function VennDiagram($names, $abc, $ab, $bc, $ca, $progress = 0)
{
$height = 300;
$width = 400;
$radius = 80;
$shiftx = 55;
$shifty = 45;
$names = convert_accented_characters($names);
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// $svg .= '<rect width="'.$width.'" height="'.$height.'" fill="black" fill-opacity="0.2" />';
// Circles
$svg .= DrawCircle($width / 2 - $shiftx, $height / 2 - $shifty, $radius);
$svg .= DrawCircle($width / 2 + $shiftx, $height / 2 - $shifty, $radius);
$svg .= DrawCircle($width / 2, $height / 2 + $shifty, $radius);
// Labels
$letters = array_map('str_split', $names);
$svg .= DrawText($width / 2 - $shiftx * 2.3, $height / 2 - $shifty * 2.3, '$' . $letters[0][0] . '$', 13);
$svg .= DrawText($width / 2 + $shiftx * 2.3, $height / 2 - $shifty * 2.3, '$' . $letters[1][0] . '$', 13);
$svg .= DrawText($width / 2, $height / 2 + $shifty * 3.2, '$' . $letters[2][0] . '$', 13);
$svg .= $progress >= 1 ? DrawText($width / 2, $height / 2 - 5, '$\\color{red}{' . $abc . '}$', 13) : '';
$svg .= $progress >= 2 ? DrawText($width / 2, $height / 2 - $shifty * 1.2, '$\\color{blue}{' . $ab . '}$', 13) : '';
$svg .= $progress >= 3 ? DrawText($width / 2 + $shiftx * 0.7, $height / 2 + 15, '$\\color{blue}{' . $bc . '}$', 13) : '';
$svg .= $progress >= 4 ? DrawText($width / 2 - $shiftx * 0.7, $height / 2 + 15, '$\\color{blue}{' . $ca . '}$', 13) : '';
$svg .= '</svg></div>';
return $svg;
}
function PieChart($angle_deg = NULL)
{
$width = 400;
$height = 260;
$cx = $width / 2;
$cy = $height / 2;
$r = 100;
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// Show angle
if ($angle_deg) {
if ($angle_deg == 360) {
$svg .= DrawCircle($cx, $cy, $r, $stroke = 'black', $strokewidth = 0, $fill = '#CCC');
} else {
$svg .= DrawPieChart($cx, $cy, $r, 0, $angle_deg, $fill = '#CCC');
}
list($x1, $y1) = polarToCartesian($cx, $cy, $r, 0);
list($x2, $y2) = polarToCartesian($cx, $cy, $r, $angle_deg);
$svg .= DrawLine($cx, $cy, $x1, $y1);
$svg .= DrawLine($cx, $cy, $x2, $y2);
}
// Circle
$svg .= DrawCircle($cx, $cy, $r);
// Ticks for every 10°
for ($i = 0; $i < 36; $i++) {
$angle = $i * 10;
list($x1, $y1) = polarToCartesian($cx, $cy, $r + 5, $angle);
list($x2, $y2) = polarToCartesian($cx, $cy, $r - 5, $angle);
$svg .= DrawLine($x1, $y1, $x2, $y2);
}
// Show hint degrees
$svg .= DrawText($cx + $r + 10, $cy + 7, '0°', 15);
$svg .= DrawText($cx + $r + 5, $cy - 13, '10°', 15);
$svg .= DrawText($cx - 8, $cy - $r - 7, '90°', 15);
$svg .= DrawText($cx - $r - 40, $cy + 7, '180°', 15);
$svg .= DrawText($cx - 15, $cy + $r + 22, '270°', 15);
$svg .= '</svg></div>';
return $svg;
}
function DrawSineFunction($a, $b, $progress = 0)
{
$width = 600;
$height = 300;
$xunits_neg = -4;
// Number of units on x-axis (unit length: pi/2)
$xunits_pos = 4;
$yunits_neg = -2;
// Number of units on y-axis (unit length: 1/2)
$yunits_pos = 2;
$yunit_original = 1 / 2;
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// $svg .= '<rect width="'.$width.'" height="'.$height.'" fill="black" fill-opacity="0.2" />';
// Draw axes
$padding1 = 10;
// Padding left/bottom
$padding2 = 30;
// Padding right/top
$xunit_length = ($width - $padding1 - $padding2) / ($xunits_pos - $xunits_neg);
$yunit_length = ($height - $padding1 - $padding2) / ($yunits_pos - $yunits_neg);
$originx = $padding1 + $xunit_length * abs($xunits_neg);
$originy = $padding2 + $yunit_length * $yunits_pos;
$svg .= DrawLine(0, $originy, $width, $originy);
$svg .= DrawLine($originx, 0, $originx, $height);
// Draw arrows
$svg .= DrawLine($width, $originy, $width - 7, $originy - 7);
$svg .= DrawLine($width, $originy, $width - 7, $originy + 7);
$svg .= DrawLine($originx, 0, $originx - 7, 7);
$svg .= DrawLine($originx, 0, $originx + 7, 7);
// Draw units
$xpos = $padding1;
$xval = $xunits_neg * pi() / 2;
while ($xpos <= $width - $padding2) {
if ($xpos != $originx) {
$svg .= DrawLine($xpos, $originy - 5, $xpos, $originy + 5);
