New Numerical Solution for Two Parametric Surfaces Intersection Dragging Problem

The problem of intersecting two parametric surfaces has been one of the main technical challenges in computer-aided design, computer graphics, solid modeling, and geometrics. This paper aims at reducing and minimizing time and space required for the computations process of parametric surface intersection. To do this, a new numerically accelerating method based on continuation technique was utilized first by calculating a starting point, and second by tracing sequential points along the intersection curve following Broyden’s method. Two factors have been identified as influential in controlling component jumping: initial points and step size. Test examples of intersecting two parametric surfaces demonstrated that this method was highly efficient with high-speed parametric solution. The intersection results are often given as curve’s points.