Lecture 5: Simplicial Complex 2-Manifolds, Simplex and Simplicial Complex
نویسنده
چکیده
Figure 1: Two greatly different curves have a small Hausdroff distance Fréchet distance is a good similarity measurement for curves in Euclidean space. It can be simply described by a daily example. Suppose a dog and its owner are walking along two different paths (curves), connected by a leash. Both of them are moving continuously and forwards only, at any speed or even stop. Then length of the shortest leash is the Fréchet distance between the two paths (curves). Fréchet distance is a good similarity measurement for curves in Euclidean space. For curves on surfaces, distance between two points can be hard to compute. Another way is using the minimal area swept when continuously deforming P and Q into one as their distance. However, it has the same problem as Fréchet distance when handling curves on surfaces. This measurement also requires P and Q to share the same start point and end point, i.e., they form a loop. If they do not, we can connect their start points and end points, respectively, to get a loop.
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