/Euler-Spiral

Takes the initial and final postion+orientataion. Return the Euler Spiral parameters k, gamma and curve length with the equations: Curvature K(s) = gamma*s + k. Here s is the arc length.

Primary LanguageCOtherNOASSERTION

Euler-Spiral

Source: Euler Spiral for Shape Completion BENJAMIN B. KIMIA, ILANA FRANKEL AND ANA-MARIA POPESCU Division of Engineering, Brown University, Providence, R1 02912, USA

Takes the initial and final postion+orientataion. Returns the Euler Spiral parameters k, gamma and curve length with the equations: Curvature K(s) = gamma*s + k (Here s is the arc length)

/* @Brief : This is used to find the parameters of a euler spiral

  •  	between two points given the tangents at the points

  •  	Since there are infinite solutions so the total curvature is 

  •  	minimised, this is achieved by keeping the change <= 2 * pi 			

  •  	Also since no straight away numerical solution exists for the

  •  	euler spiral equations gradient descent is used get the best fit.

  •  	For starting the estimation the initial conditions are to be specified.

  •  	The following code estimate the initial parameters by fitting a Biarc

  •  	on the given data.

  •  	The Curvature in Euler curve is represented as K(s) = gamma*s + k

  •  	So the purpose is to find k, gamma and the length of the curve

*/