Wednesday, November 23rd, 2016, 16:10
Gershon Elber, The Technion
Contacts related queries can be found in geometric design and other field, in numerous applications. Line-curve and plane-surface tangential contacts can serve as basic tools in the computation of convex hulls of curves and surfaces. In kinematics, contacts' analysis can be used to devise motion over freeforms. In robotics, bi- and tri-tangential contacts can be used to analyze motion of closed freeform (deformable) shapes in the plane and in manufacturing, bi-tangential and even higher order contacts can help in tool path planning of multi-axis machining.
In this talk, I will portray these problems and others and show how they can all be handled under one framework that reduces these problems to sets of algebraic constraints. These algebraic constraints are then precisely resolved using a subdivision based solver for (piecwise) polynomial multivariates we develop. Results demonstrating all these applications will also be presented.
* Some of this work has been conducted in collaboration with many others including Michael Barton, Myung-Soo Kim, Yong Joon Kim, Jonathan Mizhari, Helmut Pottmann, Aviv Segal, and Nadav Shragai.