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Moves the turtle length forward along a circular arc of constant curvature, in radians per unit of length: the arc of radius 1 / |curvature| that turns by curvature · length radians, the same way as Turtle.rotate for positive curvature. Zero curvature moves straight ahead. See curve.

Moves the turtle length forward along a clothoid (Euler spiral): the curvature changes linearly with the distance travelled, from startCurvature to endCurvature, in radians per unit of length, so the turtle turns by (startCurvature + endCurvature) / 2 · length radians in total. Clothoids join straight lines and arcs without jumps in curvature, as in road and track design. See curve.

Moves the turtle length forward while it turns as sharply as curvature prescribes: curvature(s) is the turning rate, in radians per unit of length, after a distance s from 0 to length. Positive curvature turns the same way as a positive Turtle.rotate. Where the pen is down the path is drawn; afterwards the turtle faces the way the path ends.