关键词: 椭圆抛物面, 球面, 广义特征多项式, 圆截线

Abstract: Based on the generalized characteristic polynomial，the method for judging whether an elliptic paraboloid and a sphere have intersection curves is presented.The condition that intersection curve is a circle and the important geometric parameters such as circle center，radius and normal vector are obtained，which ensures the intersection curves are drawn accurately.A coordinate transformation based on parallel circular family is achieved.A quartic equation with one unknown is obtained by substituting the parameter equation of the elliptic paraboloid into the equation of the sphere.According to the distribution of the roots，the topological structure of the intersection curves can be determined.In those subintervals that intersection points lie in，intersection curves are provided in a parametric form.Some examples are provided to demonstrate the algorithm.

Key words: elliptic paraboloid, sphere, generalized characteristic polynomial, circular section