  The terrain survey techniques of photogrammetry, LIDAR, Sonar or seismic
studies are subject to limitation of shadow zones. It is not possible to
capture the terrain pattern and requires interpolation and extrapolation for
conformal mapping of spatial coordinates for generation of terrain model. The
discrete data is mapped through a function set whose domain returns the
analytic test in Riemann map. The algorithm adopted in analysis for such
mapping does not have a certainty score or probability of degree of correctness
conforming to the physical landscape of shadow zones. The aim of the paper is
to establish a generator of certainty degree of the mapping along with a
continuous terrain model generator. The confirmed mapping of terrain presents a
continuous spatial coordinate set which form the boundary of the shadow zone
with discrete spatial coordinates. The discrete set is normalized in Gaussian
distribution through a Poisson distribution transition. The continuous data set
is represented by Laurentian series in which the function will be analytic and
can be mapped to Riemann surface with singularities within the annulus and
outside the annulus of approximate space sub set (Euclidean space).The
singularities will be discarded through Picard's theorem and analytic test at
poles with Cauchy's residual theorem is done. The resulting set of spatial
coordinates will restructure within Riemann number sphere which will be mapped
on the plane as stereographic projection. The Gaussian distribution which forms
the basis of analysis will provide with the tool for generating the probability
of certainty of every terrain model idealised to conform to the physical
landscape.
