Generalized constant ratio surfaces and quaternions

Abstract

In this study, we show that the generalized constant ratio surfaces can be obtained by the quaternion product of a unitquaternion and a pure quaternion. Also, the quaternion product of the unit quaternion and the position vector of the generalized constant ratio surface as a pure quaternion is a generalized constant ratio surface. Then we give some results about the generalized constant ratio surfaces by using the quaternions.

Keywords

• Generalized constant ratio surfaces
• kinematic
• rotation matrices
• real quaternions
• unit quaternions.