Mathieu Desbrun is the John W. & Herberta M. Miles Professor at the California Institute of Technology (Caltech), where he is the head of the Computing & Mathematical Sciences department and the director of the Information Science and Technology initiative. He leads the Applied Geometry lab, focusing on discrete differential modeling—the development of differential, yet readily discretizable foundations for computational modeling—and a wide spectrum of applications, ranging from discrete geometry processing to solid and fluid mechanics and field theory. He is the recipient of an ACM SIGGRAPH New Significant Researcher award, and of a NSF CAREER award.
The Power of Primal/Dual Meshes
Triangle meshes have found widespread acceptance in computer graphics as a simple, convenient, and versatile representation of surfaces. In particular, computing on such simplicial meshes is a workhorse in a variety of graphics applications. In this context, mesh duals (tied to Poincare duality and extending the well known relationship between Delaunay triangulations and Voronoi diagrams) are often useful, from physical simulation of fluids to mesh parameterization. However, the precise embedding of a dual diagram with respect to its triangulation (i.e., the placement of dual vertices) has mostly remained a matter of taste or a numerical after-thought, and barycentric vs. circumcentric duals are often the only options chosen in practice.In this talk we discuss the notion of orthogonal dual diagrams, and show through a series of recent works that exploring the full space of orthogonal dual diagrams to a given simplicial complex is not only powerful and numerically beneficial, but it also reveals (using tools from algebraic topology and computational geometry) discrete analogs to continuous properties. Applications varying from point sampling to masonry will be covered.