Michael Hofer Department of Electrical Engineering "Variational Curve Design on Surfaces" Thursday May 5th, 12:20-1:10, Lind 409

Abstract

Variational interpolation in curved geometries has many applications, so there has ever been demand for geometrically meaningful and efficiently computable splines in general manifolds. We extend the definition of the familiar cubic spline curves and splines in tension to surfaces and show that the geometric characterization of the solution curves is similar to the well-known unrestricted case.

For the numerical solution we use a geometric optimization algorithm which minimizes an energy of curves on surfaces of arbitrary dimension and codimension. The concept works for various applications including the computation of splines in parametric surfaces, level sets, triangle meshes, and point set surfaces, variational motion design, and the design of spline curves in the presence of obstacles via barrier surfaces. We also extended the case of one single curve to a fair network of curves. References to published papers can be found at http://www.geometrie.tuwien.ac.at/hofer/.