}
$xtext = $this->Xvalue2Fraction($xval);
$svg .= DrawText($xpos, $originy + 20, $xtext);
$xpos += $xunit_length;
$xval += pi() / 2;
}
$ypos = $padding2;
$yval = $yunits_pos * $yunit_original;
while ($ypos <= $height - $padding1) {
if (round($ypos) != round($originy)) {
$ytext = $this->Yvalue2Fraction($yval);
$svg .= DrawLine($originx - 5, $ypos, $originx + 5, $ypos);
$svg .= DrawText($originx + 20, $ypos - 5, $ytext);
}
$ypos += $yunit_length;
$yval -= $yunit_original;
}
// Draw guides
$svg .= $this->DrawGuides(1, $yunit_length, $yunit_original, $originy, $width);
$svg .= $this->DrawGuides(-1, $yunit_length, $yunit_original, $originy, $width);
// Draw function
if ($progress == 0) {
for ($i = 0; $i < $width; $i++) {
$xval1 = ($i - $originx) / $xunit_length * pi() / 2;
$xval2 = ($i + 1 - $originx) / $xunit_length * pi() / 2;
$yval1 = -sin($xval1) * $yunit_length / $yunit_original + $originy;
$yval2 = -sin($xval2) * $yunit_length / $yunit_original + $originy;
$svg .= DrawLine($i, $yval1, $i + 1, $yval2, 'red', 2);
}
} elseif ($progress == 1) {
for ($i = 0; $i < $width; $i++) {
$xval1 = ($i - $originx) / $xunit_length * pi() / 2;
$xval2 = ($i + 1 - $originx) / $xunit_length * pi() / 2;
$yval1 = -sin($xval1) * $yunit_length / $yunit_original + $originy;
$yval2 = -sin($xval2) * $yunit_length / $yunit_original + $originy;
$svg .= $i % 3 == 0 ? DrawLine($i, $yval1, $i + 1, $yval2, 'blue', 1) : '';
}
for ($i = 0; $i < $width; $i++) {
$xval1 = ($i - $originx) / $xunit_length * pi() / 2;
$xval2 = ($i + 1 - $originx) / $xunit_length * pi() / 2;
$yval1 = -sin($a * $xval1) * $yunit_length / $yunit_original + $originy;
$yval2 = -sin($a * $xval2) * $yunit_length / $yunit_original + $originy;
$svg .= DrawLine($i, $yval1, $i + 1, $yval2, 'red', 2);
}
} else {
for ($i = 0; $i < $width; $i++) {
$xval1 = ($i - $originx) / $xunit_length * pi() / 2;
$xval2 = ($i + 1 - $originx) / $xunit_length * pi() / 2;
$yval1 = -sin($a * $xval1) * $yunit_length / $yunit_original + $originy;
$yval2 = -sin($a * $xval2) * $yunit_length / $yunit_original + $originy;
$svg .= DrawLine($i, $yval1, $i + 1, $yval2, 'blue', 2);
}
for ($i = 0; $i < $width; $i++) {
$xval1 = ($i - $originx) / $xunit_length * pi() / 2;
$yval1 = -sin($a * $xval1) * $yunit_length / $yunit_original + $originy;
$yval2 = round(-$yunit_length / $yunit_original) + $originy;
if (abs(sin($a * $xval1) - $b) < 1.0E-5) {
$svg .= DrawCircle($i, $yval1, 5, 'red', 1, 'red');
if ($progress == 3 && $b != 0) {
$svg .= '<g fill="none" stroke="red" stroke-width="2"><path stroke-dasharray="5,5" d="M' . $i . ' ' . $originy . ' l0 ' . round(-$yunit_length / $yunit_original) . '" /></g>';
// for some mysterious reasons this is not working... (produces the same, though):
// $svg .= DrawPath($i, $originy, $i, $yval2, $color1='red', $width=2, $color2='none', $dasharray1=5, $dasharray2=5);
}
}
}
}
$svg .= '</svg></div>';
return $svg;
}
function Graph($graph, $step = NULL)
{
$width = 400;
$height = 300;
$centerX = $width / 2;
$centerY = $height / 2;
$radius = 100;
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// $svg .= '<rect width="'.$width.'" height="'.$height.'" fill="black" fill-opacity="0.2" />';
$size = count($graph);
$angle0 = $size == 4 ? 45 : 90;
// Edges
for ($node1 = 0; $node1 < $size; $node1++) {
if ($node1 < $step) {
$color = $node1 == $step - 1 ? '#B155CF' : 'black';
foreach ($graph[$node1] as $node2) {
if (!is_array($node2)) {
$angle1 = $angle0 + $node1 * 360 / $size;
$angle2 = $angle0 + $node2 * 360 / $size;
list($x1, $y1) = polarToCartesian($centerX, $centerY, $radius, $angle1);
list($x2, $y2) = polarToCartesian($centerX, $centerY, $radius, $angle2);
$svg .= DrawLine($x1, $y1, $x2, $y2, $color, 2);
}
}
}
}
// Nodes
for ($node = 0; $node < $size; $node++) {
$angle = $angle0 + $node * 360 / $size;
if ($node < $step - 1) {
$color = '#A1D490';
} elseif ($node == $step - 1) {
$color = '#B155CF';
