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118 lines
3.1 KiB
Matlab
118 lines
3.1 KiB
Matlab
function out = xyz2spz(xyz_data,site)
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%function out = xyz2spz(xyz_data,site)
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%
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%Function to transform (x,y,z) coordinates on an embayed beach to alongshore - cross-shore
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%coordinates (s,p,z) using the log spiral, given by the equation
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%r = r0*exp(A*theta). A = cot(alpha).
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%
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%xyz_data is a structure containing:
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%
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%xyz_data.x
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%xyz_data.y
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%xyz_data.z
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%
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%site is the name of the structure generated from the MALT graphical user interface
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%
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%Refer to paper
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%
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%Harley, M.D. and Turner,I.L. (2007) A simple data transformation technique
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%for pre-processing survey data at embayed beaches, Coast. Eng.,
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%doi:10.1016/j.coastaleng.2007.07.001, in press.
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%
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%Created by Mitch Harley
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%8th August, 2005
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%Last Modified 4th April, 2012
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%----------------------------------------------------------------
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%LOAD LOGSPIRAL-FIT PARAMETERS
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eval(['load ' site ';'])
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eval(['site = ' site ';'])
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%Define origin and A of log spiral
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origin = site.origin;
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alph = site.alpha;
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A = cot(alph*pi/180);
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r0_origin = site.r0_origin;
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%-----------------------------------------------------------------
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%DO TRANSFORMATION
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%Points need to be sorted prior to analysis %MDH 4/4/2012
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aa = [xyz_data.x xyz_data.y xyz_data.z];
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[sorted_points,Isort] = sortrows(aa);
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%Convert xyz coordinates to polar coordinates
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r = sqrt((sorted_points(:,1) - origin(1)).^2+(sorted_points(:,2) - origin(2)).^2);
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theta = unwrap(atan2((sorted_points(:,2)-origin(2)),(sorted_points(:,1)-origin(1))) );
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%Find constants delta and kappa
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delta = pi/2+acot(A)-theta; %From Equation 5
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kappa = r./(r0_origin*sin(pi/2-acot(A))); %From Equation 6
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%Find theta_s by solving implicitly using fzero function
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for i = 1:length(theta);
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%Use muller function in case any complex solutions
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theta_s(i,1) = muller(@(x) (x-(1/A)*log(kappa(i)*sin(delta(i)+x))),[theta(i)-pi/8 theta(i) theta(i)+pi/8]);%From Equation 6
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end
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%plot(theta_s*180/pi)
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%Find r_s
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r_s = r0_origin*exp(A*theta_s);%From Equation 1
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%Find s
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lamda = r0_origin*sec(acot(A));%From Equation 8
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start_point = 0; %Can be changed to make a more suitable start point
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s = lamda*(exp(A*theta_s)-exp(A*start_point));%From Equation 8
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%Find p
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p = r.*sin(theta-theta_s)./sin(pi/2-acot(A)); %From Equation 9
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%Convert any complex numbers to real numbers
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p = real(p);
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s = real(s);
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%Sort back points to get the right indices %MDH 4/4/2012
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p = sort_back(p,Isort);
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s = sort_back(s,Isort);
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%-----------------------------------------------------------------
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%POST-PROCESS DATA
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%s data
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if site.reverse_s ==0
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s = s - site.startpoint;%Make minimum s == 0
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elseif site.reverse_s ==1
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s = -(s - site.startpoint);
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end
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%p data
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if site.subtract_res ==1 %Add switch for user to subtract residuals or not - MDH 19/5/2010
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[MIN,L] = min(site.boundary.s);
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I = find(s<=MIN);
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p(I) = p(I) - site.boundary.p(L);
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[MAX,L] = max(site.boundary.s);
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I = find(s>=MAX);
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p(I) = p(I) - site.boundary.p(L);
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I = find(s>MIN&s<MAX);
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p(I) = p(I) - interp1(site.boundary.s,site.boundary.p,s(I));%Subtract logspiral errors from p data
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end
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if site.alpha<0
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p = -p;
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end
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%-----------------------------------------------------------------
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out.s = s;
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out.p = p;
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out.z = xyz_data.z;
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