The AROMATH seminar will usually happen on Tuesday at 10h30-11h30 every two weeks, except for a few deviations.
The presentations will typically take place at Inria Sophia Antipolis, Byron Blanc 106, and also online.
To join online, at https://cutt.ly/aromath or with a web browser at https://cutt.ly/aromath-web
use meeting ID: 828 5859 7791, passcode: 123
Gershon Elber -- (Geometric) Constraints Solving Using Multivariate Spline Functions
10:30
16 September 2024
Abstract: We present a subdivision based paradigm to solve a set of (piecewise) rational constraints represented by multivariate (piecewise) rational spline functions. The constraints can be formulated as either inequalities or equalities (semi-algebraic sets). The presented solver is not only capable of finding all solutions, globally, but is also capable of handling solution spaces of dimensions larger than zero. A special care is taken to guarantee all roots are isolated via a single solution geometric test.
This solver was applied to a large variety of geometric problems above the (piecewise) rationals domain that will be discussed as part of the talk. This set includes point-curve and curve-curve bi-tangents, convex hulls and kernels of planar curves and 3-space surfaces, ray-traps (bouncing billiard balls) between planar curves, the 10th Apollonius problem (circle tangent to given three circles), bounding circles, bisectors and voronoi regions, mold design, visibility and accessibility, sweeps and envelopes, and self-intersection trimming in offset approximations of curves and surfaces.
Link: https://www.microsoft.com/en-us/microsoft-teams/join-a-meeting has the following access data: ID: 359 737 944 764, Passcode: eEJmqW
