/libs/PEAR/Image/Graph/Tool.php

<?php



/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */



/**

 * Image_Graph - Main class for the graph creation.

 *

 * PHP versions 4 and 5

 *

 * LICENSE: This library is free software; you can redistribute it and/or modify

 * it under the terms of the GNU Lesser General Public License as published by

 * the Free Software Foundation; either version 2.1 of the License, or (at your

 * option) any later version. This library is distributed in the hope that it

 * will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty

 * of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser

 * General Public License for more details. You should have received a copy of

 * the GNU Lesser General Public License along with this library; if not, write

 * to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA

 * 02111-1307 USA

 *

 * @category   Images

 * @package    Image_Graph

 * @author     Jesper Veggerby <pear.nosey@veggerby.dk>

 * @copyright  Copyright (C) 2003, 2004 Jesper Veggerby Hansen

 * @license    http://www.gnu.org/copyleft/lesser.html  LGPL License 2.1

 * @version    CVS: $Id: Tool.php,v 1.3 2009/10/14 06:53:44 mhoegh Exp $

 * @link       http://pear.php.net/package/Image_Graph

 */



/**

 * This class contains a set of tool-functions.

 * 

 * These functions are all to be called statically

 *

 * @category   Images

 * @package    Image_Graph

 * @author     Jesper Veggerby <pear.nosey@veggerby.dk>

 * @copyright  Copyright (C) 2003, 2004 Jesper Veggerby Hansen

 * @license    http://www.gnu.org/copyleft/lesser.html  LGPL License 2.1

 * @version    Release: @package_version@

 * @link       http://pear.php.net/package/Image_Graph

 */

class Image_Graph_Tool

{



    /**

     * Return the average of 2 points

     *

     * @param double P1 1st point

     * @param double P2 2nd point

     * @return double The average of P1 and P2

     * @static

     */

    function mid($p1, $p2)

    {

        return ($p1 + $p2) / 2;

    }



    /**

     * Mirrors P1 in P2 by a amount of Factor

     *

     * @param double $p1 1st point, point to mirror

     * @param double $o2 2nd point, mirror point

     * @param double $factor Mirror factor, 0 returns $p2, 1 returns a pure

     * mirror, ie $p1 on the exact other side of $p2

     * @return double $p1 mirrored in $p2 by Factor

     * @static

     */

    function mirror($p1, $p2, $factor = 1)

    {

        return $p2 + $factor * ($p2 - $p1);

    }



    /**

     * Calculates a Bezier control point, this function must be called for BOTH

     * X and Y coordinates (will it work for 3D coordinates!?)

     *

     * @param double $p1 1st point

     * @param double $p2 Point to

     * @param double $factor Mirror factor, 0 returns P2, 1 returns a pure

     *   mirror, i.e. P1 on the exact other side of P2

     * @return double P1 mirrored in P2 by Factor

     * @static

     */

    function controlPoint($p1, $p2, $factor, $smoothFactor = 0.75)

    {

        $sa = Image_Graph_Tool::mirror($p1, $p2, $smoothFactor);

        $sb = Image_Graph_Tool::mid($p2, $sa);



        $m = Image_Graph_Tool::mid($p2, $factor);



        $pC = Image_Graph_Tool::mid($sb, $m);



        return $pC;

    }



    /**

     * Calculates a Bezier point, this function must be called for BOTH X and Y

     * coordinates (will it work for 3D coordinates!?)

     *

     * @param double $t A position between $p2 and $p3, value between 0 and 1

     * @param double $p1 Point to use for calculating control points

     * @param double $p2 Point 1 to calculate bezier curve between

     * @param double $p3 Point 2 to calculate bezier curve between

     * @param double $p4 Point to use for calculating control points

     * @return double The bezier value of the point t between $p2 and $p3 using

     * $p1 and $p4 to calculate control points

     * @static

     */

    function bezier($t, $p1, $p2, $p3, $p4)

    {

        // (1-t)^3*p1 + 3*(1-t)^2*t*p2 + 3*(1-t)*t^2*p3 + t^3*p4

        return pow(1 - $t, 3) * $p1 +

            3 * pow(1 - $t, 2) * $t * $p2 +

            3 * (1 - $t) * pow($t, 2) * $p3 +

            pow($t, 3) * $p4;

    }

    

    /**

     * For a given point (x,y) return a point rotated by a given angle aroung the center (xy,yc)

     *

     * @param int $x x coordinate of the point to rotate

     * @param int $y y coordinate of the point to rotate

     * @param int $xc x coordinate of the center of the rotation

     * @param int $yc y coordinate of the center of the rotation

     * @param int $angle angle of the rotation

     * @return array the coordinate of the new point

     * @static

     */

    function rotate($x, $y, $xc, $yc, $angle)

    {

        $cos = cos(deg2rad($angle));

        $sin = sin(deg2rad($angle));

        $xr= $x - $xc;

        $yr= $y - $yc;

        $x1= $xc + $cos * $xr - $sin * $yr;

        $y1= $yc + $sin * $xr + $cos * $yr;

        return array((int) $x1,(int) $y1);

    }



    /**

     * If a number is close 0 zero (i.e. 0 within $decimal decimals) it is rounded down to zero

