#### wrf-fire /other/Matlab/detect_ignition/ellipse_3d.m

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 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159``` ```function [ ] = ellipse_fit( data,ci ,rate_vector,test_flag) % function takes in a matrix of points (data) and a confidence interval % (ci)and plots a 3d cone of the fire. rate_vector is best guess as what % direction in which the fire spreads most rapidly %test_flag =1 tells function you are % using random data. Used to scale figure window % fitting of ellipse based on code from % http://www.visiondummy.com/2014/04/draw-error-ellipse-representing-covariance-matrix/ covariance = cov(data); [eigenvec, eigenval ] = eig(covariance); % Get the index of the largest eigenvector [largest_eigenvec_ind_c, r] = find(eigenval == max(max(eigenval))); largest_eigenvec = eigenvec(:, largest_eigenvec_ind_c); % Get the largest eigenvalue largest_eigenval = max(max(eigenval)); % Get the smallest eigenvector and eigenvalue if(largest_eigenvec_ind_c == 1) smallest_eigenval = max(eigenval(:,2)); smallest_eigenvec = eigenvec(:,2); else smallest_eigenval = max(eigenval(:,1)); smallest_eigenvec = eigenvec(1,:); end % Calculate the angle between the x-axis and the largest eigenvector angle = atan2(largest_eigenvec(2), largest_eigenvec(1)); % This angle is between -pi and pi. % Let's shift it such that the angle is between 0 and 2pi if(angle < 0) angle = angle + 2*pi; end % Get the coordinates of the data mean avg = mean(data); % Get the 95% confidence interval error ellipse %chisquare_val = 2.4477; %chisquare_val = 2.2; chisquare_val = ci; %parameters of initial ellipse x^2/a^2 + y^2/b^2 = 1 phi = angle; X0=avg(1); Y0=avg(2); a=chisquare_val*sqrt(largest_eigenval); b=chisquare_val*sqrt(smallest_eigenval); %set up mesh theta_incs = 40; theta_grid = linspace(0,2*pi,theta_incs); time_incs = 20; time_grid = linspace(0,1,time_incs); [u,t] = meshgrid(theta_grid,time_grid); % the ellipse in x and y coordinates ellipse_x_r = a*cos( theta_grid ); ellipse_y_r = b*sin( theta_grid ); %Define a rotation matrix R = [ cos(phi) sin(phi); -sin(phi) cos(phi) ]; %let's rotate the ellipse to some angle phi r_ellipse = [ellipse_x_r;ellipse_y_r]' * R; % Draw the error ellipse % axis square plot(r_ellipse(:,1) + X0,r_ellipse(:,2) + Y0,'-') hold on; %find dot product between rate_vector and axis of ellipse %largest_eigenvec axis_dot = dot(largest_eigenvec,rate_vector); %find location of focus of ellipse f = sqrt(a^2-b^2); %if axis_dot >=0 if (axis_dot >= 0) f_x = X0-f*cos(phi); f_y = Y0-f*sin(phi); %if axis_dot <0 else f_x = X0+f*cos(phi); f_y = Y0+f*sin(phi); end %if format long g disp('Coordinates of focus: ') fprintf('Lon: %d Lat: %d \n',f_x,f_y) %plot location of focus of ellipse plot(f_x,f_y,'*'); %generate surface for unrotated system if (axis_dot >= 0) x_s = (f*t + a*cos(u).*t); y_s = b*sin(u).*t; else x_s = -(f*t + a*cos(u).*t); y_s = -b*sin(u).*t; end %if z_s = t; %Define a rotation matrix rot = [cos(phi) sin(phi) ; sin(phi) -cos(phi) ]; %rotate layers and shift x_r = zeros(time_incs,theta_incs); y_r = x_r; for i = 1:time_incs new = rot*[x_s(i,:);y_s(i,:)]; x_r(i,:) = f_x + new(1,:); y_r(i,:) = f_y + new(2,:); end %plot cone surface view(3) surfc(x_r,y_r,z_s) hold on % Draw the error ellipse plot(r_ellipse(:,1) + X0,r_ellipse(:,2) + Y0,'-') hold on; % Plot the original data plot(data(:,1), data(:,2), '.'); x_min = min(data(:,1)); x_max = max(data(:,1)); y_min = min(data(:,2)); y_max = max(data(:,2)); xlim([x_min-0.04,x_max+0.04]); ylim([y_min-0.04,y_max+0.04]); if test_flag == 1 mindata = min(min(data)); maxdata = max(max(data)); xlim([mindata-3, maxdata+3]); ylim([mindata-3, maxdata+3]); end hold on; % Plot the eigenvectors quiver(X0, Y0, -largest_eigenvec(1)*sqrt(largest_eigenval), -largest_eigenvec(2)*sqrt(largest_eigenval), '-m', 'LineWidth',2); %quiver(X0, Y0, smallest_eigenvec(1)*sqrt(smallest_eigenval), smallest_eigenvec(2)*sqrt(smallest_eigenval), '-g', 'LineWidth',2); end ```