Partial differential equations (PDEs) with spatially varying coefficients arise throughout
science and engineering, modeling rich heterogeneous material behavior. Yet conventional …

Computer Graphics has a long history in the design of effective algorithms for handling
contact and friction between solid objects. For the sake of simplicity and versatility, most …

We introduce a Monte Carlo method for computing derivatives of the solution to a partial
differential equation (PDE) with respect to problem parameters (such as domain geometry or …

Sum-of-Squares Programming (SOSP) has recently been introduced to graphics as a unified
way to address a large set of difficult problems involving higher order primitives …

The Moment-SOS hierarchy, first introduced in optimization in 2000, is based on the theory
of the S-moment problem and its dual counterpart: polynomials that are positive on S. It turns …

Many geometry processing techniques require the solution of partial differential equations
(PDEs) on manifolds embedded in or, such as curves or surfaces. Such manifold PDEs often …

Continuous collision detection (CCD) between parametric surfaces is typically formulated as
a five-dimensional constrained optimization problem. In the field of CAD and computer …

Collision-avoiding motion planning for articulated robotic arms is one of the major
challenges in robotics. The difficulty of the problem arises from its high dimensionality and …

We propose the Medial Skeletal Diagram, a novel skeletal representation that tackles the
prevailing issues around skeleton sparsity and reconstruction accuracy in existing skeletal …

Iso-surface extraction from an implicit field is a fundamental process in various applications
of computer vision and graphics. When dealing with geometric shapes with complicated …