alec Jacobson We propose the first reduced model simulation framework for deformable solid dynamics using autoencoder neural networks.We provide a data-driven approach to generating nonlinear reduced spaces for deformation dynamics. In contrast to previous methods using machine learning which accelerate simulation by approximating the time-stepping […]

Y. Cortial, A. Peytavie, E. Galin, E. Guérin We present a procedural method for authoring synthetic tectonic planets. Instead of relying on computationally demanding physically-based simulations, we capture the fundamental phenomena into a procedural method that faithfully reproduces large-scale planetary features generated by the movement and collision of the tectonic plates. We approximate complex phenomena […]