3 dimensional geometries can be converted to 2 dimensions by mapping them to a plane. Not all 3 dimensional geometries can be converted to 2 dimensions as it requires for them to have a 2 dimensional counterpart. This rules out iso cubes, planes, and tetrahedrons. Spheres are a special case that will get converted to circles with the same radius. As no ellipsoid geometry exist the plane of circles is ignored and mapping a 3D circles thus creates a 2D circle of the same radius irrespective of the supporting plane of the circle.
A vector of geometries to project or map
A vector of planes
A vector of geometries in 2 dimensions
# Map a 3D point cloud to a plane defined by three random points p <- point(sample(10), sample(10), sample(10)) support <- p[sample(10, 3)] map_to(p, plane(support, support, support)) #> <2D points > #>  <x:0.0413, y:0.00134> <x:0.11, y:0.000257> <x:0.0744, y:0.000922> #>  <x:0.0941, y:0.000916> <x:0.105, y:0.00102> <x:0.0107, y:0.000421> #>  <x:0.106, y:0.00126> <x:0.146, y:0.00014> <x:0.0724, y:0.000587> #>  <x:0.0228, y:0.000737>