} else {
$color = 'white';
}
list($x, $y) = polarToCartesian($centerX, $centerY, $radius, $angle);
$svg .= DrawCircle($x, $y, 10, 'black', $width = 2, $color);
}
$svg .= '</svg></div>';
return $svg;
}
function Graph($min = NULL, $sec = NULL, $point = NULL)
{
$width = 400;
$height = 350;
$paddingX = 30;
$paddingY = 80;
$lines = 11;
$unitX = ($width - 30 - $paddingX) / ($lines + 1);
$unitY = ($height - 30 - $paddingY) / $lines;
$secs = ['33', '00', '66'];
$show = [323, 320, 315, 313];
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// X axis
$svg .= DrawLine(0, $height - $paddingY, $width, $height - $paddingY);
$svg .= DrawLine($width, $height - $paddingY, $width - 5, $height - $paddingY + 5);
$svg .= DrawLine($width, $height - $paddingY, $width - 5, $height - $paddingY - 5);
$svg .= DrawText($width - 20, $height - $paddingY + 15, 'idő');
// Y axis
$svg .= DrawLine($paddingX, 0, $paddingX, $height - 60);
$svg .= DrawLine($paddingX, 0, $paddingX - 5, 5);
$svg .= DrawLine($paddingX, 0, $paddingX + 5, 5);
$svg .= DrawText($paddingX + 10, 15, 'pontszám');
for ($i = 0; $i < $lines + 1; $i++) {
$x = $paddingX + ($lines - $i + 1) * $unitX;
$y = $height - $paddingY - min($lines, $i + 1) * $unitY;
$svg .= DrawPath($paddingX - 5, $y, $x, $y, 'black', 0.5, 'none', 5, 5);
$svg .= DrawPath($x, $height - $paddingY + 5, $x, $y, 'black', 0.5, 'none', 5, 5);
if ($i < $lines) {
$svg .= DrawLine($x - $unitX, $y, $x, $y, 'black', 2);
$svg .= DrawCircle($x - $unitX, $y, 3, 'black', 1, 'black');
$svg .= DrawCircle($x, $y, 3, 'black', 1, 'white');
}
if (in_array(313 + $i, $show)) {
$svg .= DrawText($paddingX - 25, $y + 4, 313 + $i);
} elseif ($point !== NULL && $i < $lines) {
$svg .= DrawText($paddingX - 25, $y + 4, 313 + $i, 10, 'blue');
}
$text = '2 perc ' . strval(9 - floor(($i + 1) / 3)) . ',' . $secs[$i % 3] . ' mp';
$svg .= DrawText($x + 3, $height - $paddingY + 77, $text, 10, 'black', -90);
}
// Draw time
if ($min !== NULL && $sec !== NULL) {
$time = $min * 100 + $sec;
$x1 = $paddingX + $unitX * ($lines + 1) * (400 - (933 - $time)) / 400;
$y1 = $height - $paddingY;
$svg .= DrawCircle($x1, $y1, 3, 'blue', 1, 'blue');
}
if ($point !== NULL) {
$x2 = $paddingX;
$y2 = $height - $paddingY - ($point - 312) * $unitY;
$svg .= DrawPath($x1, $y1, $x1, $y2, 'blue', 2, 'none', 5, 5);
$svg .= DrawPath($x1, $y2, $x2, $y2, 'blue', 2, 'none', 5, 5);
$svg .= DrawCircle($x2, $y2, 3, 'blue', 1, 'blue');
}
$svg .= '</svg></div>';
return $svg;
}
function AbsFunctionGraph($x1, $x2, $a, $b, $progress = 0)
{
$bottom = min(abs($x1 + $a), abs($x2 + $a), 0) + ($b < 0 ? $b : 0);
$top = max(abs($x1 + $a), abs($x2 + $a)) + ($b > 0 ? $b : 0);
$left = $x1;
$right = $x2;
$linesx = $top - $bottom + 3;
$linesy = $right - $left + 3;
$unit = 400 / $linesy < 40 ? 40 : 400 / $linesy;
$width = $unit * $linesy;
$height = $unit * $linesx;
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// Origo
$Ox = (1.5 - $left) * $unit;
$Oy = $height - (1.5 - $bottom) * $unit;
if ($unit < 45) {
$fontsize = 10;
} elseif ($unit < 50) {
$fontsize = 11;
} else {
$fontsize = 12;
}
// Guides
for ($i = 0; $i < $linesy; $i++) {
$x = (0.5 + $i) * $unit;
$svg .= DrawLine($x, 0, $x, $height, '#F2F2F2');
$num = $i + $left - 1;
if ($num == 0) {
$svg .= DrawText($Ox + $unit / 3, $Oy + $unit / 2, '$0$', $fontsize);
} else {
$svg .= DrawLine($x, $Oy - 5, $x, $Oy + 5, 'black', 2);
$svg .= DrawText($x, $Oy + $unit / 2, '$' . $num . '$', $fontsize);
}
}
for ($i = 0; $i < $linesx; $i++) {
$y = (0.5 + $i) * $unit;
$svg .= DrawLine(0, $y, $width, $y, '#F2F2F2');
$num = $top - $i + 1;
if ($num != 0) {
$svg .= DrawLine($Ox + 5, $y, $Ox - 5, $y, 'black', 2);
if ($num <= 9 && $num > 0) {
$shift = $unit / 3;
} elseif ($num > -10 || $num > 9) {
$shift = $unit / 2;
} else {
$shift = $unit / 1.7;
}
$svg .= DrawText($Ox - $shift, $y + $unit / 5, '$' . $num . '$', $fontsize);
}
}
// Axes
$svg .= DrawVector($Ox, $height, $Ox, 0, 'black', 10, 2);
