Abstract: Surface intersection is a fundamental problem in CAD applications. Instead of using Newton method to locate points on the curve for the marching method, a new method with dimidiate structure is proposed to trace implicit surface intersection in this paper. The starting and termination points are selected by solving constrained optimization problems. The tracing of intersection curve relies on differential geometry of the intersecting surfaces. The curvature of intersection curve determines the adaptive step. A generalized tracing method is also presented. Numerical examples show the effectiveness of both methods.