     * 

     * @param double $value The value to round

     * @param int $decimal The number of decimals

     * @return double The value or zero if "close enough" to zero

     * @static

     */

    function close2zero($value, $decimal)

    {

        if (abs($value) < pow(10, -$decimal)) {

            return 0;

        }

        else {

            return $value;

        }

    }

    

    /**

     * Calculate the dimensions and center point (of gravity) for an arc

     * 

     * @param int $v1 The angle at which the arc starts

     * @param int $v2 The angle at which the arc ends

     * @return array An array with the dimensions in a fraction of a circle width radius 1 'rx', 'ry' and the

     * center point of gravity ('cx', 'cy')

     * @static

     */

    function calculateArcDimensionAndCenter($v1, $v2)

    { 

        // $v2 always larger than $v1

        $r1x = Image_Graph_Tool::close2zero(cos(deg2rad($v1)), 3); 

        $r2x = Image_Graph_Tool::close2zero(cos(deg2rad($v2)), 3);

        

        $r1y = Image_Graph_Tool::close2zero(sin(deg2rad($v1)), 3);

        $r2y = Image_Graph_Tool::close2zero(sin(deg2rad($v2)), 3);

    

        // $rx = how many percent of the x-diameter of the entire ellipse does the arc x-diameter occupy: 1 entire width, 0 no width

        // $cx = at what percentage of the diameter does the center lie

        

        // if the arc passes through 0/360 degrees the "highest" of r1x and r2x is replaced by 1!

        if ((($v1 <= 0) && ($v2 >= 0)) || (($v1 <= 360) && ($v2 >= 360))) {

            $r1x = min($r1x, $r2x);

            $r2x = 1;

        } 

        

        // if the arc passes through 180 degrees the "lowest" of r1x and r2x is replaced by -1!

        if ((($v1 <= 180) && ($v2 >= 180)) || (($v1 <= 540) && ($v2 >= 540))) {

            $r1x = max($r1x, $r2x);

            $r2x = -1;

        }

        

        if ($r1x >= 0) { // start between [270; 360] or [0; 90]        

            if ($r2x >= 0) {

                $rx = max($r1x, $r2x) / 2;

                $cx = 0; // center lies 0 percent along this "vector"

            }

            else {

                $rx = abs($r1x - $r2x) / 2;

                $cx = abs($r2x / 2) / $rx;

            }

        }

        else {  // start between ]90; 270[

            if ($r2x < 0) {

                $rx = max(abs($r1x), abs($r2x)) / 2;

                $cx = $rx;

            }

            else {

                $rx = abs($r1x - $r2x) / 2;

                $cx = abs($r1x / 2) / $rx;

            }

        }

        

        // $ry = how many percent of the y-diameter of the entire ellipse does the arc y-diameter occupy: 1 entire, 0 none

        // $cy = at what percentage of the y-diameter does the center lie

    

        // if the arc passes through 90 degrees the "lowest" of r1x and r2x is replaced by -1!

        if ((($v1 <= 90) && ($v2 >= 90)) || (($v1 <= 450) && ($v2 >= 450))) {

            $r1y = min($r1y, $r2y);

            $r2y = 1;

        }

        

        // if the arc passes through 270 degrees the "highest" of r1y and r2y is replaced by -1!

        if ((($v1 <= 270) && ($v2 >= 270)) || (($v1 <= 630) && ($v2 >= 630))) {

            $r1y = max($r1y, $r2y);

            $r2y = -1;

        } 

            

        if ($r1y >= 0) { // start between [0; 180]        

            if ($r2y >= 0) {

                $ry = max($r1y, $r2y) / 2;

                $cy = 0; // center lies 0 percent along this "vector"

            }

            else {

                $ry = abs($r1y - $r2y) / 2;

                $cy = abs($r2y / 2) / $ry;

            }

        }

        else {  // start between ]180; 360[

            if ($r2y < 0) {

                $ry = max(abs($r1y), abs($r2y)) / 2;

                $cy = $ry;

            }

            else {

                $ry = abs($r1y - $r2y) / 2;

                $cy = abs($r1y / 2) / $ry;

            }

        }

        

        return array(

            'rx' => $rx,

            'cx' => $cx,

            'ry' => $ry,

            'cy' => $cy

        );

    }

    

    /**

     * Calculate linear regression on a dataset

     * @param array $data The data to calculate regression upon

     * @return array The slope and intersection of the "best-fit" line

     * @static

     */    

    function calculateLinearRegression(&$data)

    {

        $sumX = 0; 

        $sumY = 0;

        foreach ($data as $point) {

            $sumX += $point['X'];

            $sumY += $point['Y'];

        }        

        $meanX = $sumX / count($data);

        $meanY = $sumY / count($data);



        $sumXX = 0;

        $sumYY = 0;

        $sumXY = 0;

        foreach ($data as $point) {

            $sumXX += ($point['X'] - $meanX) * ($point['X'] - $meanX);

            $sumYY += ($point['Y'] - $meanY) * ($point['Y'] - $meanY);

            $sumXY += ($point['X'] - $meanX) * ($point['Y'] - $meanY);

        }        



        $result = array();

        $result['slope'] = ($sumXY / $sumXX);

        $result['intersection'] = $meanY - ($result['slope'] * $meanX);

        return $result;

    }

    

}



?>