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To complete the required rotation about the given axis, we have to transform the rotation axis back to its original position. This can be achieved by applying the inverse . The overall transformation matrix for rotation about an transformations T' and R. xy arbitrary axis then can be expressed as the concatenation of five individual transformations. R@) = T-R,, -R, +R) -T" a a . L 0 o 0 — Oo — Olf cos@ sine IVI lvl o 1 © ofj_-ab € _b g)\-sind cose ie. R@) = ayv] oa [¥| 0 0 1 O]} -ac -b c©§ 4g 0 0 av] ® TV] =x -¥1 —-% 1 0 o o il © 0 A abl ac gl ri oo 8 “ I¥E A[V] apyy | ‘i © =b y{jo 1 00 dR h a b c of }9 9 1 °0 IVE Ivt Iv 0 0 o ijl yi 4 1 Projections After converting the description of objects trom world coordinates to viewing coordinates, we can project the three dimensional objects onte the two dimensional view plane. There are two basic ways of projecting objects onto the view plane ; Paralic! projection and Perspective projection. Parallel Projection In parallel projection, z - coordinate is discarded and parallel lines from each vertex on the object are extended until they intersect the view plane. The point of intersection is the projection of the vertex. We connect the projected vertices by line segments which correspond to connections on the original object. View plane Parallel projection of an object to the view plane As shown in the Fig a parallel projection preserves relative proportions of objects but does not produce the realistic views 
