Cable Geometric Modeling Technology in Virtual Environment

Cable is flexible object. Its deformation is defined by material properties, cross-section sizes and length conservation gravity and friction. So it consists of variable shapes. Cubic uniform B-Spline function is chosen as the mathematical model of cable centerline in this paper. Energy-Optimization method is used to search for the positions of the control points. Firstly. a suspending cable model with both ends fixed is established; Based on that, other cable models with the constraints of endpoint tangents or passing through given points are built up by Lagrange Multiplier method; Then the method named Same-Proportion Dichotomy is used to cope with the constraint of length conservation. Secondly. two kinds of cable models are established. One is with one end hanging in the air established by Gradient-Descent method, the other is with one end dragging on the ground by Gradient Projection Descent method. Because traditional virtual modeling technology mostly focused on rigid parts or small deformation components, these studies consist of important meaning for the farther development of virtual modeling technology.