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10 Jan 2013 (Updated )

Transform cartesian to curvilinear orthogonal coordinates, e.g. a flow-oriented coordinate system.

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Analysing or interpolating scattered data that follow a common centerline, like bathymetry data in a river, may require interpreting the data in terms of their position along and distance from that centerline. For example, river bathymetry varies more strongly laterally to the river centerline than longitudinally.

This submission provides two functions, xy2sn and sn2xy, to transform between cartesian (xy) and curvilinear orthogonal (sn) coordinates using a spline representation of a centerline.

It requires the arclength, interparc, and distance2curve functions by John D'Errico. In the distance2curve function, there is a small bug that needs to be corrected in order for xy2sn to work: Line 453 in distance2curve.m should read "if nargout == 3" instead of "if nargout > 3".

The approach is based on Merwade et al (2005) "Geospatial Representation of River Channels", Journal of Hydrological Engineering, 10, 243-251.


Distance2curve, Arclength, and Interparc inspired this file.

Required Products MATLAB
MATLAB release MATLAB 8.0 (R2012b)
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Comments and Ratings (4)
08 Sep 2014 Matt Wolinsky

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).

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03 Jun 2014 Chad Greene

Chad Greene (view profile)

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.

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17 Dec 2013 Juernjakob Dugge

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.

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12 Dec 2013 Jie

Jie (view profile)

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.

27 Feb 2013 1.1

Added check for a bug in "distance2curve.m"

17 Dec 2013 1.2

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

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