Reorganize the epicell class.

src/epicell.m → src/@epicell/epicell.m

@@ -75,7 +75,7 @@ classdef epicell
         end
     end
     
-    %% Static methods: compute final properties value.
+    %% Private static methods: compute final properties value.
     methods ( Access = private, Hidden = true, Static = true )
         
         function p = centered_points( p )
@@ -142,8 +142,34 @@ classdef epicell
             p = p - repmat( c, size( p, 1 ), 1 );
             % Fit a plane to these points.
             [ ~, ~, v ] = svd( p );
-            E = rot2eulerZXZ( v );
+            E = epicell.rot2eulerZXZ( v );
         end
+        
+       
+        
+    end
+    
+    %% Public static methods: utilities.
+    
+    methods ( Access = public, Hidden = false, Static = true )
+        % Convert euler angles to rotation matrix.
+        R = euleurZXZ2rot( E )
+        
+        % Convert rotation matrix to euler angles.
+        [ E, E_deg ] = rot2eulerZXZ( R )
+        
+        % Fit a 2D ellipse to a set of 2D points.
+        [ f, Q ] = fit_ellipse_2d( p, method )
+        
+        % Fit a 2D ellipse to a set of 3D points.
+        [ f3d, v ] = fit_ellipse_3d( p, E, method )
+        
+        % Plot a 2D ellipse in 3D.
+        h = plot_ellipse_3d( f3d, v, npoints )
+        
+        % Plot an ellipse in XY plane.
+        h = plot_ellipse_2d( f, npoints )
+        
     end
 end
 

src/fit_ellipse_3d.m → src/@epicell/fit_ellipse_3d.m

 function [ f3d, v ] = fit_ellipse_3d( p, E, method )
-%FIT_ELLIPSE_3D Fit a 2D ellipse on the 3D points.
-%   The fit requires the Euler angles of the plane fitted through the
-%   opints, so that we can project them on this plane. We then make a 2D 
-%   ellipse fit on the projected points. This turns to be much more robust 
-%   than a 3D fit, and also closely match our configuration.
-%   This function returns f3d = [ x0 y0 z0 a b theta ]
-%   and v, the ransformation matrix that rotates the 3D points close to the
+%FIT_ELLIPSE_3D Fit a 2D ellipse to a set of 3D points.
+%   The fit requires (or compute) the Euler angles of the plane fitted
+%   through the opints, so that we can project them on this plane. We then
+%   make a 2D ellipse fit on the projected points. This turns to be much
+%   more robust than a 3D fit, and also closely match our configuration.
+%
+%   This function returns f3d = [ x0 y0 z0 a b theta ]. These are the
+%   cartesian parameters of the ellipse in the rotated plane. The ellipse
+%   semi-major axis and semi-minor axis are always so that a >= b and theta
+%   measure the angle of the semi-major axis with respect to the X axis (in
+%   the rotated plane).
+%
+%   v is the transformation matrix that rotates the 3D points close to the
 %   XY plane. It will be used to plot the ellipse in 3D.
 
 %   Greatly inspired from https://stackoverflow.com/questions/29051168
@@ -28,7 +34,7 @@ function [ f3d, v ] = fit_ellipse_3d( p, E, method )
     % Rotate the points into the principal axes frame.
     pt = p * v;
 
-    f = fit_ellipse_2d( pt( :, 1:2 ), method );
+    f = epicell.fit_ellipse_2d( pt( :, 1:2 ), method );
     
     f( 1 ) = f( 1 ) + c( 1 );
     f( 2 ) = f( 2 ) + c( 2 );

src/rot2eulerZXZ.m → src/@epicell/rot2eulerZXZ.m

-function[E,E_deg]=rot2eulerZXZ(R)
+function[ E, E_deg ] = rot2eulerZXZ( R )
 %ROT2EULERZXZ Convert rotation matrix to ZX'Z' Euler angles.
 
