Math Conventions¶
A Clothoid for the purposes of this software is any curve for which the curvature is a linear function of arc length. Put another way, the derivative of curvature with respect to arc length must be a constant value. Any such curve can be expressed parametrically in the following form:
With curvature and tangent angle described by:
Where each math symbol is mapped to a name in the software and a description according to the following table:
Math Symbol | Code Symbol | Description |
---|---|---|
x0 | initial X coordinate | |
y0 | initial Y coordinate | |
s | arc length | |
kd | derivative of curvature | |
k0 | initial curvature | |
t0 | initial tangent angle |