Constructing self-supporting surfaces with planar quadrilateral elements

Abstract We present a simple yet effective method for constructing 3D self-supporting surfaces with planar quadrilateral (PQ) elements. Starting triangular discretization of surface, we first compute the principal curvatures and directions each face using new discrete differential geometry approach, yielding more accurate results than existing methods. Then, smooth direction field to reduce number singularities. Next, partition all faces into two groups in terms curvature difference. For small difference, stretch matrix that turns pair conjugate directions. remaining faces, simply keep their smoothed Finally, applying mixed-integer programming solver mixed field, obtain mesh. Experimental show our is computationally efficient can yield high-quality PQ meshes well approximate input maintain properties.