[英]How to find intersection point (CGPoint) between QuadCurve and Line UIBezierPaths in swift?
I've a QuadCurve and Line drawn using UIBezierPath in my custom view class. 我在自定义视图类中使用UIBezierPath绘制了QuadCurve和Line。 How can I get their intersection point as CGPoint?
如何将他们的交点设为CGPoint?
For QuadCurve: 对于QuadCurve:
let path = UIBezierPath()
path.lineWidth = 3.0
path.move(to: CGPoint(x: 0, y: self.frame.size.height))
path.addQuadCurve(to: CGPoint(x: self.frame.size.width, y: 0), controlPoint: CGPoint(x: self.frame.size.width-self.frame.size.width/3, y: self.frame.size.height))
For Line: 对于行:
let path2 = UIBezierPath()
path2.lineWidth = 3.0
path2.move(to: CGPoint(x: 250, y: 0))
path2.addLine(to: CGPoint(x: 250, y: self.frame.size.height))
If your line is always vertical, calculations are quite simple: x-coordinate is known, so you task is to find y-coordinate. 如果您的线始终是垂直的,则计算非常简单:x坐标已知,因此您的任务是找到y坐标。 Quadratic Bezier curve has parametric representation:
二次贝塞尔曲线具有参数表示形式:
P(t) = P0*(1-t)^2 + 2*P1*(1-t)*t + P2*t^2 =
t^2 * (P0 - 2*P1 + P2) + t * (-2*P0 + 2*P1) + P0
where P0, P1, P2
are starting, control and ending points. 其中
P0, P1, P2
是起点,控制点和终点。
So you have to solve quadratic equation 所以你必须解二次方程
t^2 * (P0.X - 2*P1.X + P2.X) + t * (-2*P0.X + 2*P1.X) + (P0.X - LineX) = 0
for unknown t
, get root in range 0..1
, and apply t
value to the similar expression for Y-coordinate 对于未知的
t
,获得0..1
范围内的根,并将t
值应用于Y坐标的类似表达式
Y = P0.Y*(1-t)^2 + 2*P1.Y*(1-t)*t + P2.Y*t^2
For arbitrary line make equation system for line parametric representation and curve, and solve that system 对于任意线,建立用于线参数表示和曲线的方程组,并求解该系统
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