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TABLE 1. Key characters and abbreviations for the family of 12 spirals.

Type of spiral Change in spiral angle (expansion rate)
Constant or continuous Episodic or segmented
log-piecewise L1 L2, L3, L4
log-curved Q, C, QQ LQ, QL, LQL, L2QL, LQL2

 

 

TABLE 2. Glossary of terms used.

radius Length between the spiral axis to a point on the spiral.
log-radius The natural logarithm of the radius.
angle The angle turned anticlockwise about the spiral axis to a point on the spiral.
spiral angle Angle between the radius the spiral, constant for a simple logarithmic spiral. A measure of how a spiral expands with angle. Units are in radians for calculations, but reported in degrees.
breakpoint Location of an abrupt change in spiral angle along an outline.
transition A continuous change in spiral angle between episodes of otherwise constant spiral angle.
phase change A breakpoint or a transition in spiral angle along an outline.
log-piecewise A logarithmic spiral with a breakpoint between episodes of otherwise constant spiral angle.
log-polynomial A logarithmic spiral with continuous change in the spiral angle.
log-curved A log-polynomial spiral or a log-piecewise spiral with a transition.
spiral deviation The difference between the radius of an actual outline and that of the fitted spiral.
residual standard deviation The square root of the sum of all squared spiral deviations from a spiral fit, divided by the number of outline points less the parameters in a spiral fit.

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