BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Henrik Schumacher (TU Chemnitz) DTSTART:20220509T134000Z DTEND:20220509T151000Z DTSTAMP:20260405T174944Z UID:NSCM/62 DESCRIPTION:Title: Re pulsive Curves and Surfaces\nby Henrik Schumacher (TU Chemnitz) as par t of Nečas Seminar on Continuum Mechanics\n\n\nAbstract\nFunctionals that penalize bending or stretching of a surface play a key role in geometric and scientific\ncomputing\, but to date have ignored a very basic requirem ent: in many situations\, surfaces must not pass\nthrough themselves or ea ch other. This paper develops a numerical framework for optimization of su rface\ngeometry while avoiding (self-)collision. The starting point is the tangent-point energy\, which effectively pushes\napart pairs of points th at are close in space but distant along the surface. We develop a discreti zation of\nthis energy for triangle meshes and introduce a novel accelerat ion scheme based on a fractional Sobolev inner\nproduct. In contrast to si milar schemes developed for curves (cf. [2])\, we avoid the complexity of building a\nmultiresolution mesh hierarchy by decomposing our precondition er into two ordinary Poisson equations\, plus\nforward application of a fr actional differential operator. We further accelerate this scheme via hier archical\napproximation and describe how to incorporate a variety of const raints (on area\, volume\, etc.). Finally\, we\nexplore how this machinery might be applied to problems in mathematical visualization\, geometric mo deling\,\nand geometry processing.\nJoint work with: Chris Yu\, Caleb Brak ensiek\, Keenan Crane\nReferences\n[1] C. Yu\, C. Brakensiek\, H. Schumach er\, and C. Keenan Repulsive Surfaces. ACM Trans. Graph.\, 40(6):1–19\,\ n2021.\n[2] C. Yu\, H. Schumacher\, and C. Keenan Repulsive Curves. ACM Tr ans. Graph.\, 40(2):1-21\, 2021.\n LOCATION:https://researchseminars.org/talk/NSCM/62/ END:VEVENT END:VCALENDAR