  The point inclusion tests for polygons, in other words the point-in-polygon
(PIP) algorithms, are fundamental tools for many scientific fields related to
computational geometry, and they have been studied for a long time. The PIP
algorithms get direct or indirect geometric definition of a polygonal entity,
and validate its containment of a given point. The PIP algorithms, which are
working directly on the geometric entities, derive linear boundary definitions
for the edges of the polygons. Moreover, almost all direct test methods rely on
the two-point form of the line equation to partition the space into
half-spaces. Voronoi tessellations use an alternate approach for half-space
partitioning. Instead of line equation, distance comparison between generator
points is used to accomplish the same task. Voronoi tessellations consist of
convex polygons, which are defined between generator points. Therefore, Voronoi
tessellations have become an inspiration for us to develop a new approach of
the PIP testing, specialized for convex polygons. The equations, essential to
the conversion of a convex polygon to a Voronoi polygon, are derived. As a
reference, a very standard convex PIP testing algorithm, \textit{the sign of
offset}, is selected for comparison. For generalization of the comparisons,
\textit{the ray crossing} algorithm is used as another reference. All
algorithms are implemented as vector and matrix operations without any
branching. This enabled us to benefit from the CPU optimizations of the
underlying linear algebra libraries. Experimentation showed that, our proposed
algorithm can have comparable performance characteristics with the reference
algorithms. Moreover, it has simplicity, both from a geometric representation
and the mental model.
