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mStat_amplitude.m
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mStat_amplitude.m
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function[amplitudeOfBends] = mStat_amplitude(inflectionX, inflectionY,...
nBends, maxCurvX, maxCurvY, newInflectionPts,numMaxPts)
% Last Modified: November 2014 by Kristin Dauer.
% Last Modified: April 2016 by Lucas Dominguez.
%
% This function takes the x,y coordinates of the peaks and troughs
% of a given river reach and calculates the planimetric amplitude
% of each bend. Note: the planimetric amplitude is defined as the
% distance between the point of maximum curvature and the line between
% the limiting inflection points of each bend. In this function, the
% amplitude is found using the vector distance formula and the
% "createLine" and "projPointOnLine" functions from the MATLAB file
% exchange.
%
% INPUTS:
%
% inflectionX = the X-coordinates of each inflection point defined
% along the river reach.
% inflectionY = the Y-coordinates of each inflection point defined
% along the river reach.
% nBends = the number of bends in the river reach of interest.
% maxCurvX = the x-coordinates of the peaks and troughs along the
% river reach.
% maxCurvY = the y-coordinates of the peaks and troughs along the
% river reach.
% numMaxPts = an array, where each row represents a bend, and the
% number in that row tells how many points of maximum curvature are in
% that bend.
%
% OUTPUTS:
% amplitudeOfBends = a structure that contains the planarmetric
% amplitude of each river bend in order from upstream to downstream.
%--------------------------------------------------------------------------
% The x,y coordinates of the peaks/troughs of each bend are known
% already as maxCurvX and maxCurvY. Make a matrix to
% contain all of these maximum curvature points.
maxCurvXY = [maxCurvX maxCurvY];
% Thus, the first step in the calculation is to estimate a point along
% the line between the limiting inflection points that can serve as
% the other end of the amplitude distance. This point is found below
% by projecting the point of maximum curvature onto the constructed
% line between the two limiting inflection points.
% Construct lines between the two limiting inflection points of each
% bend. Store these lines in the matrix called "lineC".
%lineC = createLine((newInflectionPts(1,:)), newInflectionPts(2,:));
for i = 1:nBends
lineC(i,:) = createLine((newInflectionPts(i,:)), newInflectionPts(i+1,:));
end
% Now, we can find the amplitude of each bend using the distance
% formula between the peaks/troughs and the projected points.
% If there are more than one points of maximum curvature in a bend,
% then the amplitude is calculated at each of the points of maximum
% curvature in that bend, and the largest value is assigned as the
% amplitude of the bend.
sizeMax = max(numMaxPts);
p = 0;
amplitudeOfBends = zeros(nBends,1);
for i = 1:length(numMaxPts)
%If there are multiple points of maximum curvature in a bend, enter this loop
if numMaxPts(i)> 1
k=1;
amplitudeOfBend = zeros(sizeMax,1);
for j = i+p:i+p+numMaxPts(i)-1
maxCurvXYPt = maxCurvXY(j,:);
lineCPt = lineC(i,:);
projection = projPointOnLine(maxCurvXYPt, lineCPt);
amplitudeOfBend(k,1)= sqrt((maxCurvXY(j,1)-projection(1,1)).^(2) +...
(maxCurvXY(j,2)-projection(1,2)).^(2));
k = k+1;
end
maxAmplitudeOfBend=max(amplitudeOfBend);
amplitudeOfBends(i,1)= maxAmplitudeOfBend;
p2 = numMaxPts(i)-1;
p = p2+p;
%If only one point of maximum curvature in bend
elseif numMaxPts(i) ==0
p = p-1;
else
if i==length(numMaxPts)
else
maxCurvXYPt = maxCurvXY(i+p,:);
lineCPt = lineC(i,:);
projection = projPointOnLine(maxCurvXYPt, lineCPt);
amplitudeOfBends(i,1) = sqrt((maxCurvXY(i+p,1)-projection(1,1)).^(2) +...
(maxCurvXY(i+p,2)-projection(1,2)).^(2));
end
end
end