Our approach to mesh smoothing is that we use premeshed model and try to improve internal node positions with physically based connections. Our algorithm is not bound to triangular type of elements. Note that Simada[6] uses physically based relaxation for node placement. Delaunay triangulation is applied after relaxation.
We use premeshed input which can be Non-manifold geometry e.g. line segments, faces or volumes. Mesh is then constrained with equations that are basis for relaxation. Node movement is governed by equation of motion. Constraints can be length between nodes and angles of elements. Desired length between nodes can be used for node spacing function and angles in elements can be used for desired shape of each element.