Surface Patches with Rounded Corners
Benjamin Marussig, Ulrich Reif
TL;DR
This paper investigates surface patches with rounded corners where derivatives are antiparallel, providing conditions for smoothness, analyzing curvature integrability, and presenting illustrative examples.
Contribution
It offers new sufficient and nearly necessary conditions for G^1 smoothness of surface patches with rounded corners and explores their curvature properties.
Findings
Provided conditions for G^1 smoothness of rounded corner patches
Analyzed curvature integrability of such surface patches
Presented examples illustrating theoretical results
Abstract
We analyze surface patches with a corner that is rounded in the sense that the partial derivatives at that point are antiparallel. Sufficient conditions for smoothness are given, which, up to a certain degenerate case, are also necessary. Further, we investigate curvature integrability and present examples
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Numerical Analysis Techniques · Analytic and geometric function theory