如何确定点 (X,Y) 是否包含在圆的弧段内(即饼图切片)? [英] How to determine whether a point (X,Y) is contained within an arc section of a circle (i.e. a Pie slice)?

问题描述

想象一个圆圈.想象一个馅饼.想象一下，试图返回一个布尔值来确定所提供的 X、Y 参数是否包含在其中一个饼图中.

我对弧线的了解:

我有 CenterX、CenterY、Radius、StartingAngle、EndingAngle、StartingPoint(圆周上的点)、EndingPoint(圆周上的点).

给定 X,Y 坐标，我想确定该坐标是否包含在饼图幻灯片中的任何位置.

解决方案

我知道这个问题很老，但没有一个答案考虑圆弧的位置.

该算法认为所有角度都在 0 到 360 度之间，弧线沿数学正方向(逆时针)绘制

首先您可以转换为极坐标:半径 (R) 和角度 (A).注意:如果可用，请使用 Atan2 功能.

2) 如果 S > E 那么有两种可能的情况

• 如果 A > S

那么这个点就在切片里面

• 如果 A <埃

那么这个点就在切片里面

在所有其他情况下，该点位于切片之外.

Imagine a circle. Imagine a pie. Imagine trying to return a bool that determines whether the provided parameters of X, Y are contained within one of those pie pieces.

What I know about the arc:

I have the CenterX, CenterY, Radius, StartingAngle, EndingAngle, StartingPoint (point on circumference), EndingPoint (point on circumference).

Given a coordinate of X,Y, I'd like to determine if this coordinate is contained anywhere within the pie slide.

解决方案

I know this question is old but none of the answers consider the placement of the arc on the circle.

This algorithm considers that all angles are between 0 and 360, and the arcs are drawn in positive mathematical direction (counter-clockwise)

First you can transform to polar coordinates: radius (R) and angle (A). Note: use Atan2 function if available. wiki

R = sqrt ((X - CenterX)^2 + (Y - CenterY)^2)

A = atan2 (Y - CenterY, X - CenterX)

Now if R < Radius the point is inside the circle.

To check if the angle is between StartingAngle (S) and EndingAngle (E) you need to consider two possibilities:

1) if S < E then if S < A < E the point lies inside the slice

2) if S > E then there are 2 possible scenarios

• if A > S

then the point lies inside the slice

• if A < E

then the point lies inside the slice

In all other cases the point lies outside the slice.

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