$svg .= DrawVector(0, $Oy, $width, $Oy, 'black', 10, 2);
$svg .= DrawText($width - $unit / 2, $Oy - $unit / 3, '$x$', $fontsize * 1.5);
$svg .= DrawText($Ox + $unit / 2, $unit / 3, '$y$', $fontsize * 1.5);
// Coordinates for |x|
list($X1A, $Y1A) = $this->Coordinates2($x1, abs($x1), $height, $left, $bottom, $unit);
list($X2A, $Y2A) = $this->Coordinates2(0, 0, $height, $left, $bottom, $unit);
list($X3A, $Y3A) = $this->Coordinates2($x2, abs($x2), $height, $left, $bottom, $unit);
// Coordinates for |x+a|
list($X1B, $Y1B) = $this->Coordinates2($x1, abs($x1 + $a), $height, $left, $bottom, $unit);
list($X2B, $Y2B) = $this->Coordinates2(-$a, 0, $height, $left, $bottom, $unit);
list($X3B, $Y3B) = $this->Coordinates2($x2, abs($x2 + $a), $height, $left, $bottom, $unit);
// Coordinates for |x+a|+b
list($X1C, $Y1C) = $this->Coordinates2($x1, abs($x1 + $a) + $b, $height, $left, $bottom, $unit);
list($X2C, $Y2C) = $this->Coordinates2(-$a, $b, $height, $left, $bottom, $unit);
list($X3C, $Y3C) = $this->Coordinates2($x2, abs($x2 + $a) + $b, $height, $left, $bottom, $unit);
if ($progress == 0) {
// End points for |x|
$svg .= DrawCircle($X1A, $Y1A, 3, 'red', 1, 'red');
$svg .= DrawCircle($X3A, $Y3A, 3, 'red', 1, 'red');
// Lines for |x|
$svg .= DrawLine($X1A, $Y1A, $X2A, $Y2A, 'red', 2);
$svg .= DrawLine($X2A, $Y2A, $X3A, $Y3A, 'red', 2);
} elseif ($progress == 1) {
// End points for |x|
$svg .= DrawCircle($X1A, $Y1A, 3, 'blue', 1, 'blue');
$svg .= DrawCircle($X3A, $Y3A, 3, 'blue', 1, 'blue');
// Lines for |x|
$svg .= DrawPath($X1A, $Y1A, $X2A, $Y2A, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray2asharray1 = 5, $dasharray2 = 5);
$svg .= DrawPath($X2A, $Y2A, $X3A, $Y3A, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray2asharray1 = 5, $dasharray2 = 5);
// Vector from old to new
$svg .= DrawVector($X2A, $Y2A, $X2B, $Y2B, 'green', 10, 2, 30);
// End points for |x+a|
$svg .= DrawCircle($X1B, $Y1B, 3, 'red', 1, 'red');
$svg .= DrawCircle($X3B, $Y3B, 3, 'red', 1, 'red');
// Lines for |x+a|
$svg .= DrawLine($X1B, $Y1B, $X2B, $Y2B, 'red', 2);
$svg .= DrawLine($X2B, $Y2B, $X3B, $Y3B, 'red', 2);
} elseif ($progress == 2) {
// End points for |x+a|
$svg .= DrawCircle($X1B, $Y1B, 3, 'blue', 1, 'blue');
$svg .= DrawCircle($X3B, $Y3B, 3, 'blue', 1, 'blue');
// Lines for |x+a|
$svg .= DrawPath($X1B, $Y1B, $X2B, $Y2B, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray2asharray1 = 5, $dasharray2 = 5);
$svg .= DrawPath($X2B, $Y2B, $X3B, $Y3B, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray2asharray1 = 5, $dasharray2 = 5);
// Vector from old to new
$svg .= DrawVector($X2B, $Y2B, $X2C, $Y2C, 'green', 10, 2, 30);
// End points for |x+a|+b
$svg .= DrawCircle($X1C, $Y1C, 3, 'red', 1, 'red');
$svg .= DrawCircle($X3C, $Y3C, 3, 'red', 1, 'red');
// Lines for |x+a|+b
$svg .= DrawLine($X1C, $Y1C, $X2C, $Y2C, 'red', 2);
$svg .= DrawLine($X2C, $Y2C, $X3C, $Y3C, 'red', 2);
} else {
// Lines between end points and y axis
if (abs($x1 + $a) > abs($x2 + $a)) {
if (abs($x1 + $a) + $b != 0) {
list($X1D, $Y1D) = $this->Coordinates2(0, abs($x1 + $a) + $b, $height, $left, $bottom, $unit);
$svg .= DrawPath($X1C, $Y1C, $X1D, $Y1D, $color1 = 'green', $width = 2, $color2 = 'none', $dasharray2asharray1 = 5, $dasharray2 = 5);
}
} else {
if (abs($x2 + $a) + $b != 0) {
list($X3D, $Y3D) = $this->Coordinates2(0, abs($x2 + $a) + $b, $height, $left, $bottom, $unit);
$svg .= DrawPath($X3C, $Y3C, $X3D, $Y3D, $color1 = 'green', $width = 2, $color2 = 'none', $dasharray2asharray1 = 5, $dasharray2 = 5);
}
}
if ($b != 0) {
list($X2D, $Y2D) = $this->Coordinates2(0, $b, $height, $left, $bottom, $unit);
$svg .= DrawPath($X2C, $Y2C, $X2D, $Y2D, $color1 = 'green', $width = 2, $color2 = 'none', $dasharray2asharray1 = 5, $dasharray2 = 5);
}
// End points for |x+a|+b
$svg .= DrawCircle($X1C, $Y1C, 3, 'red', 1, 'red');
$svg .= DrawCircle($X3C, $Y3C, 3, 'red', 1, 'red');
