如何投射3D指向一个三维平面 [英] How to project a 3d point to a 3d plane

问题描述

我有一个三维点（point_x，point_y，point_z），我想其投影到（normal_dx它（飞机）是由一个点的坐标（orig_x，orig_y，orig_z）和一元垂直向量定义的三维平面，normal_dy，normal_dz）。

I have a 3d point (point_x,point_y,point_z) and I want to project it onto a 3d plane which (the plane) is defined by a point coordinates (orig_x,orig_y,orig_z) and a unary perpendicular vector (normal_dx,normal_dy,normal_dz).

我应该如何处理呢？

How should I handle this?

推荐答案

1）从制作矢量原稿点的兴趣点：

V =点原稿（每个尺寸）;

2）采取与单位法向量的向量 N 的点积：

2) Take the dot product of that vector with the unit normal vector n:

DIST = VX * NX + VY *纽约+ VZ * NZ; DIST由点到面沿法线=标距离

dist = vx*nx + vy*ny + vz*nz; dist = scalar distance from point to plane along the normal

3）距离乘以单位法向量，并从你的观点减去载体。

3) Multiply the unit normal vector by the distance, and subtract that vector from your point.

projected_point =点 - 距离*正常;

编辑与图片：
我修改你的照片了一下。红色是V; 'V'点'正常'=长度的蓝色和绿色（ DIST 以上）。蓝色是正常* DIST 。 绿色=蓝色* -1 ：找planar_xyz，从起始点并添加绿色向量。

Edit with picture: I've modified your picture a bit. Red is 'v'; 'v' dot 'normal' = length of blue and green (dist above). Blue is normal*dist. Green = blue * -1 : to find planar_xyz, start from point and add the green vector.

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