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Visualization of the Pectoral Motions

 

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 tex2html_wrap_inline4040 and the four other vertices, ordered clockwise, as tex2html_wrap_inline4042 to tex2html_wrap_inline4044 respectively (see Fig. gif(a)). The visualization problem is then to determine the time-varying trajectories of tex2html_wrap_inline4046 , i=1,2,3,4. It is reasonable to assume constant lengths of the vectors tex2html_wrap_inline4050 , i=1, 2, 3, 4 pointing from tex2html_wrap_inline4040 to the other vertices. Therefore the control problem becomes that of determining the directions of these vectors over time.

   figure2200
Figure: Visualization of pectoral fin motion.

Expressing vectors tex2html_wrap_inline4050 , i=1, 2, 3, 4, in the fish's local coordinate system (see Fig. gif) simplifies the implementation of the fin motions. Once the new positions of tex2html_wrap_inline4050 's are computed in the fish's local coordinate system, they are transformed back to the world coordinates system for graphics display.


next up previous contents
Next: Animating the Pectoral Flapping Motion Up: Artificial Animals For Computer Animation Previous: Deformable Contour Models
Xiaoyuan TuJanuary 1996