Parameterized function for clothoid

Question

I\'m coding renderer for road network, which based on the RoadXML format.

Road curves from this format has four types:

• segment,
• circle arc, <

Answer 1

See the paper The Clothoid, by Ryan Seng and Molly Severdia. Generally, clothoids are defined by Fresnel integrals. It turns out that a clothoid C(t) has arclength t. So right off the bat the formula for the general curve is expressed in terms of arclength. A particular curve is just a subsection of the general spiral, going from start curvature to end curvature. You would have to do a rotation and translation for the general case.