Abstract :
This article provides a useful perspective of understanding, representing, and manipulating 3D orientation and rotation for geometric computing. Coordinate-free geometric programming and affine geometry, which makes a distinction between points and vectors and defines operations for combining them, inspires our approach. Based upon affine geometry, Goldman and DeRose pioneered a method of writing graphics programs that are independent of the choice of reference coordinate frames. The study on geometric algebra pursues a similar goal with various geometric primitives rather than just vectors and points.
Keywords :
algebra; computer graphics; geometric programming; 3D computer graphics; 3D orientations; 3D rotations; Coordinate-free geometric programming; geometric algebra; geometric computing; Algebra; Computer graphics; Geometry; Mathematical programming; Mathematics; Quaternions; Writing; axis-angle representation; coordinate-free geometric programming; rotation and orientation; rotation vector; unit quaternion;
