The intersecting is an important factor which influences the efficiency and the reliability of Boolean algorithms in solid modeling based on curved surfaces

and the intersecting algorithm is closely related to the geometric representation of curved surfaces. Although curved surfaces can be commonly represented with NURBS

unnecessary complexities are caused for the intersecting of quadric surfaces

which are frequently used to describe geometric features of shafts

holes and grooves etc. in mechanical part designing. Therefore

intersecting algorithms of them are required to have higher accuracy

higher efficiency and higher robustness. For this reason

we introduce a practical representation of quadric surfaces

and on the basis of that

algorithms of intersection points between quadric surfaces and several conics

fourth degree nonplanar space curves constructing their boundaries are developed.