About the dimension

[CheungBH]

Hello. Thanks for your great job. I am currently reading your paper, but I felt confusion about some details about volumetric method.
You said in your paper while illustrating the cube that
"We discretize the bounding box by a volumetric cube Vcoords ∈ R 64,64,64,3, filling it with the global coordinates of the center of each voxel"
Could you kindly explain the physical meaning of the 4-dimension cube? I know that the (64, 64, 64) means 3 dimensions of (length, width, height). But what's the physical meaning of the forth dimension 3?

[yurymalkov]

The last dimension are the (x,y,z) coordinates in meters. E.g. Vcoords[0,0,0,0] corresponds to X coordinate of the zero voxel, Vcoords[0,0,0,1] corresponds to Y coordinate of the zero voxel and so on.