Differentiable renderers provide a direct mathematical link between an object's 3D
representation and images of that object. In this work, we develop an approximate …

We consider the optimal control of mechanical systems on Lie groups and develop
numerical methods that exploit the structure of the state space and preserve the system …

This study derives geometric, variational discretization of continuum theories arising in fluid
dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central …

Given a sequence of poses of a body we study the motion resulting when the body is
immersed in a (possibly) moving, incompressible medium. With the poses given, say, by an …

We introduce Spiral, a third-order integration algorithm for the rotational motion of extended
bodies. It requires only one force calculation per time step, does not require quaternion …

Our goal is to design robust algorithms that can be used for building real-time systems, but
rather than starting with overly simplistic particle-based methods, we aim to modify higher …

In this paper, we introduce a novel approach for designing invariant control laws through
potential functions for fully actuated dynamical systems evolving on manifolds by leveraging …

The penalty method is a simple and popular approach to resolving contact in computer
graphics and robotics. Penalty-based contact, however, suffers from stability problems due …

We propose a novel projection scheme that corrects energy fluctuations in simulations of
deformable objects, thereby removing unwanted numerical dissipation and numerical" …

Lie group integrators preserve by construction the Lie group structure of a nonlinear
configuration space. In multibody dynamics, they support a representation of (large) …