FAST ROTATION OF A 3D IMAGE ABOUT AN ARBITRARY LINE

A graphical computer system must give the user an opportunity to look at an object from different angles. For that, we must be able, given t wo points P1 and P2 in space and an angle PHI, to rotate an object by the angle PHI about the line P1P2. This is usually done by rotating ve rtices (or other points that represent an object) and connecting them. Since an image can have lots of vertices, it is important to be able to rotate each of them quickly. Therefore, we are interested in a rota tion method that would consist of the smallest possible number of comp utational steps. The usual method (see, eg., [1]) includes four nonari thmetic operations (namely, computing sin PHI, cos PHI, and two square roots), and seven multiplications of 4 x 4 matrices. Nonarithmetic op erations are necessary because the known expression for a rotated poin t includes sin PHI, cos PHI, and a square root. However, we can try to reduce the number of arithmetic operations (+, -, X, :).In this paper , we propose an algorithm that consists of only 30 arithmetic steps: i t is less than 1/10 of the number of steps used in the traditional met hod.