Based on the Morse theory

a novel approach to create quad-mesh multiresolution from triangular mesh models is proposed. A smooth Morse function on a given triangular mesh is firstly defined as the solution of a Laplacian equation with constraints in which critical points are either specified by user or exacted from an eigenfunction of the Laplacian matrix of the mesh．As critical point layout has been carefully treated

maximum

minimum and saddle points of the function will automatically possess of structure of a quad mesh whose connectivity is then produced by tracing the stream lines of the function guided under the gradient field of the function. A critical point exchange rule is employed to generate the structure of the next finer quad mesh whose connectivity is finally also generated through stream line tracing. Parameterization is not required in the process as all resolution levels are created using the stream lines method．