Calculating Material/Texture Placement from Bitmap to 3D Model
For each visible voxel side you need to iterate over all triangles and find if ray from voxel side normal intersects that particular triangle. Having intersection point you can then calculate barycentric coordinates of this point within intersected triangle. And with barycentric coordinates you can calculate UV of intersection point and therefore sample color from original texture. If you need more than one pixel per voxel side then you can cast more rays.