Is there a way to find out the points on a clothoid, i.e. their coordinates, if one knows the start point and the end point of the clothoid and its curvature?
You can do that for any planar curve with known curvature, .
Let the curve be , parametrized for arclength.
Then , which implies there exists a function such that
From the formula for curvature, ,
and so the curve is .
Now use to determine the constants.