Special canal surfaces with Bishop frame and quaternions

Abstract

The purpose of this paper is to show that canal and tubular surfaces can be obtained by special curves. Also, we reckon the equations of these surfaces with Bishop frame and acquire some corollaries for special curves. Besides, these surfaces are acquired by quaternion and homothetic motion.

Keywords

• canal surface
• bertrand curve
• involute-evolute curve
• mannheim curve
• quaternion
• rotation matrices
• homothetic motion