// Lines for |x+a|+b
$svg .= DrawLine($X1C, $Y1C, $X2C, $Y2C, 'red', 2);
$svg .= DrawLine($X2C, $Y2C, $X3C, $Y3C, 'red', 2);
}
$svg .= '</svg></div>';
return $svg;
}
function Rhombus($Cx, $Cy, $vx, $vy, $mult, $progress = 0)
{
// Calculate coordinates (nodes)
list($Tx, $Ty, $Rx, $Ry, $Px, $Py, $Sx, $Sy) = $this->Coordinates1($Cx, $Cy, $vx, $vy, $mult);
$bottom = min($Py, $Ry, $Sy, $Ty, 0);
$top = max($Py, $Ry, $Sy, $Ty, 0);
$left = min($Px, $Rx, $Sx, $Tx, 0);
$right = max($Px, $Rx, $Sx, $Tx, 0);
// print_r('bottom: '.$bottom.'<br />');
// print_r('top: '.$top.'<br />');
// print_r('left: '.$left.'<br />');
// print_r('right: '.$right.'<br />');
$linesx = $top - $bottom + 3;
$linesy = $right - $left + 3;
$unit = 400 / $linesy < 40 ? 40 : 400 / $linesy;
$width = $unit * $linesy;
$height = $unit * $linesx;
// Calculate coordinates (labels)
list($C2x, $C2y) = $this->Coordinates3($Rx, $Ry, $Tx, $Ty, 'center');
list($T2x, $T2y) = $this->Coordinates3($Cx, $Cy, $Tx, $Ty);
list($R2x, $R2y) = $this->Coordinates3($Cx, $Cy, $Rx, $Ry);
list($S2x, $S2y) = $this->Coordinates3($Cx, $Cy, $Sx, $Sy);
list($P2x, $P2y) = $this->Coordinates3($Cx, $Cy, $Px, $Py);
// Calculate coordinates on canvas (nodes)
list($C3x, $C3y) = $this->Coordinates2($Cx, $Cy, $height, $left, $bottom, $unit);
list($T3x, $T3y) = $this->Coordinates2($Tx, $Ty, $height, $left, $bottom, $unit);
list($R3x, $R3y) = $this->Coordinates2($Rx, $Ry, $height, $left, $bottom, $unit);
list($S3x, $S3y) = $this->Coordinates2($Sx, $Sy, $height, $left, $bottom, $unit);
list($P3x, $P3y) = $this->Coordinates2($Px, $Py, $height, $left, $bottom, $unit);
// Calculate coordinates on canvas (labels)
list($C4x, $C4y) = $this->Coordinates2($C2x, $C2y, $height, $left, $bottom, $unit);
list($T4x, $T4y) = $this->Coordinates2($T2x, $T2y, $height, $left, $bottom, $unit);
list($R4x, $R4y) = $this->Coordinates2($R2x, $R2y, $height, $left, $bottom, $unit);
list($S4x, $S4y) = $this->Coordinates2($S2x, $S2y, $height, $left, $bottom, $unit);
list($P4x, $P4y) = $this->Coordinates2($P2x, $P2y, $height, $left, $bottom, $unit);
// print_r('T('.$Tx.';'.$Ty.')<br />');
// print_r('R('.$Rx.';'.$Ry.')<br />');
// print_r('S('.$Sx.';'.$Sy.')<br />');
// print_r('P('.$Px.';'.$Py.')<br />');
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// Origo
$Ox = (1.5 - $left) * $unit;
$Oy = $height - (1.5 - $bottom) * $unit;
if ($unit < 45) {
$fontsize = 10;
} elseif ($unit < 50) {
$fontsize = 11;
} else {
$fontsize = 12;
}
// Guides
for ($i = 0; $i < $linesy; $i++) {
$x = (0.5 + $i) * $unit;
$svg .= DrawLine($x, 0, $x, $height, '#F2F2F2');
$num = $i + $left - 1;
if ($num == 0) {
$svg .= DrawText($Ox + $unit / 3, $Oy + $unit / 2, '$0$', $fontsize);
} else {
$svg .= DrawLine($x, $Oy - 5, $x, $Oy + 5, 'black', 2);
$svg .= DrawText($x, $Oy + $unit / 2, '$' . $num . '$', $fontsize);
}
}
for ($i = 0; $i < $linesx; $i++) {
$y = (0.5 + $i) * $unit;
$svg .= DrawLine(0, $y, $width, $y, '#F2F2F2');
$num = $top - $i + 1;
if ($num != 0) {
$svg .= DrawLine($Ox + 5, $y, $Ox - 5, $y, 'black', 2);
if ($num <= 9 && $num > 0) {
$shift = $unit / 3;
} elseif ($num > -10 || $num > 9) {
$shift = $unit / 2;
} else {
$shift = $unit / 1.7;
}
$svg .= DrawText($Ox - $shift, $y + $unit / 5, '$' . $num . '$', $fontsize);
}
}
// Axes
$svg .= DrawVector($Ox, $height, $Ox, 0, 'black', 10, 2);
$svg .= DrawVector(0, $Oy, $width, $Oy, 'black', 10, 2);
$svg .= DrawText($width - $unit / 2, $Oy - $unit / 3, '$x$', $fontsize * 1.5);
$svg .= DrawText($Ox + $unit / 2, $unit / 3, '$y$', $fontsize * 1.5);
if ($progress == 0) {
if ($Cy != 0) {
$svg .= DrawPath($Ox, $C3y, $C3x, $C3y, $color1 = 'red', $width = 2, $color2 = 'none', $dasharray2asharray1 = 5, $dasharray2 = 5);
}
if ($Cx != 0) {
$svg .= DrawPath($C3x, $C3y, $C3x, $Oy, $color1 = 'red', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
// Draw point K
$svg .= DrawCircle($C3x, $C3y, 3, 'red', 1, 'red');
