Some properties of the curve straightening flow in the plane
Some properties of the curve straightening flow in the plane
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平面内曲线矫直流的一些性质
DOI：
10.1090/s0002-9947-1989-0989580-5
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发表时间：
1989
影响因子：
1.3
通讯作者：
Anders Linnér
中科院分区：
文献类型：
--
作者：
Anders Linnér
。我们将显式计算闭曲线空间上的全平方曲率泛函的梯度。算例表明，沿梯度轨迹的流动可能会导致曲线的自交。我们证明了瞬时变为非凸的严格凸曲线的存在性。总而言之，我们使用计算机图形学来说明自交叉是如何产生的。
. We will explicitly compute the gradient of the total squared curvature functional on a space of closed curves. An example shows that the flow along the gradient trajectory may cause curves to develop self-intersections. We prove the existence of strictly convex curves that momentarily turn nonconvex. In conclusion we use computer graphics to illustrate how self-intersections come about.