Construction and Analysis of a $G^1$-smooth polynomial family of Approximate Catmull-Clark Surfaces

Abstract: Subdivision surfaces are a widely used numerical method to reconstruct smooth surfaces starting from a polyhedral mesh of any topology. However, in presence of the so-called extraordinary vertices, i.e. vertices with valence $N\neq4$, the limit surface presents a loss of regularity like, for instance, the Catmull-Clark surface. 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 masks, employing quadratic glueing data functions I modify the previous scheme 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 involved control points. Moreover, I conduct a curvature analysis in order to assert the quality of the resulting surfaces, both visually and numerically. Furthermore, dimension formula and basis construction for the obtained space are presented.

computational geometryalgebraic geometry

Audience: researchers in the topic

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Aromath seminar

Series comments: The AROMATH seminar takes place typically every other Wednesday at 14:00 (FR), except from a few deviations. Remote participation via Zoom: cutt.ly/aromath Meeting ID: 828 5859 7791 Passcode: 123 Join via web browser: cutt.ly/aromath-web