     r13 = R( 1, 3 );

src/fit_ellipse.m

-function f = fit_ellipse( p, E )
-%FIT_ELLIPSE Fit a 2D ellipse to the 3D points.
-%   The fit requires the Euler angles of the plane fitted through the
-%   opints, so that we can project them on this plane. We then make a 2D 
-%   ellipse fit on the projected points. This turns to be much more robust 
-%   than a 3D fit, and also closely match our configuration.
-
-%   Greatly inspired from 
-% https://stackoverflow.com/questions/29051168/data-fitting-an-ellipse-in-3d-space
-
-    % Fit a plane to these points.
-    if nargin < 2
-        [ ~, ~, v ] = svd( p );
-    else
-        v = euleurZXZ2rot( E );
-    end
-    
-    % Rotate the points into the principal axes frame.
-    p = p * v;
-    
-    % Direct ellipse fit.
-%     A = direct_ellipse_fit( p( :, 1:2 ) );
-    A = taubin_ellipse_fit( p( :, 1:2 ) );    
-    f = quadratic_to_cartesian( A );
-    
-    %% Subfunctions
-    
-    function f = quadratic_to_cartesian( A )
-    % Equations taken from Wolfram website.
-        
-        a = A(1);
-        b = A(2);
-        c = A(3);
-        d = A(4);
-        f = A(5);
-        g = A(6);
-        
-        x0 = ( c * d - b * f ) / ( b^2 - a * c );
-        y0 = ( a * f - b * d ) / ( b^2 - a * c );
-        
-        l1 = sqrt( 2*(a*f^2+c*d^2+g*b^2-2*b*d*f-a*c*g) / ((b^2-a*c)*(sqrt((a-c)^2+4*b^2)-(a+c))));
-        l2 = sqrt( 2*(a*f^2+c*d^2+g*b^2-2*b*d*f-a*c*g) / ((b^2-a*c)*(-sqrt((a-c)^2+4*b^2)-(a+c))));
-        
-        if b == 0 && a < c
-            phi = 0;
-        elseif b == 0 && a > c
-            phi = 0.5*pi;
-        elseif b ~= 0 && a < c
-            phi = 0.5* acot((a-c)/(2*b));
-        else
-            phi = 0.5*pi + 0.5* acot((a-c)/(2*b));
-        end
-        
-        f = [ x0 y0 l1 l2 phi ];
-        
-    end
-    
-    function A = direct_ellipse_fit(XY) %#ok<DEFNU>
-    %  Direct ellipse fit, proposed in article
-    %    A. W. Fitzgibbon, M. Pilu, R. B. Fisher
-    %     "Direct Least Squares Fitting of Ellipses"
-    %     IEEE Trans. PAMI, Vol. 21, pages 476-480 (1999)
-    %
-    % Adapted from https://fr.mathworks.com/matlabcentral/fileexchange/22684-ellipse-fit-direct-method
-
-        centroid = mean(XY);   % the centroid of the data set
-        D1 = [(XY(:,1)-centroid(1)).^2, (XY(:,1)-centroid(1)).*(XY(:,2)-centroid(2)),...
-            (XY(:,2)-centroid(2)).^2];
-        D2 = [XY(:,1)-centroid(1), XY(:,2)-centroid(2), ones(size(XY,1),1)];
-        S1 = D1'*D1;
-        S2 = D1'*D2;
-        S3 = D2'*D2;
-        T = -inv(S3)*S2';
-        M = S1 + S2*T;
-        M = [M(3,:)./2; -M(2,:); M(1,:)./2];
-        [evec,eval] = eig(M); %#ok<ASGLU>
-        cond = 4*evec(1,:).*evec(3,:)-evec(2,:).^2;
-        A1 = evec(:,find(cond>0)); %#ok<FNDSB>
