291 lines
9.9 KiB
PHP
291 lines
9.9 KiB
PHP
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<?php
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/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */
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/**
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* Image_Graph - Main class for the graph creation.
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*
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* PHP versions 4 and 5
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*
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* LICENSE: This library is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or (at your
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* option) any later version. This library is distributed in the hope that it
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* will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty
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* of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser
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* General Public License for more details. You should have received a copy of
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* the GNU Lesser General Public License along with this library; if not, write
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* to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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* 02111-1307 USA
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*
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* @category Images
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* @package Image_Graph
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* @author Jesper Veggerby <pear.nosey@veggerby.dk>
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* @copyright Copyright (C) 2003, 2004 Jesper Veggerby Hansen
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* @license http://www.gnu.org/copyleft/lesser.html LGPL License 2.1
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* @version CVS: $Id: Tool.php,v 1.4 2005/09/14 20:27:24 nosey Exp $
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* @link http://pear.php.net/package/Image_Graph
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*/
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/**
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* This class contains a set of tool-functions.
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*
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* These functions are all to be called statically
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*
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* @category Images
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* @package Image_Graph
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* @author Jesper Veggerby <pear.nosey@veggerby.dk>
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* @copyright Copyright (C) 2003, 2004 Jesper Veggerby Hansen
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* @license http://www.gnu.org/copyleft/lesser.html LGPL License 2.1
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* @version Release: @package_version@
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* @link http://pear.php.net/package/Image_Graph
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*/
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class Image_Graph_Tool
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{
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/**
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* Return the average of 2 points
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*
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* @param double P1 1st point
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* @param double P2 2nd point
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* @return double The average of P1 and P2
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* @static
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*/
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function mid($p1, $p2)
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{
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return ($p1 + $p2) / 2;
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}
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/**
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* Mirrors P1 in P2 by a amount of Factor
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*
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* @param double $p1 1st point, point to mirror
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* @param double $o2 2nd point, mirror point
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* @param double $factor Mirror factor, 0 returns $p2, 1 returns a pure
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* mirror, ie $p1 on the exact other side of $p2
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* @return double $p1 mirrored in $p2 by Factor
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* @static
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*/
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function mirror($p1, $p2, $factor = 1)
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{
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return $p2 + $factor * ($p2 - $p1);
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}
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/**
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* Calculates a Bezier control point, this function must be called for BOTH
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* X and Y coordinates (will it work for 3D coordinates!?)
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*
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* @param double $p1 1st point
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* @param double $p2 Point to
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* @param double $factor Mirror factor, 0 returns P2, 1 returns a pure
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* mirror, i.e. P1 on the exact other side of P2
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* @return double P1 mirrored in P2 by Factor
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* @static
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*/
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function controlPoint($p1, $p2, $factor, $smoothFactor = 0.75)
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{
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$sa = Image_Graph_Tool::mirror($p1, $p2, $smoothFactor);
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$sb = Image_Graph_Tool::mid($p2, $sa);
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$m = Image_Graph_Tool::mid($p2, $factor);
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$pC = Image_Graph_Tool::mid($sb, $m);
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return $pC;
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}
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/**
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* Calculates a Bezier point, this function must be called for BOTH X and Y
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* coordinates (will it work for 3D coordinates!?)
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*
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* @param double $t A position between $p2 and $p3, value between 0 and 1
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* @param double $p1 Point to use for calculating control points
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* @param double $p2 Point 1 to calculate bezier curve between
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* @param double $p3 Point 2 to calculate bezier curve between
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* @param double $p4 Point to use for calculating control points
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* @return double The bezier value of the point t between $p2 and $p3 using
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* $p1 and $p4 to calculate control points
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* @static
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*/
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function bezier($t, $p1, $p2, $p3, $p4)
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{
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// (1-t)^3*p1 + 3*(1-t)^2*t*p2 + 3*(1-t)*t^2*p3 + t^3*p4
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return pow(1 - $t, 3) * $p1 +
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3 * pow(1 - $t, 2) * $t * $p2 +
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3 * (1 - $t) * pow($t, 2) * $p3 +
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pow($t, 3) * $p4;
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}
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/**
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* For a given point (x,y) return a point rotated by a given angle aroung the center (xy,yc)
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*
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* @param int $x x coordinate of the point to rotate
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* @param int $y y coordinate of the point to rotate
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* @param int $xc x coordinate of the center of the rotation
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* @param int $yc y coordinate of the center of the rotation
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* @param int $angle angle of the rotation
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* @return array the coordinate of the new point
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* @static
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*/
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function rotate($x, $y, $xc, $yc, $angle)
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{
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$cos = cos(deg2rad($angle));
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$sin = sin(deg2rad($angle));
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$xr= $x - $xc;
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$yr= $y - $yc;
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$x1= $xc + $cos * $xr - $sin * $yr;
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$y1= $yc + $sin * $xr + $cos * $yr;
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return array((int) $x1,(int) $y1);
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}
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/**
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* If a number is close 0 zero (i.e. 0 within $decimal decimals) it is rounded down to zero
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*
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* @param double $value The value to round
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* @param int $decimal The number of decimals
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* @return double The value or zero if "close enough" to zero
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* @static
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*/
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function close2zero($value, $decimal)
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{
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if (abs($value) < pow(10, -$decimal)) {
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return 0;
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}
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else {
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return $value;
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}
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}
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/**
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* Calculate the dimensions and center point (of gravity) for an arc
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*
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* @param int $v1 The angle at which the arc starts
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* @param int $v2 The angle at which the arc ends
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* @return array An array with the dimensions in a fraction of a circle width radius 1 'rx', 'ry' and the
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* center point of gravity ('cx', 'cy')
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* @static
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*/
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function calculateArcDimensionAndCenter($v1, $v2)
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{
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// $v2 always larger than $v1
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$r1x = Image_Graph_Tool::close2zero(cos(deg2rad($v1)), 3);
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$r2x = Image_Graph_Tool::close2zero(cos(deg2rad($v2)), 3);
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$r1y = Image_Graph_Tool::close2zero(sin(deg2rad($v1)), 3);
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$r2y = Image_Graph_Tool::close2zero(sin(deg2rad($v2)), 3);
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// $rx = how many percent of the x-diameter of the entire ellipse does the arc x-diameter occupy: 1 entire width, 0 no width
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// $cx = at what percentage of the diameter does the center lie
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// if the arc passes through 0/360 degrees the "highest" of r1x and r2x is replaced by 1!
