Research On A New Tracing Method For Implicit Surface Intersection

Surface-surface intersection problem is very fundamental in CAGD, which can be applied widely in solid modeling, geometric processing, CAD, numerical control, visualization, robot and so on. So far, there are mainly following algorithms solving surface-surface intersection problem:algebra method, subdivision method, lattice method, marching method and hybrid method. But if measured by accuracy, topology coherence and efficiency, they can have all kinds of problems. And with the development of the surface modeling technology, it is not limited to express surfaces and curves just using the traditional continual method. Discrete modeling method especially subdivision surface has the trend to conquer.In this paper, history and background about surface intersection is introduced, we can understand the challenges surface intersection faces with the development of CAGD. Then knowledge about problems involved in surface-surface intersection, e.g. different kind of surface-surface intersection description and introduction to differential geometry properties of intersected implicit surfaces, the most effective algorithms solving surface-surface intersection problem is introduced. In the end, a new method with dimidiate structure is proposed to trace implicit surface-surface intersection instead of using Newton method to locate points on the curve for the marching method is introduced. The starting points are selected by solving a constrained optimization problem. The tracing of intersection curve relies on differential geometry of the intersected surfaces. The curvature of intersection curve determines the adaptive step. A generalized tracing method is also presented, no faster but can be more widely applied. Relative to parametric surface and implicit surface, subdivision surface has more wide application. A method about subdivision surface is introduced, and we also recommend a simple algorithm to solve the intersection between subdivision surface and plane.Lots of numerical experiments can verify their effectiveness and high efficiency.