The problem of determining visibility locations (VLs) on/inside a domain bounded by a planar C1-continuous curve (without vertices), such that entire domain is covered, is discussed in this paper. The curved boundary has been used without being approximated into lines or polygons. Initially, a few observations regarding the VLs for a curved boundary have been made. It is proposed that the set of VLs required to cover the domain be placed in a manner that the VLs and the lines connecting them form a spanning tree. Along with other observations, an algorithm has been provided which gives a near optimal number of VLs. The obtained number of VLs is then compared with a visibility disjoint set, called as witness points, to obtain a measure of the ‘nearness' of the number of VLs to the optimum. The experiments on different curved shapes illustrate that the algorithm captures the optimal solution for many shapes and near-optimal for most others. © 2017 Elsevier Ltd