$svg .= DrawText($C4x, $C4y, '$K$', 15);
} elseif ($progress == 1) {
if ($Ty != 0) {
$svg .= DrawPath($Ox, $T3y, $T3x, $T3y, $color1 = 'red', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
if ($Tx != 0) {
$svg .= DrawPath($T3x, $T3y, $T3x, $Oy, $color1 = 'red', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
// Draw point T
$svg .= DrawCircle($T3x, $T3y, 3, 'red', 1, 'red');
$svg .= DrawText($T4x, $T4y, '$T$', 15);
// Draw point K
$svg .= DrawCircle($C3x, $C3y, 3, 'blue', 1, 'blue');
$svg .= DrawText($C4x, $C4y, '$K$', 15);
} elseif ($progress == 2) {
$svg .= DrawVector($C3x, $C3y, $T3x, $T3y, 'blue', 7, 2, 30);
$svg .= DrawVector($C3x, $C3y, $R3x, $R3y, 'red', 7, 2, 30);
// Draw point R
$svg .= DrawText($R4x, $R4y, '$R$', 15);
// Draw point K
$svg .= DrawText($C4x, $C4y, '$K$', 15);
// Draw point T
$svg .= DrawText($T4x, $T4y, '$T$', 15);
} elseif ($progress == 3) {
$svg .= DrawVector($C3x, $C3y, $T3x, $T3y, 'blue', 7, 2, 30);
$svg .= DrawVector($C3x, $C3y, $R3x, $R3y, 'blue', 7, 2, 30);
$svg .= DrawVector($C3x, $C3y, $P3x, $P3y, 'red', 7, 2, 30);
$svg .= DrawVector($C3x, $C3y, $S3x, $S3y, 'red', 7, 2, 30);
// Draw point K
$svg .= DrawText($C4x, $C4y, '$K$', 15);
// Draw point T
$svg .= DrawText($T4x, $T4y, '$T$', 15);
// Draw point R
$svg .= DrawText($R4x, $R4y, '$R$', 15);
// Draw point S
$svg .= DrawText($S4x, $S4y, '$S$', 15);
// Draw point P
$svg .= DrawText($P4x, $P4y, '$P$', 15);
} else {
$svg .= DrawLine($P3x, $P3y, $T3x, $T3y, 'red', 2);
$svg .= DrawLine($S3x, $S3y, $R3x, $R3y, 'red', 2);
$svg .= DrawLine($T3x, $T3y, $S3x, $S3y, 'red', 2);
$svg .= DrawLine($R3x, $R3y, $P3x, $P3y, 'red', 2);
if ($Py != $Ry && $Py != $Ty && $Py != 0) {
$svg .= DrawPath($Ox, $P3y, $P3x, $P3y, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
if ($Px != $Rx && $Px != $Tx && $Px != 0) {
$svg .= DrawPath($P3x, $P3y, $P3x, $Oy, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
if ($Ry != $Py && $Ry != $Sy && $Ry != 0) {
$svg .= DrawPath($Ox, $R3y, $R3x, $R3y, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
if ($Rx != $Px && $Rx != $Sx && $Rx != 0) {
$svg .= DrawPath($R3x, $R3y, $R3x, $Oy, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
if ($Sy != $Ry && $Sy != $Ty && $Sy != 0) {
$svg .= DrawPath($Ox, $S3y, $S3x, $S3y, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
if ($Sx != $Rx && $Sx != $Tx && $Sx != 0) {
$svg .= DrawPath($S3x, $S3y, $S3x, $Oy, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
if ($Ty != $Py && $Ty != $Sy && $Ty != 0) {
$svg .= DrawPath($Ox, $T3y, $T3x, $T3y, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
if ($Tx != $Px && $Tx != $Sx && $Tx != 0) {
$svg .= DrawPath($T3x, $T3y, $T3x, $Oy, $color1 = 'blue', $width = 2, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
// Draw point T
$svg .= DrawText($T4x, $T4y, '$T$', 15);
// Draw point R
$svg .= DrawText($R4x, $R4y, '$R$', 15);
// Draw point S
$svg .= DrawText($S4x, $S4y, '$S$', 15);
// Draw point P
$svg .= DrawText($P4x, $P4y, '$P$', 15);
}
$svg .= '</svg></div>';
return $svg;
}
function Graph($a, $b, $c, $x1, $x2, $relation, $progress = 0)
{
$padding1 = 20;
// Padding left/bottom
$padding2 = 20;
// Padding right/top
$x_avg = ($x1 + $x2) / 2;
$x_min = min(0, floor($x_avg) - 2, $x1 - 1);
$x_max = max(0, ceil($x_avg) + 2, $x2 + 1);
$y_avg = $this->Equation_val($a, $b, $c, $x_avg);
$diff = abs($y_avg) > 4 ? 1 : 2;
$y_max = $this->Equation_val($a, $b, $c, $x1 - $diff);
$y_min = $a > 0 ? floor($y_avg) : $y_max;
$y_max = $a > 0 ? $y_max : ceil($y_avg);
$height = 300;
$width = 400;
$unitx = ($width - $padding1 - $padding2) / ($x_max - $x_min);
$unity = ($height - $padding1 - $padding2) / ($y_max - $y_min);
$unit = max(30, min($unitx, $unity));
$width = $unit * ($x_max - $x_min) + $padding1 + $padding2;
$height = $unit * ($y_max - $y_min) + $padding1 + $padding2;
$originx = $padding1 + $unit * abs($x_min);
$originy = $padding2 + $unit * $y_max;
