<head>
<title>59</title>
</head>
<?php
/**
* Using the Leng and Area functions from the tasks Proc56 and Proc58,
* write a real-valued function Dist(xP, yP, xA, yA, xB, yB) that returns
* the distance D(P, AB) between a point P and a line AB:
* D(P, AB) = 2·SPAB/|AB|,
* where SPAB is the area of the triangle PAB. Using this function, find the distance
* between a point P and each of lines AB, AC, BC provided that coordinates of
* points P, A, B, C are given.
*/
echo '<div style="display: none">';
include '58.php';
echo '</div>';
function Dist($xA, $yA, $xB, $yB, $xP, $yP)
{
$result = Area($xA, $yA, $xB, $yB, $xP, $yP);
$area = $result['triangle_area'];
$a = $result['data_about_triangle']['length']['a'];
$distance = 2 * $area / $a;
return $distance;
}
$distance1 = Dist(2, 2, 2, 6, 6, 2);
$distance2 = Dist(0, 0, 0, 1, 1, 0);
echo $distance1 . '<br/>';
echo $distance2 . '<br/>';
function Alts($xA, $yA, $xB, $yB, $xC, $yC, &$hA, &$hB, &$hC)
{
$hA = Dist($xA, $yA, $xB, $yB, $xC, $yC);
$hB = Dist($xB, $yB, $xC, $yC, $xA, $yA);
$hC = Dist($xA, $yA, $xC, $yC, $xB, $yB);
}
<?php /** * Using the TPoint and TTriangle types and the Dist function (see Param64, Param65, Param67), write a procedure Alts * (T, h1, h2, h3) that evaluates the altitudes h1, h2, h3 drawn from the vertices T.A, T.B, T.C of a triangle T (T is * an input parameter of TTriangle type, h1, h2, h3 are output real-valued parameters). Using this procedure, evaluate * the altitudes of each of triangles ABC, ABD, ACD provided that the coordinates of points A, B, C, D are given. */ echo '<div style="display: none;">'; // include 'helper.php'; include '67.php'; require_once '66.php'; require_once '64.php'; echo '</div >'; use TPoint\TPoint; use ParamPhpJavaScrit\TTriangle\TTriangle; $t1 = new TTriangle(2, 6, 7, 1, 2, 1); $s = Area($t1); $a = new TPoint($t1->getAx(), $t1->getAy()); $b = new TPoint($t1->getBx(), $t1->getBy()); $c = new TPoint($t1->getCx(), $t1->getCy()); $length1 = Leng2($a, $b); $length2 = Leng2($a, $c); $length3 = Leng2($b, $c); echo Dist($s, $length1) . '<br/>'; echo Dist($s, $length2) . '<br/>'; echo Dist($s, $length3) . '<br/>';
function Arrange($circle)
{
global $debug;
$nodcircle = array();
$sortednod = array();
$hubweight = array();
$nbrnumber = array();
if ($debug) {
echo "<div class=\"textpad code txta\"><h3>ARRANGE</h3>\n";
}
foreach (array_keys($circle) as $node) {
if (is_array($circle[$node]['alk'])) {
$nbr = array_keys($circle[$node]['alk']);
if (count($nbr) == 1) {
# 1 neighbor
$nodcircle[$node] = $nbr[0];
if ($debug) {
echo "LEAF:{$node} -> {$nbr['0']}<br>";
}
} else {
# Several neighbors
if ($debug) {
echo "<p>HUB :{$node}<br>";
}
$nodcircle[$node] = $node;
foreach ($nbr as $n) {
if (is_array($circle[$n]['alk'])) {
$hubweight[$node] += count(array_keys($circle[$n]['alk'])) > 1 ? 2 : 1;
}
if ($debug) {
echo "NBR :{$n}<br>";
}
}
if ($debug) {
echo "WGHT:{$hubweight[$node]}<br>";
}
}
} else {
$nodcircle[$node] = 0;
if ($debug) {
echo "UNL :{$node}<br>";
}
}
}
if ($debug) {
echo "Align Hubs:\n";
}
arsort($hubweight);
foreach ($hubweight as $curh => $cw) {
if ($cw < 4) {
if ($debug) {
echo "HUB :{$curh} pos{$cw}<br>";
}
foreach ($hubweight as $nexth => $nw) {
if (in_array($curh, array_keys($circle[$nexth]['alk'])) and $cw < $nw) {
if ($debug) {
echo "HLNK:{$curh} {$nexth} = {$nw}<br>";
}
if ($nodcircle[$curh] == $curh) {
# Only align hub, if not done before
$nodcircle[$curh] = $nexth . "0" . $curh;
# Hub will come in before the one it's aligned to
if ($debug) {
echo "HALI:{$nexth} to {$curh}<br>";
}
} else {
if ($debug) {
echo "HDON:{$nexth} is {$nodcircle[$nexth]}<br>";
}
}
}
}
}
}
if ($debug) {
echo "Arrange:\n";
}
asort($nodcircle);
foreach ($nodcircle as $node => $nbr) {
if (array_key_exists($node, $hubweight)) {
$sortednod[$node] = $nbr . "2";
# Hubs weight 2
if ($debug) {
echo "<p>HUB :{$nbr}<br>";
}
} else {
$nbrnumber[$nbr]++;
if ($nbrnumber[$nbr] % 2) {
# Distribute LEAFs around HUBs
$sortednod[$node] = $nodcircle[$nbr] . "1{$node}";
if ($debug) {
echo "LEAF:{$node} = {$nbr} BELOW<br>";
}
} else {
$sortednod[$node] = $nodcircle[$nbr] . "3{$node}";
if ($debug) {
echo "LEAF:{$node} = {$nbr} ABOVE<br>";
}
}
}
if ($debug) {
echo "SORT:{$sortednod[$node]}<br>";
}
}
asort($sortednod);
$sortedkeys = array_keys($sortednod);
$csiz = count($sortedkeys);
$iter = 0;
if ($debug) {
echo "<h3>Reposition nodes with 2 links crossing ({$csiz} total)</h3>\n";
}
do {
$kpos = 0;
$movednods = array();
foreach ($sortedkeys as $k) {
if ($debug) {
echo "REPO{$iter}: {$k} ";
