WIP: Document epicell methods.

DeProjMethods.md

+# DeProj methods.
+
+We document here the methods of the two DeProj classes `deproj` and `epicell`. We separate methods in the ones that are useful for users of DeProj and the secondary ones that are used by other methods.
+
+[TOC]
+
+## The `epicell` class methods.
+
+In the following we suppose that `o` is an instance of `epicell`, for instance obtained by executing the a [self-contained example](RunExample.m) in this repository and for instance:
+
+```matlab
+>> o = dpr.epicells(4)
+
+o = 
+
+  epicell with properties:
+
+                 boundary: [26×3 single]
+                   center: [2.4705 11.1826 3.1008]
+             junction_ids: [5×1 double]
+                     area: 8.0176
+                perimeter: 12.5227
+             euler_angles: [-2.0734 0.4195 -0.2500]
+               curvatures: [0.0110 -4.8103e-05 0.0240 -0.0020]
+              ellipse_fit: [2.2284 11.1114 3.1008 2.3848 1.1178 0.4528]
+             eccentricity: 0.8834
+           proj_direction: 1.2539
+         uncorrected_area: 7.3173
+    uncorrected_perimeter: 12.1116
+                       id: 4
+```
+
+### Main `epicell` methods.
+
+There are no important user methods for `epicell`. All the important information is already in the properties. 
+
+### Secondary `epicell` methods.
+
+#### `plot_contour_2d`
+
+`h = plot_contour_2d( obj )`
+
+Plot the cell contour (closed) projected on the XY plane, on the current axes. Return `h` the handle to the contour `Line` object.
+
+#### `plot_ellipse_2d`
+
+`h = plot_ellipse_2d( obj, npoints, ax )`
+
+Plot the ellipse fitted on the contour, projected on the XY plane.
+
+The `npoints` parameter specifies how much points to use for the contour, and `ax` the axes to plot them on. Return `h` the handle to the contour `Line` object.
+
+```matlab
+>> o.plot_contour_2d;
+>> axis equal
+>> hold on
+>> h = o.plot_ellipse_2d( 20, gca );
+>> h.Color = 'red'
+>> xlabel('x'), ylabel('y')
+```
+
+<img src="static/plot_contour_2d.png" alt="EllipsePlot"  width="400" />
+
+#### `plot_contour_3d`
+
+`h = plot_contour_3d( obj )`
+
+Plot the cell contour (closed) on the tissue surface in 3D. The plot is added to the current axes. Return `h` the handle to the contour `Line` object.
+
+#### `plot_ellipse_3d`
+
+`h = plot_ellipse_3d( obj, npoints, ax )`
+
+Plot the ellipse fitted on the contour, on the tissue surface in 3D.
+
+The `npoints` parameter specifies how much points to use for the contour, and `ax` the axes to plot them on. Return `h` the handle to the contour `Line` object.
+
+```matlab
+>> o.plot_contour_3d;
+>> axis equal
+>> hold on
+>> h = o.plot_ellipse_3d( 20, gca );
+>> h.Color = 'red'
+>> xlabel('x'), ylabel('y'), zlabel('z')
+```
+
+<img src="static/plot_contour_3d.png" alt="EllipsePlot3D"  width="400" />
+
+#### `get_ellipse_points`
+
+```matlab
+p = get_ellipse_points( obj, npoints )
+```
+
+Used by `plot_ellipse_2d` and `plot_ellipse_3d`.
+
+#### `plot_patch_2d`
+
+`h = plot_patch_2d( obj, val )`
+
+Plot the cell contour projected on the XY plane with interior filled according to the specified value `val` and the current axes colormap.
+
+```matlab
+>> # We need a second epicell for this example.
+>> o2 = dpr.epicells(7);
+>> o.plot_patch_2d( 1 );
+>> hold on, axis equal
+>> o2.plot_patch_2d( 2 );
+>> xlabel('x'), ylabel('y')
+```
+
+
+
+<img src="static/plot_patch_2d.png" alt="plot_patch_2d"  width="400" />
+
+#### `plot_patch_3d`
+
+`h = plot_patch_3d( obj, val )`
+
+Plot the cell contour in 3D on the tissue surface with interior filled according to the specified value `val` and the current axes colormap.
