Transition Functions¶
Symmetric Transition Functions¶
These transition functions exhibit a symmetry about the transition center in both the X and Y dimensions. In TableCurve 2D, the transition width is the X distance between Ymin+.75*Yrange and Ymin+.25*Yrange. This width will be positive for an ascending transition and negative for a descending transition.
Some transition functions will produce the opposite direction transition simply by changing the sign on the width term. When this property exists, TableCurve 2D will use this to enable the fitting of descending transitions with the zero-intercept version of the function. When this property is absent, descending transitions will require the intercept form. When a function can model a descending transition with a negative width term, such will be illustrated in the accompanying graph.
Unless otherwise indicated, a represents the transition magnitude or height, b represents the midpoint of the transition (the X where Y=Ymin+.5*Yrange), c controls the width of the transition, and d, if present, controls the shape of the transition.
Cumulative SDS (Symmetric Double Sigmoidal)
Asymmetric Transition Functions¶
These transition functions normally exhibit an asymmetry about the transition center. For asymmetric functions, this center remains defined as the x at half transition height. The analysis is identical to the symmetric transitions except that any d term present, unless otherwise indicated, controls the degree of asymmetry.
Pulse Cumulative with Power Term