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if ((($v1 <= 0) && ($v2 >= 0)) || (($v1 <= 360) && ($v2 >= 360))) {
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$r1x = min($r1x, $r2x);
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$r2x = 1;
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}
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// if the arc passes through 180 degrees the "lowest" of r1x and r2x is replaced by -1!
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if ((($v1 <= 180) && ($v2 >= 180)) || (($v1 <= 540) && ($v2 >= 540))) {
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$r1x = max($r1x, $r2x);
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$r2x = -1;
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}
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if ($r1x >= 0) { // start between [270; 360] or [0; 90]
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if ($r2x >= 0) {
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$rx = max($r1x, $r2x) / 2;
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$cx = 0; // center lies 0 percent along this "vector"
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}
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else {
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$rx = abs($r1x - $r2x) / 2;
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$cx = abs($r2x / 2) / $rx;
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}
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}
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else { // start between ]90; 270[
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if ($r2x < 0) {
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$rx = max(abs($r1x), abs($r2x)) / 2;
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$cx = $rx;
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}
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else {
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$rx = abs($r1x - $r2x) / 2;
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$cx = abs($r1x / 2) / $rx;
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}
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}
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// $ry = how many percent of the y-diameter of the entire ellipse does the arc y-diameter occupy: 1 entire, 0 none
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// $cy = at what percentage of the y-diameter does the center lie
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// if the arc passes through 90 degrees the "lowest" of r1x and r2x is replaced by -1!
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if ((($v1 <= 90) && ($v2 >= 90)) || (($v1 <= 450) && ($v2 >= 450))) {
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$r1y = min($r1y, $r2y);
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$r2y = 1;
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}
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// if the arc passes through 270 degrees the "highest" of r1y and r2y is replaced by -1!
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if ((($v1 <= 270) && ($v2 >= 270)) || (($v1 <= 630) && ($v2 >= 630))) {
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$r1y = max($r1y, $r2y);
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$r2y = -1;
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}
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if ($r1y >= 0) { // start between [0; 180]
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if ($r2y >= 0) {
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$ry = max($r1y, $r2y) / 2;
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$cy = 0; // center lies 0 percent along this "vector"
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}
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else {
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$ry = abs($r1y - $r2y) / 2;
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$cy = abs($r2y / 2) / $ry;
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}
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}
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else { // start between ]180; 360[
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if ($r2y < 0) {
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$ry = max(abs($r1y), abs($r2y)) / 2;
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$cy = $ry;
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}
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else {
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$ry = abs($r1y - $r2y) / 2;
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$cy = abs($r1y / 2) / $ry;
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}
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}
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return array(
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'rx' => $rx,
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'cx' => $cx,
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'ry' => $ry,
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'cy' => $cy
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);
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}
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/**
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* Calculate linear regression on a dataset
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* @param array $data The data to calculate regression upon
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* @return array The slope and intersection of the "best-fit" line
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* @static
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*/
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function calculateLinearRegression(&$data)
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{
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$sumX = 0;
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$sumY = 0;
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foreach ($data as $point) {
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$sumX += $point['X'];
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$sumY += $point['Y'];
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}
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$meanX = $sumX / count($data);
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$meanY = $sumY / count($data);
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$sumXX = 0;
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$sumYY = 0;
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$sumXY = 0;
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foreach ($data as $point) {
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$sumXX += ($point['X'] - $meanX) * ($point['X'] - $meanX);
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$sumYY += ($point['Y'] - $meanY) * ($point['Y'] - $meanY);
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$sumXY += ($point['X'] - $meanX) * ($point['Y'] - $meanY);
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}
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$result = array();
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$result['slope'] = ($sumXY / $sumXX);
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$result['intersection'] = $meanY - ($result['slope'] * $meanX);
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return $result;
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}
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}
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?>
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