Contact With Circles and Euclidean Invariants of Smooth Surfaces in R3
Contact With Circles and Euclidean Invariants of Smooth Surfaces in R3
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R3 中圆和光滑表面的欧几里得不变量的接触
DOI：
10.1093/qmath/haab058
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Giblin P
中科院分区：
文献类型：
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作者：
Giblin P
我们研究顶点曲线，即实 3 空间中光滑表面的双曲区域中的点集，其中切平面中有一个圆与表面至少有 5 点接触。顶点曲线与平行于且靠近切平面的表面平面部分的微分几何相关，并且与等光度曲线的对称集（即二维图像中的强度的水平集）相关。我们还研究了顶点曲线与抛物线和折线曲线的关系，以及顶点曲线在光滑表面的通用 1 参数族中的演化。
We investigate the vertex curve, that is the set of points in the hyperbolic region of a smooth surface in real 3-space at which there is a circle in the tangent plane having at least 5-point contact with the surface. The vertex curve is related to the differential geometry of planar sections of the surface parallel to and close to the tangent planes, and to the symmetry sets of isophote curves, that is level sets of intensity in a 2-dimensional image. We investigate also the relationship of the vertex curve with the parabolic and flecnodal curves, and the evolution of the vertex curve in a generic 1-parameter family of smooth surfaces.