AbstractThis paper presents a new algorithm for torus/torus intersection. The pre-image of the intersection in the parametric space of one torus is represented by an implicit equation. The pre-image is divided into one-valued function curve segments by characteristic points. The topological feature of these characteristic points is analyzed to obtain the structure of the pre-image. Intersection curves satisfying required precision are found by a self-adaptive refinement method. Experiment results are presented to illustrate the stability and efficiency of the method.