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// $svg .= '<rect width="'.$width.'" height="'.$height.'" fill="black" fill-opacity="0.2" />';
// Draw guides
$xpos = $padding1;
while ($xpos <= $width - $padding2) {
if ($xpos != $originx) {
$svg .= DrawLine($xpos, 0, $xpos, $height, '#F2F2F2');
}
$xpos += $unit;
}
$ypos = $padding2;
while ($ypos <= $height - $padding1) {
if ($ypos != $originy) {
$svg .= DrawLine(0, $ypos, $width, $ypos, '#F2F2F2');
}
$ypos += $unit;
}
// Draw axes
$svg .= DrawLine(0, $originy, $width, $originy);
$svg .= DrawLine($originx, 0, $originx, $height);
// Draw arrows
$svg .= DrawLine($width, $originy, $width - 7, $originy - 7);
$svg .= DrawLine($width, $originy, $width - 7, $originy + 7);
$svg .= DrawLine($originx, 0, $originx - 7, 7);
$svg .= DrawLine($originx, 0, $originx + 7, 7);
// Draw units
$xpos = $padding1;
$xval = $x_min;
while ($xpos <= $width - $padding2) {
if ($xpos != $originx) {
$svg .= DrawLine($xpos, $originy - 5, $xpos, $originy + 5);
$svg .= DrawText($xpos + 5, $originy + 17, $xval);
}
$xpos += $unit;
$xval += 1;
}
$ypos = $padding2;
$yval = $y_max;
while ($ypos <= $height - $padding1) {
if ($ypos != $originy) {
$svg .= DrawLine($originx - 5, $ypos, $originx + 5, $ypos);
}
$svg .= DrawText($originx + 10, $ypos - 5, $yval);
$ypos += $unit;
$yval -= 1;
}
// Draw function
for ($i = 0; $i < $width; $i++) {
$xval1 = ($i - $originx) / $unit;
$xval2 = ($i + 1 - $originx) / $unit;
$yval1 = -$this->Equation_val($a, $b, $c, $xval1) * $unit + $originy;
$yval2 = -$this->Equation_val($a, $b, $c, $xval2) * $unit + $originy;
$color = $progress == 0 ? 'red' : 'blue';
$svg .= DrawLine($i, $yval1, $i + 1, $yval2, $color, 2);
}
if ($progress == 1) {
// Calculate abscissas for zero points
$x_zero1 = $x1 * $unit + $originx;
$x_zero2 = $x2 * $unit + $originx;
// Draw solution (segment)
if ($a > 0 && in_array($relation, ['\\leq', '<']) || $a < 0 && in_array($relation, ['\\geq', '>'])) {
$svg .= DrawLine($x_zero1, $originy, $x_zero2, $originy, $color = 'red', $width = 2);
} else {
$svg .= DrawLine($x_zero2, $originy, $width, $originy, $color = 'red', $width = 2);
$svg .= DrawLine(0, $originy, $x_zero1, $originy, $color = 'red', $width = 2);
}
// Draw solution (end points)
if ($x1 != $x2) {
$color = in_array($relation, ['<', '>']) ? 'white' : 'red';
$svg .= DrawCircle($x_zero1, $originy, 4, 'red', 2, $color);
$svg .= DrawCircle($x_zero2, $originy, 4, 'red', 2, $color);
}
}
$svg .= '</svg></div>';
return $svg;
}
function Graph($A, $B, $axis, $progress = 0)
{
list($C, $r, $P1, $P2) = $this->Solution($A, $B, $axis);
$bottom = min(0, $C[1] - $r);
$top = max(0, $C[1] + $r);
$left = min(0, $C[0] - $r);
$right = max(0, $C[0] + $r);
// print_r('bottom: '.$bottom.'<br />');
// print_r('top: '.$top.'<br />');
// print_r('left: '.$left.'<br />');
// print_r('right: '.$right.'<br />');
$linesx = $top - $bottom + 3;
$linesy = $right - $left + 3;
$unit = 500 / $linesy;
$width = $unit * $linesy;
$height = $unit * $linesx;
// print_r('width: '.$width.', height: '.$height.'<br />');
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// Origo
$OO = $this->CanvasCoordinates([0, 0], $height, $left, $bottom, $unit);
if ($unit < 35) {
$fontsize_axis = 0;
// Hide text if coordinate system is too big
$axis_width = 1;
} elseif ($unit < 45) {
$fontsize_axis = 10;
$axis_width = 2;
} elseif ($unit < 50) {
$fontsize_axis = 11;
$axis_width = 2;
} else {
$fontsize_axis = 12;
$axis_width = 2;
}
$fontsize_label = round($fontsize_axis * 1.2);
// Guides
for ($i = 0; $i < $linesy; $i++) {
$x = (0.5 + $i) * $unit;
$svg .= DrawLine($x, 0, $x, $height, '#F2F2F2');
$num = $i + $left - 1;
if ($num == 0) {
$svg .= DrawText($OO[0] + $unit / 3, $OO[1] + $unit / 2, '$0$', $fontsize_axis);
} else {
$svg .= DrawLine($x, $OO[1] - 5, $x, $OO[1] + 5, 'black', $axis_width);
$svg .= DrawText($x, $OO[1] + $unit / 2, '$' . $num . '$', $fontsize_axis);