+
+```matlab
+>> o2 = dpr.epicells(7);
+>> o.plot_patch_3d( 1 );
+>> hold on, axis equal
+>> o2.plot_patch_3d( 2 );
+>> xlabel('x'), ylabel('y'), zlabel('z')
+```
+
+<img src="static/plot_patch_3d.png" alt="plot_patch_3d"  width="400" />
+
+#### Static method `euleurZXZ2rot`
+
+`R = euleurZXZ2rot( E )` converts the Euler angles, given with the ZX'Z'' convention into a 3D rotation matrix. The Euler angles come for instance from the `euler_angles` field of an `epicell`.
+
+```matlab
+>> R = epicell.euleurZXZ2rot( o.euler_angles )
+
+R =
+
+   -0.6647    0.6563   -0.3569
+   -0.7403   -0.6431    0.1962
+   -0.1008    0.3946    0.9133
+```
+
+#### Static method `rot2eulerZXZ`
+
+`[ E, E_deg ] = rot2eulerZXZ( R )` is the converse method. It returns the Euler angles (in the ZX'Z'' convention) computed from the specified rotation matrix.
+
+```matlab
+>> E = epicell.rot2eulerZXZ( R )
+
+E =
+
+   -2.0734    0.4195   -0.2500
+```
+
+The angles are returned in radians. The second output argument `E_deg` is the angles in degrees.
+
+#### Static method `fit_ellipse_2d`
+
+`[ f, Q ] = fit_ellipse_2d( p, method )`
+
+Fit a 2D ellipse to 2D points. The points must be specified as a `N x 2` matrix of coordinates. The `method` can be `direct` (the default) or `taubin`. The `direct` method use an algorithm proposed in:
+
+> [A. W. Fitzgibbon, M. Pilu, R. B. Fisher, "*Direct Least Squares Fitting of Ellipses*", IEEE Trans. PAMI, Vol. 21, pages 476-480 (1999).](https://ieeexplore.ieee.org/document/546029)
+
+The `taubin` method relies on the algorithm proposed 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)](https://ieeexplore.ieee.org/document/103273)
+
+The first output argument `f` contains the ellipse parameter in cartesian form. It is a `1 x 5` array made respectively of:
+
+- The x coordinate of the ellipse center.
+- The y coordinate of the ellipse center.
+- The [semi-major axis of the ellipse](https://en.wikipedia.org/wiki/Ellipse#Semi-major_and_semi-minor_axes) `a`.
+- The semi-minor axis of the ellipse `b`. We always have `a > b` and both values are positive.
+- The angle of the semi-major axis with the X axis.
+
+The second output argument `Q` contains the parametric ellipse parameter. It is a `6 x 1` array such that if its elements are A, B, C … the ellipse is given by:
+
+*A x² + B x y + C y² + D x + E y + F = 0*
+
+### Static method `fit_ellipse_3d`
+
+`[ f3d, R ] = fit_ellipse_3d( p, E, method )`
+
+Fit a 2D ellipse to a set of 3D points. The fit requires (or computes) the Euler angles of the plane fitted through the points, 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.
+
+The inputs are `p` the matrix of `N x 3` points to fit, `E` the Euler angles (as `1 x 3` array) of the plane on which to project the points, and `method` the fitting method. See the documentation of `fit_ellipse_2d` for a description of the methods. If `method` is not specified, the method uses the `direct` algorithm. If the Euler angles `E` are not specified, they are computed using singular value decomposition.
+
+The first output arguments `f3d` contains the ellipse parameter in cartesian form. It is a `1 x 6` array made respectively of:
+
+- The x coordinate of the ellipse center.
+- The y coordinate of the ellipse center.
+- The z coordinate of the ellipse center.
+- The [semi-major axis of the ellipse](https://en.wikipedia.org/wiki/Ellipse#Semi-major_and_semi-minor_axes) `a`.
+- The semi-minor axis of the ellipse `b`. We always have `a > b` and both values are positive.
+- The angle of the semi-major axis with the X'' axis, after the composed rotation by the Euler angles.
+
+The second argument `R` is the rotation matrix computed from the Euler angles.
+
+## The `deproj` class methods.
+
+### Main `deproj` methods.
+
+### Secondary `deproj` methods.
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