BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michelangelo Marsala (Aromath\, Inria) DTSTART:20220406T090000Z DTEND:20220406T100000Z DTSTAMP:20260423T021302Z UID:Aromath/1 DESCRIPTION:Title: Construction and Analysis of a $G^1$-smooth polynomial family of Approxima te Catmull-Clark Surfaces\nby Michelangelo Marsala (Aromath\, Inria) a s part of Aromath seminar\n\n\nAbstract\nSubdivision surfaces are a widely used numerical method to reconstruct smooth surfaces starting from a poly hedral mesh of any topology. However\, in presence of the so-called extrao rdinary vertices\, i.e. vertices with valence $N\\neq4$\, the limit surfac e presents a loss of regularity like\, for instance\, the Catmull-Clark su rface. To recover smoothness around these particular points the multipatch approach can be used\, for instance\, imposing tangent plane continuity ( $G^1$ smoothness) around the extraordinary patches. Starting from the work of Loop and Shaefer (2008) which presents an approximate bicubic Bézier patching of the Catmull-Clark limit surface defined by local smoothing mas ks\, employing quadratic glueing data functions I modify the previous sche me to obtain $G^1$ continuity around the EVs. This construction leads to a family of surfaces that are given by means of explicit formulas for all i nvolved control points. Moreover\, I conduct a curvature analysis in order to assert the quality of the resulting surfaces\, both visually and numer ically. Furthermore\, dimension formula and basis construction for the obt ained space are presented.\n\nRemote participation via Zoom: https://cutt. ly/aromath\nMeeting ID: 828 5859 7791\nPasscode: 123\nJoin via web browser : https://cutt.ly/aromath-web\n LOCATION:https://researchseminars.org/talk/Aromath/1/ END:VEVENT END:VCALENDAR