Cartesian to Curvilinear coordinate forward and backward transformation

Transform 2D cartesian coordinates to channel fitted curvilinear coordinates and backward

These functions transform Cartesian coordinates to channel fitted curvilinear coordinates with respect to a given curve.
It uses splines to parameterize the curve to its arc-length. The three given functions are:
xy2sn - Transforms the input poins from cartesian coordinates to channel fitted coordinates
sn2xy - Tranform channel fitted coordinates to cartesian coordinates
pp_cline - Creates a parameterized version of the given curve, or channel centreline (used by xy2sn)

Below the help of the functions:
****************** XY2SN:
XY2SN Transforms Cartesian coordinates to channel fitted coordinates

[Si,Ni]=XY2SN(Xc,Yc,Xi,Yi) Converts the Cartesian coordinates Xi and Yi
to the channel fitted coordinate Si and Ni using the centreline defined
through the Cartesian coordinates of its vertices Xc and Yc.

[Si,Ni]=XY2SN(...,'ParamName',Value) Allows to set the following
options:

'MaximumIterations'
Scalar number indicating the maximum number of iterations performed by
the algorithm, default is 500.

'Tolerance'
Scalar number indicating the maximum tolerance in the estimated
coordinates. Default is 1/1000 of the mean sampling distance of the
centerline

See also: sn2xy

****************** SN2XY:
SN2XY Transforms channel fitted coordinates to Cartesian coordinates

[Xi,Yi]=SN2XY(Xc,Yc,Si,Ni) Converts the channel fitted coordinate Si
and Ni to the Cartesian coordinates Xi and Yi using the centreline
defined through the Cartesian coordinates of its vertices Xc and Yc.

See also: xy2sn

****************** PP_CLINE:
PP_CLINE make splines of centreline parameterized to centreline length

PPC = PP_CLINE(X_C,Y_C) computes two cubic piecewise polynomials
representing the x and y coordinates of the centreline parameterized in
in the centreline arc length. The centreline is given throgh vertex
coordinates X_C and Y_C. This function is a helper function for XY2SN
and SN2XY.