如何找到一个点的正交投影到平面 [英] How do I find the orthogonal projection of a point onto a plane

问题描述

可以说我有一点（X，Y，Z）和平面，点（A，B，C）和正常（D，E，F）。我想找到该点，它是第一个点的正交投影到平面上的结果。我在3D图形编程用这个。我想实现某种剪裁上飞机的。

Lets say I have point (x,y,z) and plane with point (a,b,c) and normal (d,e,f). I want to find the point that is the result of the orthogonal projection of the first point onto the plane. I am using this in 3d graphics programming. I want to achieve some sort of clipping onto the plane.

推荐答案

一个点的投影 Q =（X，Y，Z）到由给定的飞机点 P =（A，B，C）和正常 N =（D，E，F）是

The projection of a point q = (x, y, z) onto a plane given by a point p = (a, b, c) and a normal n = (d, e, f) is

q_proj = q - dot(q - p, n) * n

该计算假设 N 是一个单位向量。

This calculation assumes that n is a unit vector.

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