{{x1,y1,z1},{x2,y2,z2}...}

Interpolation::fememtlq: The quality 0.` of the underlying mesh is too low.
The quality needs to be larger than 0.`.

epsilon = 10^-5;
  perturbData = {#1 + RandomReal[epsilon {-1, 1}], #2 +
  RandomReal[epsilon {-1, 1}], #3 +
  RandomReal[epsilon {-1, 1}]} & @@@ intrct;
  reg = ConvexHullMesh[perturbData[[All, 1 ;; 2]]];
  f = Interpolation[perturbData, InterpolationOrder -> 1]