(1) 𝑃𝑃 * ∶= 𝑓𝑓(𝑃𝑃) = {𝑝𝑝 1 , … 𝑝𝑝 𝑛𝑛 }, 𝑑𝑑�𝑝𝑝 𝑖𝑖 , 𝑝𝑝 𝑗𝑗 � ≥ 𝑟𝑟, ∀𝑝𝑝 𝑖𝑖 , 𝑝𝑝 𝑗𝑗 ∈ 𝑃𝑃 * When provided a target number of points, the Poisson disk downsampling of point clouds is initialized by generating grid cells within the spatial boundaries of the point cloud and calculating upper and lower sample size tolerances. Since the radius is not provided, in our case, it is first defined in relation to the spatial size of the point cloud, and then adaptively scaled as the algorithm iterates. During each iteration, grid cells are generated with face lengths (s), where 𝑠𝑠 = 𝑟𝑟 √3 ⁄ , ensuring that each grid cell can only contain a single point given the Poisson disk constraint. Given the radius resulting grid cells, a random grid cell with points inside is selected to initiate the inner-loop of the algorithm and the downsampling of the point cloud. After the initial grid cell is selected, a random point within the cell is selected followed by the selection of an adjacent cell which in turn has its points checked for one being outside the Poisson disks of other selected points. The process then continues until all grid cells have been evaluated, and is repeated with varying radius values until the downsampled point cloud falls within the target size tolerances.