Voronoi diagram is one of the most sought after geometric structures, which has a wide application in various fields of science and engineering. Application of Voronoi diagram can be found in image segmentation and feature extraction, motion planning, collision avoidance, determining the optimal deployment of infrastructure in town planning, mesh generation, dimensional reduction, surface reconstruction, etc. For a set of geometric entities (such as points, lines, curves, or surfaces), the Voronoi diagram can be considered as the locus of a point that is equidistant from more than one entity. A Voronoi diagram tessellates the space into regions called Voronoi regions such that there is a Voronoi region corresponding to every entity in the given set. Each Voronoi region is a collection of points that are nearest to the corresponding geometric entity than any other entity in the given set. Discretizing the input curves into points or lines is a way of constructing an approximate Voronoi diagram. Sampling the input curves into points requires a fine sample density to obtain a reasonable topological and geometrical accuracy of the Voronoi diagram. We propose algorithms that accurately compute the Voronoi diagram of planar closed curves and that of closed surfaces with coarse sample points. We also present a sample based algorithm that accurately computes the Voronoi diagram of a set of non-intersecting circles