线段圆交点 [英] Line Segment Circle Intersection

问题描述

我试图确定线段与圆相交的点。例如，给定P0和P3之间的任何点（还假设你知道半径），确定P3的最简单方法是什么？

I am trying to determine the point at which a line segment intersect a circle. For example, given any point between P0 and P3 (And also assuming that you know the radius), what is the easiest method to determine P3?

推荐答案

方程组。该圆定义为： x ^ 2 + y ^ 2 = r ^ 2 。该行由 y = y0 + [（y1 - y0）/（x1 - x0）]·（x - x0）定义。将第二个代入第一个，得到 x ^ 2 +（y0 + [（y1 - y0）/（x1 - x0）]·（x - x0））^ 2 = r ^ 2 。解决这个问题，你会得到0-2的值。将它们插回到任一等式中以获得y的值。

You have a system of equations. The circle is defined by: x^2 + y^2 = r^2. The line is defined by y = y0 + [(y1 - y0) / (x1 - x0)]·(x - x0). Substitute the second into the first, you get x^2 + (y0 + [(y1 - y0) / (x1 - x0)]·(x - x0))^2 = r^2. Solve this and you'll get 0-2 values for x. Plug them back into either equation to get your values for y.

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