The geometric model of a pectoral fin is a five-vertex polygonal surface with one vertex, i.e. the ``root'', fixed at a certain control point of the NURBS surface of the display fish model. Let us denote the root vertex as and the four other vertices, ordered clockwise, as to respectively (see Fig. (a)). The visualization problem is then to determine the time-varying trajectories of , i=1,2,3,4. It is reasonable to assume constant lengths of the vectors , i=1, 2, 3, 4 pointing from to the other vertices. Therefore the control problem becomes that of determining the directions of these vectors over time.
Figure: Visualization of pectoral fin motion.
Expressing vectors , i=1, 2, 3, 4, in the fish's local coordinate system (see Fig. ) simplifies the implementation of the fin motions. Once the new positions of 's are computed in the fish's local coordinate system, they are transformed back to the world coordinates system for graphics display.
|Xiaoyuan Tu||January 1996|