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Next: Prior Action Selection Mechanisms Up: Visualization of the Pectoral Motions Previous: Animating the Pectoral Flapping Motion

Animating the Pectoral Oaring Motion

The oaring motion of the pectoral fins is most distinguishable in natural fishes with relatively large, flat bodies that do not bend as much when swimming or turning. We capture this visual detail in our artificial butterfly fish and emperor angelfish.

To achieve the oaring motion of the pectoral fins, we let tex2html_wrap_inline4046 , i=1,2,3,4 rotate about a pre-defined unit vector tex2html_wrap_inline4112 such that each tex2html_wrap_inline4066 traces out a cone shape (see Fig. gif(c)). The rotation is computed using unit quaternions tex2html_wrap_inline4116 , where tex2html_wrap_inline4118 is the rotation angle [Shoemake1985]. Let the initial tex2html_wrap_inline4066 , before rotation, be denoted by tex2html_wrap_inline4122 , then we can compute the new tex2html_wrap_inline4066 with the formula

displaymath4106

where tex2html_wrap_inline4126 denotes the conjugate of q. With tex2html_wrap_inline4118 varying from 0 to tex2html_wrap_inline4132 , each tex2html_wrap_inline4066 sweeps a complete cone corresponding to one full stroke of rowing. The speed with which tex2html_wrap_inline4118 changes represents the speed of rowing. We choose tex2html_wrap_inline4138 where parameter tex2html_wrap_inline3300 is proportional to the fish's swimming speed tex2html_wrap_inline4142 thus the faster the fish swims the faster the fins beat. Note that the above q defines a ``forward'' oaring motion towards the direction of swimming tex2html_wrap_inline2962 . To obtain a backward oaring motion, we can simply let tex2html_wrap_inline4148 .

In our animations, when a butterfly fish or an emperor angelfish turns, one of the pectoral fins rows forward and the other backward as is observed in many natural, flat-body fishes. The backward oaring motions of both fins are useful when an artificial fish brakes and retreats. Fig. gif shows snapshots of a butterfly fish with its forward oaring pectoral fins.


next up previous contents
Next: Prior Action Selection Mechanisms Up: Visualization of the Pectoral Motions Previous: Animating the Pectoral Flapping Motion
Xiaoyuan TuJanuary 1996