}
if (is_array($circle[$k]['alk'])) {
# Any links?
$nbr = array_keys($circle[$k]['alk']);
$nnbr = count($nbr);
if ($nnbr == 2 and !in_array($k, $movednods)) {
# We got 2 links?
$npos1 = array_search($nbr[0], $sortedkeys);
$npos2 = array_search($nbr[1], $sortedkeys);
$ndst1 = Dist($kpos, $npos1, $csiz);
$ndst2 = Dist($kpos, $npos2, $csiz);
$ktonb = $ndst1 + $ndst2;
$nbdst = Dist($npos1, $npos2, $csiz);
if ($debug) {
echo "pos{$kpos} connects to {$nbr['0']} on pos{$npos1} len{$ndst1} and {$nbr['1']} on pos{$npos2} len{$ndst2} (dist{$ktonb} vs nbrdist{$nbdst}) ";
}
# TODO add logic to detect crossing links or align and group nodes with 2 neighbors?
if ($ktonb > $nbdst + 1) {
# add 1 to avoid flapping
$mpos = $npos1 < $npos2 ? $npos1 : $npos2;
$nb1 = count(array_keys($circle[$nbr[0]]['alk']));
$nb2 = count(array_keys($circle[$nbr[1]]['alk']));
$mpos = $nb1 < $nb2 ? $npos1 : $npos2;
if ($debug) {
echo "{$nbr['0']} has {$nb1} links and {$nbr['1']} has {$nb2}, <span class=\"warn\">moving to {$mpos}</span>\n";
}
array_splice($sortedkeys, $kpos, 1);
# remove it
#if($nbdst > 0){
array_splice($sortedkeys, $mpos, 0, $k);
# and insert after nbr with less links
#}else{
# array_splice($sortedkeys,$mpos,0,$k); # or before if 0 crossing
#}
if ($debug) {
print_r($sortedkeys);
}
$movednods[] = $k;
break 1;
} else {
if ($debug) {
echo "stays\n";
}
}
} else {
if ($debug) {
echo "has {$nnbr} neighbor" . ($nnbr == 1 ? '' : 's') . "\n";
}
}
} else {
if ($debug) {
echo "no links\n";
}
}
$kpos++;
}
if ($kpos == $csiz) {
# Went through whole array lets end
if ($debug) {
echo "REPO:iter{$iter} reached pos{$kpos}, done!\n";
}
$iter = $csiz;
}
$iter++;
} while ($iter < $csiz);
if ($debug) {
echo "</div>";
}
return $sortedkeys;
}
* function Dist(P, A, B) that returns the distance D(P, AB) between a point P and a line AB:
* D(P, AB) = 2·SPAB/|AB|,
* where SPAB is the area of the triangle PAB (parameters P, A, B are input parameters of TPoint type). Using this
* function, find the distance between a point P and each of lines AB, AC, BC provided that the coordinates of
* points P, A, B, C are given.
*/
echo '<div style="display: none;">';
include 'helper.php';
//include '66.php';
require_once '66.php';
require_once '64.php';
echo '</div >';
use TPoint\TPoint;
use ParamPhpJavaScrit\TTriangle\TTriangle;
function Dist($S, $A)
{
return 2 * $S / $A;
}
function Leng2($a, $b)
{
$length = pow($a->getX() - $b->getX(), 2) + pow($a->getY() - $b->getY(), 2);
$len = sqrt($length);
return $len;
}
$t1 = new TTriangle(2, 6, 7, 1, 2, 1);
$s = Area($t1);
$a = new TPoint($t1->getAx(), $t1->getAy());
$b = new TPoint($t1->getBx(), $t1->getBy());
$length = Leng2($a, $b);
echo Dist($s, $length);
