如何将点投影到3D平面上？ [英] How to project a point onto a plane in 3D?

问题描述

我有一个3D点（point_x，point_y，point_z），我想将其投影到3D空间中的2D平面上，该平面由点坐标（orig_x，orig_y，orig_z）和一元垂直线定义向量（normal_dx，normal_dy，normal_dz）。

我应该如何处理？

解决方案

1）从您的 orig 指向兴趣点：

v =点源（在每个维度中）；

2）取该向量与单位法向向量 n 的点积：

dist = vx * nx + vy * ny + vz * nz; dist =沿法线从点到平面的标量距离/ p>

3）将单位法向向量乘以距离，然后从您的点减去该向量。

projected_point = point-dist * normal;

编辑图片：
我对您的照片做了一些修改。红色为 v ; v 点 normal =蓝色和绿色的长度（ dist 以上）。蓝色是 normal * dist 。 Green = blue * -1 ：要找到plane_xyz，从点开始并添加绿色矢量。

I have a 3D point (point_x,point_y,point_z) and I want to project it onto a 2D plane in 3D space 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).

How should I handle this?

解决方案

1) Make a vector from your orig point to the point of interest:

v = point-orig (in each dimension);

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

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

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

projected_point = point - dist*normal;

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.

这篇关于如何将点投影到3D平面上？的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！