Effective Quaternion Rotation in An Ellipsoid through Sphere Transformation: A Linear Approach

Abstract

The application of quaternion rotation in ellipsoids and spheres is an intriguing field with significant implications in computer graphics, robotics, and physics simulations. The necessity to decipher quaternion rotation in ellipsoid is crucial. This research aims to utilize the principles of quaternion rotation in spheres to compute the equivalent in the ellipsoid. This involves the application of a linear transformation to convert quaternion rotation in ellipsoids into spheres. By controlling the full rotation of quaternions, the spheres can be transformed back into ellipsoids, achieving the ultimate goal of controlling quaternion rotation within an ellipsoid. The results demonstrate that this approach effectively addresses the quaternion rotation on the ellipsoid and aligns with the fundamental properties of quaternions. Furthermore, it serves as a significant aid in implementing quaternion rotation on the ellipse.