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 |