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 $svg;
}
function Graph($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 $svg;
}
function Vectors($angle, $size, $option = 0)
{
$width = 400;
$height = 250;
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
if ($angle == 60) {
$paddingX = 50;
$paddingY = 50;
$length = 170;
$Ax = $paddingX;
$Ay = $height - $paddingY;
$Bx = $Ax + $length;
$By = $Ay;
list($Cx, $Cy) = Rotate($Ax, $Ay, $Bx, $By, 60);
$Dx = $Cx + $length;
$Dy = $Cy;
$svg .= DrawText($Ax - 5, $Ay + 30, '$A$', 12);
$svg .= DrawText($Bx - 5, $By + 30, '$B$', 12);
$svg .= DrawText($Cx - 5, $Cy - 10, '$C$', 12);
$svg .= DrawArc($Ax, $Ay, $Bx, $By, $Cx, $Cy, 70);
$svg .= DrawVector($Ax, $Ay, $Bx, $By, 'black', 10, 2, 30);
$svg .= DrawVector($Ax, $Ay, $Cx, $Cy, 'black', 10, 2, 30);
$svg .= DrawText(($Ax + $Bx) / 2, ($Ay + $By) / 2 + 30, '$' . $size . '$', 12);
$svg .= DrawText(($Ax + $Cx) / 2 - 13, ($Ay + $Cy) / 2, '$' . $size . '$', 12);
if (!$option) {
$svg .= DrawText($Ax + 40, $Ay - 15, '$60°$', 12);
} else {
$svg .= DrawPath($Bx, $By, $Cx, $Cy, 'black', 2, 'none', 2, 2);
if ($option == 2) {
$svg .= DrawPath($Bx, $By, $Dx, $Dy, 'black', 2, 'none', 2, 2);
$svg .= DrawPath($Cx, $Cy, $Dx, $Dy, 'black', 2, 'none', 2, 2);
$svg .= DrawVector($Ax, $Ay, $Dx, $Dy, 'black', 10, 2, 30);
$svg .= DrawText($Dx - 15, $Dy - 10, '$\\overrightarrow{AB}+\\overrightarrow{AC}$', 12, 'black');
} else {
$svg .= DrawText($Ax + 40, $Ay - 15, '$60°$', 12);
}
}
} elseif ($angle == 90) {
$paddingX = 50;
$paddingY = 40;
$length = 170;
$Ax = ($width - $length) / 2;
$Ay = $height - $paddingY;
$Bx = $Ax + $length;
$By = $Ay;
list($Cx, $Cy) = Rotate($Ax, $Ay, $Bx, $By, $angle);
$Dx = $Cx + $length;
$Dy = $Cy;
$svg .= DrawText($Ax - 5, $Ay + 30, '$A$', 12);
$svg .= DrawText($Bx - 5, $By + 30, '$B$', 12);
$svg .= DrawText($Cx - 5, $Cy - 10, '$C$', 12);
$svg .= DrawArc($Ax, $Ay, $Bx, $By, $Cx, $Cy, 60);
$svg .= DrawVector($Ax, $Ay, $Bx, $By, 'black', 10, 2, 30);
$svg .= DrawVector($Ax, $Ay, $Cx, $Cy, 'black', 10, 2, 30);
$svg .= DrawText(($Ax + $Bx) / 2, ($Ay + $By) / 2 + 30, '$' . $size . '$', 12);
$svg .= DrawText(($Ax + $Cx) / 2 - 13, ($Ay + $Cy) / 2, '$' . $size . '$', 12);
if (!$option) {
$svg .= DrawText($Ax + 25, $Ay - 15, '$90°$', 12);
} else {
$svg .= DrawPath($Bx, $By, $Dx, $Dy, 'black', 2, 'none', 2, 2);
$svg .= DrawPath($Cx, $Cy, $Dx, $Dy, 'black', 2, 'none', 2, 2);
if ($option == 2) {
$svg .= DrawVector($Ax, $Ay, $Dx, $Dy, 'black', 10, 2, 30);
$svg .= DrawText($Dx - 15, $Dy - 10, '$\\overrightarrow{AB}+\\overrightarrow{AC}$', 12, 'black');
} else {
$svg .= DrawText($Ax + 25, $Ay - 15, '$90°$', 12);