}
}
for ($i = 0; $i < $linesx; $i++) {
$y = (0.5 + $i) * $unit;
$svg .= DrawLine(0, $y, $width, $y, '#F2F2F2');
$num = $top - $i + 1;
if ($num != 0) {
$svg .= DrawLine($OO[0] + 5, $y, $OO[0] - 5, $y, 'black', $axis_width);
if ($num <= 9 && $num > 0) {
$shift = $unit / 3;
} elseif ($num > -10 || $num > 9) {
$shift = $unit / 2;
} else {
$shift = $unit / 1.7;
}
$svg .= DrawText($OO[0] - $shift, $y + $unit / 5, '$' . $num . '$', $fontsize_axis);
}
}
// Axes
$svg .= DrawVector($OO[0], $height, $OO[0], 0, 'black', 10, $axis_width);
$svg .= DrawVector(0, $OO[1], $width, $OO[1], 'black', 10, $axis_width);
$svg .= DrawText($width - $unit / 2, $OO[1] - $unit / 3, '$x$', $fontsize_label);
$svg .= DrawText($OO[0] + $unit / 2, $unit / 3, '$y$', $fontsize_label);
// Calculate canvas coordinates for nodes
$CC = $this->CanvasCoordinates($C, $height, $left, $bottom, $unit);
$AA = $this->CanvasCoordinates($A, $height, $left, $bottom, $unit);
$BB = $this->CanvasCoordinates($B, $height, $left, $bottom, $unit);
$PP1 = $this->CanvasCoordinates($P1, $height, $left, $bottom, $unit);
$PP2 = $this->CanvasCoordinates($P2, $height, $left, $bottom, $unit);
// print_r('C('.$CC[0].';'.$CC[1].')<br />');
// print_r('A('.$AA[0].';'.$AA[1].')<br />');
// print_r('B('.$BB[0].';'.$BB[1].')<br />');
// Calculate coordinates (labels)
$Clabel = $this->LabelCoordinates($A, $B, 'center');
$Alabel = $this->LabelCoordinates($B, $A);
$Blabel = $this->LabelCoordinates($A, $B);
$P1label = $this->LabelCoordinates($C, $P1, 'minus');
$P2label = $this->LabelCoordinates($C, $P2, 'minus');
// Calculate canvas coordinates for labels
$CClabel = $this->CanvasCoordinates($Clabel, $height, $left, $bottom, $unit);
$AAlabel = $this->CanvasCoordinates($Alabel, $height, $left, $bottom, $unit);
$BBlabel = $this->CanvasCoordinates($Blabel, $height, $left, $bottom, $unit);
$PP1label = $this->CanvasCoordinates($P1label, $height, $left, $bottom, $unit);
$PP2label = $this->CanvasCoordinates($P2label, $height, $left, $bottom, $unit);
if ($progress == 1) {
// Draw points
$svg .= DrawCircle($AA[0], $AA[1], 3, 'red', 1, 'red');
$svg .= DrawCircle($BB[0], $BB[1], 3, 'red', 1, 'red');
// Draw labels
$svg .= DrawText($AAlabel[0], $AAlabel[1], '$A$', $fontsize_label);
$svg .= DrawText($BBlabel[0], $BBlabel[1], '$B$', $fontsize_label);
} elseif ($progress == 2) {
// AB
$svg .= DrawLine($AA[0], $AA[1], $BB[0], $BB[1], 'blue', 2);
// Draw points
$svg .= DrawCircle($AA[0], $AA[1], 3, 'red', 1, 'red');
$svg .= DrawCircle($BB[0], $BB[1], 3, 'red', 1, 'red');
$svg .= DrawCircle($CC[0], $CC[1], 3, 'red', 1, 'red');
// Draw labels
$svg .= DrawText($AAlabel[0], $AAlabel[1], '$A$', $fontsize_label);
$svg .= DrawText($BBlabel[0], $BBlabel[1], '$B$', $fontsize_label);
$svg .= DrawText($CClabel[0], $CClabel[1], '$C$', $fontsize_label);
} elseif ($progress == 3) {
// Circle
$svg .= DrawCircle($CC[0], $CC[1], $r * $unit, 'blue', 2);
// Draw points
$svg .= DrawCircle($AA[0], $AA[1], 3, 'red', 1, 'red');
$svg .= DrawCircle($BB[0], $BB[1], 3, 'red', 1, 'red');
$svg .= DrawCircle($CC[0], $CC[1], 3, 'red', 1, 'red');
// Draw labels
$svg .= DrawText($AAlabel[0], $AAlabel[1], '$A$', $fontsize_label);
$svg .= DrawText($BBlabel[0], $BBlabel[1], '$B$', $fontsize_label);
$svg .= DrawText($CClabel[0], $CClabel[1], '$C$', $fontsize_label);
} elseif ($progress == 4) {
// Axes
if ($axis == 'x') {
$svg .= DrawLine(0, $OO[1], $width, $OO[1], 'limegreen', 2);
} else {
$svg .= DrawLine($OO[0], $height, $OO[0], 0, 'limegreen', 2);
}
// Circle
$svg .= DrawCircle($CC[0], $CC[1], $r * $unit, 'blue', 2);
// Draw points
$svg .= DrawCircle($PP1[0], $PP1[1], 3, 'red', 1, 'red');
$svg .= DrawCircle($PP2[0], $PP2[1], 3, 'red', 1, 'red');
// Draw labels
$svg .= DrawText($PP1label[0], $PP1label[1], '$P_1$', $fontsize_label);
$svg .= DrawText($PP2label[0], $PP2label[1], '$P_2$', $fontsize_label);
}
$svg .= '</svg></div>';
return $svg;
}
