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. |