找到的旋转中心的点的集合 [英] Finding centre of rotation for a set of points

问题描述

如果我有一个任意点的集合，然后在相同的点的集合某种程度的旋转，没有人知道任何算法来计算/估算，其中旋转中心？或学习的一个领域，都需要这些类型的算法？ 我无法找到任何相关信息。

If I have an arbitrary set of points, and then the same set of points rotated by some degree, does anyone know of any algorithms to calculate/estimate where the centre of the rotation is? Or an area of study where these kinds of algorithms are needed? I am having trouble finding any relevant information.

感谢

推荐答案

假设你有一个点（X，Y），即转移到（X'，Y'）。

Lets say you have one point (x, y), that moved to (x', y').

然后转动中心必须位于垂直于（X，Y）的线 - （X'，Y'），以及交叉的中心（X，Y） - （X'，Y'）。

Then the center of rotation must lie on the line that is perpendicular to (x,y)-(x',y'), and that intersects the center (x,y)-(x',y').

现在采取的另一点，（X2，Y2），即迁往（X'2，Y'2）。这也产生了一个线在其上旋转的中心必须位于

Now take another point, (x2, y2), that moved to (x'2, y'2). This also gives rise to a line on which the center of rotation must be located on.

现在走这两条线，并计算交会。有你有旋转的中心。

Now take these two lines and compute the intersection. There you have the center of rotation.

更新：如果你没有对应这点去的地方，应该不会太难搞清楚。这是从我头顶上的建议：找到的前-points重心。根据来自该点的距离订购点。现在做同样的后-points。两组的顺序，现在应该匹配。 （该点之前最接近质量的的中心的旋转，应该最接近质量中心的点的后的旋转。）

Update: If you don't have the correspondence of which point went where, it shouldn't be too hard to figure out. Here is a suggestion from top of my head: Find the center of mass of the "before"-points. Order the points according to their distance from this point. Now do the same with the "after"-points. The order of the two sets should now match. (The point closest to the center of mass before rotation, should be the point closest to the center of mass after rotation.)

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