3D线平面相交，与简单平面 [英] 3D line plane intersection, with simple plane

问题描述

我在 3D 空间中有两个点，它们的 X 坐标具有不同的符号.所以其中一个肯定位于 X 平面的一侧，另一个位于另一侧.

i have two points in 3D space which have X-coordinates with different signum. so one of them lies definitely on one side of the X-plane and one on the other.

现在我想以最简单和优化的方式找到这个平面与两点组成的直线的交点.

now i want to find the intersection of this plane and the line made up by the two points in the most simple and optimized way.

我知道如何做一般的线平面相交，但由于在这种情况下平面只是 x 平面，我认为应该有一些我可以走的捷径.

i know how to do general line plane intersection, but since in this case the plane is just the x-plane, i think there should be some shortcuts i can take.

谢谢！

推荐答案

使用 两点形式(3D泛化很简单).

Connect the two points and get the equation of line using two-point form (the 3D generalization is simple).

然后解方程 x = 0.

Then solve the equation for x = 0.

获得解决方案后，将它们翻译成您的编程语言.

After you've got the solutions, translate them into your programming language.

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