Stream Normal Coordinate Transformation Compatibility: Python 3.10

• 2023 Feb 01 - swiched code structure to be function based, added 'reverse' transformations (sn2xy) to go from sn coords back to xy coords.

This code is based on an academic research article:

Legleiter CJ, Kyriakidis PC. 2006. Forward and Inverse Transformation between Cartesian and Channel-fitted Coordinate Systems for Meandering Rivers. Mathematical Geology 38 : 927–958. DOI: 10.1007/s11004-006-9056-6

• The original source code from this article was in Matlab (acquired by Dietrich from Carl Legleiter, cjl@usgs.gov). This code is a translation of that original Matlab code with some added features/tweaks.

Given a digitized stream centerline and a set of input x,y coordinates. This software will transform the input x,y coordinates into a curvalinear coordinate system based on the stream centerline. This stream normal coordinate system is:

• ds - a downstream distance (from the most upstream point)
• xs - a cross-stream distance (an orthogonal distance to the centerline along the normal vector)

The reverse transofrmation is also possible.

In the demo folder there are two(2) notebook files that show examples of the code in action.

The inputs to the fuctions are arrays of points or pandas dataframes

X,Y points describing the centerline

a spatially variable search radii can be added by adding extra columns to the input centerline data and used in the fuctions

• downstream variable radii, but symmetric - 1-D Array
• downstream variable, but non-symmetric - 2-D Array
• Column 1 = left bank, Column 2 = right bank)

X,Y data points to be transformed

• the order of the inputs is kept, so concatenating with point attributes should be easy

Ensure you have the following packages installed:

• scipy, numpy, pandas, matplotlib

The transformation parameters are important, but require some trial and error. A lot will depend on what your initial point spacing is on your centerline and how tight your meander bends are.

• nDiscr = number of segments to split the centerline into
  • a good place to start is your total length / desired segment length
• rMax = maximum distance away from the centerline the code will search for points (see above how to make this spatially variable)

• nFilt = number of filtering iterations (default is 5)
• order = polynomial order of the filter (default is 3, cubic )
• window = number of points to include in the filter window (default is 5)

• More in-depth description of the process
• Overlapping search radii in sharp corners
  • Spatially variable rMax values helps
  • With Uniform RMax there is the possibility of overlapping cells
  • 
  • With Variable RMax there overlapping cells can be avoided
  • 
• Downstream distance variability as a function of transform parameters

Colors are based onthe Y-coordinates of the points

Colors are based onthe Downstream-coordinates of the points