如何找到圆弧切片的中点? [英] How to find the middle point of an arc slice?

问题描述

我有一个圆形的切片(由moveTo，lineTo，arc等组成)，需要找到切片的中点.

I have a slice of a circle (that is made of moveTo,lineTo,arc,etc) and need to find the middle point of the slice.

找到下图所示的点背后的数学原理是什么?

What is the math behind finding the point shown in the image below?

推荐答案

在我看来，该部门的质心".

It looks "centroid" of the sector to me.

它的坐标(x轴沿着穿过质心并在原点处的半径)

The co-ordinates of it (with x axis along the radius passing through the centroid and origin at the centre)

centroidX =(4/3) r (sin(A)/A)

centroidX = (4/3)r(sin(A)/A)

centroidY = 0

centroidY = 0

其中"A"是圆弧在中心的角度(以弧度为单位)，"r"是半径.

where 'A' is the angle made by the arc at the centre(in radians) and 'r' is the radius.

这是一种易于推导的公式. 任何形状的几何质心都是所有点的平均值(加权平均值). 在物理学中，物体的质心(AKA质心)是可以假定整个物体的质量集中的点(例如，可以将物体平衡在质心处的针上).有些公式可以直接用于常规形状.对于不规则形状，它是通过积分计算的.

This is sort of a formula which can be easily derived. Geometric Centroid of any shape is average(weighted mean) of all it's points. In physics, centroid(AKA centre of mass) of an object is the point at which the mass of the whole object can be assumed to be concentrated(eg, the object can be balanced on a needle at the centroid). There are formulae which can be directly used for regular shapes. For irregular shapes, it is calculated by integration.

基本逻辑是将所有点的x坐标相加并除以总数.的点数，它给出质心的x坐标，而y坐标相似. 由于形状上的点不是离散的，所以使用积分.

It's basic logic is adding x co-ordinates of all the points and dividing by total no. of points, which gives x co-ordinate of the centroid and similar for y co-ordinate. As the points on a shape are not discrete, integration is used.

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