Abstract—In this paper we give a further investigation of the problem about blending different radiuses circular tubes whose axes are in non-coplaner. On the premise of smooth blending axes, we construct an intersection line of conical surfaces, the line smoothly blends generatrix of two tubes. Furthermore, obtain that the conical intersection line rotates the axis to form a tube, which smothly blends two circular tubes whose axes are in non-coplaner. This is of theoretical significance and application value for the study on smooth blending different radiuses tubes whose axes are in non-coplaner.

Index Terms—Generatrix, non-coplaner tubes, rational bezier curve, smooth blending.

Gen-Zhu Bai is with School of Mathematics, Inner Mongolia University for the Nationalities, Tongliao, China. He is also with Zhe Jiang Chang Zheng Vocational & Technical College, Hangzhou, China (email: bgz049@163.com).
Zhi Wu is with School of Mathematics, Inner Mongolia University for the Nationalities, Tongliao, China.

Cite: Gen-Zhu Bai, Zhi Wu, "Intersection Line of Conical Surfaces and Its Application in the Blending of Tubes with Non-coplanar Axes," International Journal of Applied Physics and Mathematics vol. 9, no. 4, pp. 152-157, 2019.