  We present a meshfree collocation scheme to discretize intrinsic surface
differential operators over scalar fields on smooth curved surfaces with given
normal vectors and a non-intersecting tubular neighborhood. The method is based
on Discretization-Corrected Particle Strength Exchange (DC-PSE), which
generalizes finite difference methods to meshfree point clouds. The proposed
Surface DC-PSE method is derived from an embedding theorem, but we analytically
reduce the operator kernels along surface normals to obtain a purely intrinsic
computational scheme over surface point clouds. We benchmark Surface DC-PSE by
discretizing the Laplace-Beltrami operator on a circle and a sphere, and we
present convergence results for both explicit and implicit solvers. We then
showcase the algorithm on the problem of computing Gauss and mean curvature of
an ellipsoid and of the Stanford Bunny by approximating the intrinsic
divergence of the normal vector field. Finally, we compare Surface DC-PSE with
Surface Finite Elements (SFEM) and Diffuse-Interface Finite Elements (DI FEM)
in a validation case.
