Abstract: This paper aims is to discuss the intersections determination of two plane tangent convolutes,
a cylinder and a cone, and to analyze different intersection results under different parameters entry, so
as to deliver a kind of effective mathematical basis for CAD intersection construction. For a cylinder
and a cone, the existence-judgment equation of intersection lines is given. It is also analyzed that
intersection existence conditions, numbers and shape properties in both parametric formulas and
geometry at special spatial positions, while the method discussion was made of getting exact tangent
point of two surfaces at normal spatial position. The structural diagram is delivered of parametric
drawing program of multiview, some processing methods coping with several key problems of drawing
intersection curve are listed, too. Different intersection lines resulting in connection with corresponding
parameters entry are analyzed. The implementation has the functions of multiview drawing,
dimensioning and writing main parameters and coordinate data to a data file for intersection lines.

Key words: surface of revolution, intersection line, parametric equations, drawing