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version (141 KB) by Juernjakob Dugge
Transform cartesian to curvilinear orthogonal coordinates, e.g. a flow-oriented coordinate system.


Updated 17 Aug 2015

GitHub view license on GitHub

Matlab functions to transform between cartesian (xy) and curvilinear orthogonal (sn) coordinates using a spline representation of a centerline.

Cite As

Juernjakob Dugge (2019). jdugge/xy2sn (, GitHub. Retrieved .

Comments and Ratings (10)

Thank you Juernjakob. I am using these invaluable tools with citation in my research.

Chad Greene

These are really fantastic functions that have been tremendously helpful for my research. Thanks Juernjakob!

Chad Greene

Chad, thanks for your feedback, and apologies for my very delayed response. I've updated the submission to now use the absolute length along the centerline for the s-coordinate.

Brian, I don't know how this compares to CRG, sorry. If you can provide some detail on how that project converts between Cartesian and curvilinear coordinates, I might be able to comment.

How does this compare to curved regular grid (CRG) work being done for vehicle/road/terrain data?

Nice submission overall.
A warning though: the spline interpolant is not necessarily monotone, particularly at the end-points. As a result, in my tests it was common to get major discontinuities in "Nsign" at the boundaries.
You might consider adding a pchip() option to avoid this (pchip is guaranteed monotone).

Chad Greene

These functions have proven quite helpful for me, Juernjakob! I would make one change: For most applications, the normalized s is awkward and unintuitive. For river flow applications it makes little sense to describe data points as being one-half of one river unit downstream. If data start out in meters, why not keep the data in meters? In every case I've needed to follow xy2sn with distanceAlongFlow=S*L. Then I often think I'm done with the L variable, only to realize that I should have kept it to transform back into the xy coordinate system.

In this situation, I have tried the following incorrect way of getting back to x,y:

[x,y] = sn2xy(distanceAlongFlow/max(distanceAlongFlow),N,centerlineX,centerlineY);

The above solution would only be correct if the maximum value in distanceAlongFlow is located at the endpoint of the centerline. If you find yourself in a similar situation, the correct solution can be obtained by

[x,y] = sn2xy(distanceAlongFlow/arclength(centerlineX,centerlineY,'sp'),N,centerlineX,centerlineY);

Despite this minor issue, the functions are quite useful--thanks for sharing.

Thanks for the feedback, Jie. I've edited the function to now use a linear approximation of the smoothed pathline, which speeds up the process significantly.


Hi, Juernjakob, this program is very useful for handling river data. The problem is that the efficiency of this program need to be improved. I tried it for just 150,000 points, and it is not finished for more than half an hour. You know, for most of field applications, data sets with more than one million data points is very common. So, it will be more useful, if the efficiency of this program could be improved in future.


The s-coordinate is no longer normalised, but uses distance units. This is consistent with Merwade's description of the method. (Thanks to Chad Greene for raising this issue)

Dramatically increased performance by using a piecewise linear approximation for the smoothed centerline.

Added check for a bug in "distance2curve.m"

MATLAB Release Compatibility
Created with R2012b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired by: distance2curve, arclength, interparc