  Domain discretization is considered a dominant part of solution procedures
for solving partial differential equations. It is widely accepted that mesh
generation is among the most cumbersome parts of the FEM analysis and often
requires human assistance, especially in complex 3D geometries. When using
alternative mesh-free approaches, the problem of mesh generation is simplified
to the problem of positioning nodes, a much simpler task, though still not
trivial. In this paper we present an algorithm for generation of nodes on
arbitrary $d$-dimensional surfaces. This algorithm complements a recently
published algorithm for generation of nodes in domain interiors, and represents
another step towards a fully automated dimension-independent solution procedure
for solving partial differential equations. The proposed algorithm generates
nodes with variable density on surfaces parameterized over arbitrary parametric
domains in a dimension-independent way in $O(N\log N)$ time. It is also
compared with existing algorithms for generation of surface nodes for mesh-free
methods in terms of quality and execution time.
