  A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired
technique for evaluating definite integrals over bounded volumes that have
smooth boundaries in three dimensions is described. A key aspect of this
approach is that it allows the user to approximate the value of the integral
without explicit knowledge of an expression for the boundary surface. Instead,
a tesselation of the node set is utilized to inform the algorithm of the domain
geometry. Further, the method applies to node sets featuring spatially varying
density, facilitating its use in Applied Mathematics, Mathematical Physics and
myriad other application areas, where the locations of the nodes might be fixed
by experiment or previous simulation. By using the RBF-FD-like approach, the
proposed algorithm computes quadrature weights for $N$ arbitrarily scattered
nodes in only $O(N\mbox{ log}N)$ operations with tunable orders of accuracy.
