A Discrete Spring Model to Generate Fair Curves and Surfaces

To generate fair curves and surfaces is an important tool in the area of computer graphics (CG), computer-aided design (CAD), and other geometric modeling applications. In this paper, we present an iteration-based algorithm to generate fair polygonal curves and surfaces that is based on a new discrete spring model. In the spring model, a linear spring, which length approximately represents a curvature, is attached along the normal line of each polygon node. Energy is assigned to the difference of the lengths, that is, difference in curvature, of nearby springs. Our algorithm then minimizes total energy by iterative approach. Our algorithm accepts as inputs (1) an initial polygonal curve (surface), which consists of a set of polygonal segments (faces) and a set of nodes as polygon-vertices, and (2) constraints for controlling the shape. The outputs are polygonal curve (surface) in smooth shape. We also describe a method for improving performance of our iterative process into a linear execution time. Our algorithm provides a tool for fair curve and surface design in interactive environment.