Local analysis of curves and surfaces intersection problem using tracing

The tracing method for finding intersections of parametric curves and surfaces is considered. The suggested approach is based on the numeric predictor-corrector method, where Runge–Kutta or Adams method is the predictor, and Newton’s method is the corrector. Special equation system is used to find simple singular intersections, its rank is analysed. The tracing step is chosen adaptively. The resulting curve is represented as cubic spline. Finally, the problems of finishing tracing exactly and tracing along boundary are considered.