数学背后从深度框架投射到点云 [英] Math behind back-projecting from depth frame to point cloud

问题描述

我一直在使用kinect fusion api生成点云和网格，但我想知道将深度帧点/深度投影到3d体积背后的数学是什么？以前我只是简单地绘制了（pixel_x，pixel_y，深度）
的点，但我知道这会出错... 

解决方案

将光线投射到3D世界的光线投影将是相同的数学。 这里有一个很好的解释：

http://www.mvps.org/directx/articles/rayproj.htm

这与此基本相反：

http://stackoverflow.com/questions/5024758/math-how-to-convert-a-3d-world-to-2d-screen-coordinate

I have been producing point clouds and meshes using the kinect fusion api, however I was wondering what is the math behind projecting the depth frame points/depths into a 3d volume? Previously I have simply just plotted the points at (pixel_x,pixel_y,depth) but I know this would wrong... 

解决方案

It would be the same math for ray casting a 2d point into a 3D world. A good explanation is here:

http://www.mvps.org/directx/articles/rayproj.htm

Which is essentially the inverse of this:

http://stackoverflow.com/questions/5024758/math-how-to-convert-a-3d-world-to-2d-screen-coordinate

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