A new method is proposed to determine the points on the medial axis transform (MAT) of an object from its surface mesh representation. Current art typically uses a Voronoi diagram-based approach to generate the medial axis of a given point cloud on the boundary of the object or a surface mesh representation as input. This approach defines the MAT points as a subset of the Voronoi vertices close to the medial axis, where the accuracy and density of the points on the medial axis depend on the sampling density of the input point cloud representation. Therefore, the set of medial axis points is incomplete and may lack various topological features of the MAT and its reconstruction property. Instead of filtering the Voronoi vertices that are not medial points, the method proposed in this paper searches for the correct MAT point in the vicinity of such Voronoi vertices and finds the pair of corresponding footpoints using the properties of the MAT point. Hence, the algorithm can determine points on the medial axis without being dependent on the given sampling density and even in the presence of inputs having non-manifold entities. As the MAT points are generated based on the definition of medial axis (MA), the result obtained is accurate to within a specified tolerance.