  This paper presents a novel geometrical approach to investigate the convexity
of a density-based cluster. Our approach is grid-based and we are about to
calibrate the value space of the cluster. However, the cluster objects are
coming from an infinite distribution, their number is finite, and thus, the
regarding shape will not be sharp. Therefore, we establish the precision of the
grid properly in a way that, the reliable approximate boundaries of the cluster
are founded. After that, regarding the simple notion of convex sets and
midpoint convexity, we investigate whether or not the density-based cluster is
convex. Moreover, our experiments on synthetic datasets demonstrate the
desirable performance of our method.