-        A = [A1; T*A1];
-        A4 = A(4)-2*A(1)*centroid(1)-A(2)*centroid(2);
-        A5 = A(5)-2*A(3)*centroid(2)-A(2)*centroid(1);
-        A6 = A(6)+A(1)*centroid(1)^2+A(3)*centroid(2)^2+...
-            A(2)*centroid(1)*centroid(2)-A(4)*centroid(1)-A(5)*centroid(2);
-        A(4) = A4;  A(5) = A5;  A(6) = A6;
-        A = A/norm(A);
-    end
-
-    function A = taubin_ellipse_fit(XY)
-    %   Ellipse fit by Taubin's Method published in
-    %      G. Taubin, "Estimation Of Planar Curves, Surfaces And Nonplanar
-    %                  Space Curves Defined By Implicit Equations, With
-    %                  Applications To Edge And Range Image Segmentation",
-    %      IEEE Trans. PAMI, Vol. 13, pages 1115-1138, (1991)
-    %
-    %     Input:  XY(n,2) is the array of coordinates of n points x(i)=XY(i,1), y(i)=XY(i,2)
-    %
-    %     Output: A = [a b c d e f]' is the vector of algebraic
-    %             parameters of the fitting ellipse:
-    %             ax^2 + bxy + cy^2 +dx + ey + f = 0
-    %             the vector A is normed, so that ||A||=1
-    %
-    %     Among fast non-iterative ellipse fitting methods,
-    %     this is perhaps the most accurate and robust
-    %
-    %     Note: this method fits a quadratic curve (conic) to a set of points;
-    %     if points are better approximated by a hyperbola, this fit will
-    %     return a hyperbola. To fit ellipses only, use "Direct Ellipse Fit".
-
-        centroid = mean(XY);   % the centroid of the data set
-        Z = [(XY(:,1)-centroid(1)).^2, (XY(:,1)-centroid(1)).*(XY(:,2)-centroid(2)),...
-            (XY(:,2)-centroid(2)).^2, XY(:,1)-centroid(1), XY(:,2)-centroid(2), ones(size(XY,1),1)];
-        M = Z'*Z/size(XY,1);
-        P = [M(1,1)-M(1,6)^2, M(1,2)-M(1,6)*M(2,6), M(1,3)-M(1,6)*M(3,6), M(1,4), M(1,5);
-            M(1,2)-M(1,6)*M(2,6), M(2,2)-M(2,6)^2, M(2,3)-M(2,6)*M(3,6), M(2,4), M(2,5);
-            M(1,3)-M(1,6)*M(3,6), M(2,3)-M(2,6)*M(3,6), M(3,3)-M(3,6)^2, M(3,4), M(3,5);
-            M(1,4), M(2,4), M(3,4), M(4,4), M(4,5);
-            M(1,5), M(2,5), M(3,5), M(4,5), M(5,5)];
-        Q = [4*M(1,6), 2*M(2,6), 0, 0, 0;
-            2*M(2,6), M(1,6)+M(3,6), 2*M(2,6), 0, 0;
-            0, 2*M(2,6), 4*M(3,6), 0, 0;
-            0, 0, 0, 1, 0;
-            0, 0, 0, 0, 1];
-        [V,D] = eig(P,Q);
-        [Dsort,ID] = sort(diag(D)); %#ok<ASGLU>
-        A = V(:,ID(1));
-        A = [A; -A(1:3)'*M(1:3,6)];
-        A4 = A(4)-2*A(1)*centroid(1)-A(2)*centroid(2);
-        A5 = A(5)-2*A(3)*centroid(2)-A(2)*centroid(1);
-        A6 = A(6)+A(1)*centroid(1)^2+A(3)*centroid(2)^2+...
-            A(2)*centroid(1)*centroid(2)-A(4)*centroid(1)-A(5)*centroid(2);
-        A(4) = A4;  A(5) = A5;  A(6) = A6;
-        A = A/norm(A);
-    end  %  Taubin
-
-    
-end
-