问题
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.
回答1:
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 and A > E
then the point lies inside the slice
- if A < S and A < E
then the point lies inside the slice
In all other cases the point lies outside the slice.
回答2:
Check:
- The angle from the centerX,centerY through X,Y should be between start&endangle.
- The distance from centerX,centerY to X,Y should be less then the Radius
And you'll have your answer.
回答3:
Convert X,Y to polar coordinates using this:
Angle = arctan(y/x); Radius = sqrt(x * x + y * y);
Then Angle must be between StartingAngle and EndingAngle, and Radius between 0 and your Radius.
来源：https://stackoverflow.com/questions/6270785/how-to-determine-whether-a-point-x-y-is-contained-within-an-arc-section-of-a-c