Hi,

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?

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- Jul 30th 2011, 01:05 PMschmimonaCalculate Points on a Clothoid
Hi,

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? - Feb 5th 2015, 01:30 AMRebesquesRe: Calculate Points on a Clothoid
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.