/*
Copyright (c) 2019- Ferhat Kurtulmuş
Boost Software License - Version 1.0 - August 17th, 2003
Permission is hereby granted, free of charge, to any person or organization
obtaining a copy of the software and accompanying documentation covered by
this license (the "Software") to use, reproduce, display, distribute,
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Software, and to permit third-parties to whom the Software is furnished to
do so, all subject to the following:
The copyright notices in the Software and this entire statement, including
the above license grant, this restriction and the following disclaimer,
must be included in all copies of the Software, in whole or in part, and
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works are solely in the form of machine-executable object code generated by
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
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*/

module measure.ellipsefit;

import std.stdio;
import std.math;
import std.range;
import std.algorithm;
import std.algorithm.searching;

import measure.types;
import measure.regionprops;
import measure.eigen;

// gives exact results of matlab
Ellipse ellipseFit(XYList xylist)
{
    const double meanX = xylist.xs.mean;
    const double meanY = xylist.ys.mean;
    
    auto cov = covNx2(xylist.xs, xylist.ys);

    auto eigSolver = new Eig(cov);
    auto V = eigSolver.getV();
    auto lambda = eigSolver.getD();
    
    auto lambda_d = lambda.diag();
    foreach(ref val; lambda_d) val = 4*sqrt(val);

    const double minorAxisLength = minElement(lambda_d);
    //const auto minor_idx = minIndex(lambda_d);
    const double majorAxisLength = maxElement(lambda_d);
    auto major_idx = maxIndex(lambda_d);
    
    
    double[2] major_vec = [V[1, major_idx], V[0, major_idx]] ;
    
    double orientation;
    if (majorAxisLength == minorAxisLength)
      orientation = 0;
    else if (major_vec[1] == 0)
      orientation = 90;
    else
      orientation = -(180/PI) * atan (major_vec[0] / major_vec[1]);
    
    return Ellipse(orientation, meanX + 1, meanY + 1, majorAxisLength, minorAxisLength);
}

Mat2D!double covNx2(U)(U[] xs, U[] ys)
{
    const auto npoints = xs.length;
    const auto _npoints = ys.length;
    
    assert(npoints == _npoints, "array sizes are mismatch!");
    
    auto _cov = Mat2D!double(npoints, 2);

    const double meanX = xs.mean;
    const double meanY = ys.mean;
    
    foreach(i; 0..npoints)
    {
        _cov[i, 0] = xs[i] - meanX;
        _cov[i, 1] = ys[i] - meanY;
    }
    
    auto rescov = _cov.transpose() * _cov;
    double[2] d; d[0..$] = 1.0/12;
    
    auto covv = Mat2D!double.diagFromArray(d);
    
    for(size_t i = 0; i < covv.rows; i++)
        for(size_t j = 0; j < covv.cols; j++)
        {
            rescov[i, j] = rescov[i, j] * (1.0/cast(double)npoints);
            rescov[i, j] = rescov[i, j] + covv[i, j];
        }
    return rescov;
}

// gives exact results of matlab and 1 ms faster :)
Ellipse ellipseFit2(Region rg) @nogc
{
    const double center_x = rg.m10/rg.m00;
    const double center_y = rg.m01/rg.m00;
    
    // central moments
    const double a = rg.m20/rg.m00 - center_x^^2 + 1.0/12;
    const double b = 2*(rg.m11/rg.m00 - center_x*center_y);
    const double c = rg.m02/rg.m00 - center_y^^2 + 1.0/12;

    const double theta = 0.5*atan(b/(a-c)) + (a<c)*PI/2;

    const double axis1 = sqrt(8*(a+c-sqrt(b^^2+(a-c)^^2)))/2;
    const double axis2 = sqrt(8*(a+c+sqrt(b^^2+(a-c)^^2)))/2;

    double orientation;
    if (axis1 == axis2)
        orientation = 0;
    else
    {
        orientation = -(180/PI) * theta;
        if (abs(orientation) > 90)
            orientation = 180 - abs(orientation);
    }
        
    return Ellipse(orientation, rg.bBox.x + center_x + 1, rg.bBox.y + center_y + 1, 2*axis2, 2*axis1);
}