Triangulations from 3D scattered point sets play an important role in surface modeling. The applied criterion determines the final triangulation. Since curvature is one of the intrinsic properties of a surface

an algorithm for estimating the curvature of a convex quadrilateral is given in this paper. Then a new criterion of minimizing this curvature is proposed. Comparisons between this minimal curvature criterion and other criteria are concisely enunciated through detailed analyses to an example. The results indicate that the triangulations based on the criterion have the tendency to hold better geometric properties. This has practical value for surface reconstructions and surface designs etc.