}
}
} elseif ($angle == 120) {
$paddingX = 50;
$paddingY = 40;
$length = 170;
$Ax = $width - $paddingX - $length;
$Ay = $height - $paddingY;
$Bx = $Ax + $length;
$By = $Ay;
list($Cx, $Cy) = Rotate($Ax, $Ay, $Bx, $By, $angle);
$Dx = $Cx + $length;
$Dy = $Cy;
$svg .= DrawText($Ax - 5, $Ay + 30, '$A$', 12);
$svg .= DrawText($Bx - 5, $By + 30, '$B$', 12);
$svg .= DrawText($Cx - 5, $Cy - 10, '$C$', 12);
$svg .= DrawVector($Ax, $Ay, $Bx, $By, 'black', 10, 2, 30);
$svg .= DrawVector($Ax, $Ay, $Cx, $Cy, 'black', 10, 2, 30);
$svg .= DrawText(($Ax + $Bx) / 2, ($Ay + $By) / 2 + 30, '$' . $size . '$', 12);
$svg .= DrawText(($Ax + $Cx) / 2 - 13, ($Ay + $Cy) / 2, '$' . $size . '$', 12);
if (!$option) {
$svg .= DrawArc($Ax, $Ay, $Bx, $By, $Cx, $Cy, 50);
$svg .= DrawText($Ax + 20, $Ay - 15, '$120°$', 12);
} else {
$svg .= DrawArc($Ax, $Ay, $Bx, $By, $Dx, $Dy, 50);
$svg .= DrawArc($Ax, $Ay, $Bx, $By, $Cx, $Cy, 60);
$svg .= DrawPath($Bx, $By, $Dx, $Dy, 'black', 2, 'none', 2, 2);
$svg .= DrawPath($Cx, $Cy, $Dx, $Dy, 'black', 2, 'none', 2, 2);
$svg .= DrawVector($Ax, $Ay, $Dx, $Dy, 'black', 10, 2, 30);
$svg .= DrawText($Dx - 15, $Dy - 10, '$\\overrightarrow{AB}+\\overrightarrow{AC}$', 12, 'black');
$svg .= DrawText($Ax + 30, $Ay - 10, '$60°$', 12);
}
}
$svg .= '</svg></div>';
return $svg;
}
function Trapez($bottom, $top, $side, $progress = 0)
{
$width = 350;
$height = 250;
$paddingX_top = 110;
$paddingX_bottom = 20;
$paddingY = 50;
$radius = 40;
$Ax = $paddingX_bottom;
$Ay = $height - $paddingY;
$Bx = $width - $paddingX_bottom;
$By = $height - $paddingY;
$Cx = $width - $paddingX_top;
$Cy = $paddingY;
$Dx = $paddingX_top;
$Dy = $paddingY;
$Ex = $paddingX_top;
$Ey = $height - $paddingY;
$Fx = $width - $paddingX_top;
$Fy = $height - $paddingY;
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// Sides
$svg .= DrawLine($Ax, $Ay, $Bx, $By, 'black', 2);
$svg .= DrawLine($Bx, $By, $Cx, $Cy, 'black', 2);
$svg .= DrawLine($Cx, $Cy, $Dx, $Dy, 'black', 2);
$svg .= DrawLine($Dx, $Dy, $Ax, $Ay, 'black', 2);
// Nodes
$svg .= DrawText($Ax - 13, $Ay, '$A$', 12);
$svg .= DrawText($Bx + 13, $By, '$B$', 12);
$svg .= DrawText($Cx + 13, $Cy, '$C$', 12);
$svg .= DrawText($Dx - 13, $Dy, '$D$', 12);
if ($progress == 0) {
// Arcs
$svg .= DrawArc($Ax, $Ay, $Bx, $By, $Dx, $Dy, $radius);
$svg .= DrawArc($Bx, $By, $Cx, $Cy, $Ax, $Ay, $radius);
$svg .= DrawArc($Cx, $Cy, $Dx, $Dy, $Bx, $By, $radius);
$svg .= DrawArc($Dx, $Dy, $Ax, $Ay, $Cx, $Cy, $radius);
// Lengths
$svg .= DrawText(($Ax + $Bx) / 2, ($Ay + $By) / 2 + 17, '$' . $bottom . '$', 12);
$svg .= DrawText(($Bx + $Cx) / 2 + 15, ($By + $Cy) / 2 - 5, '$' . round2($side) . '$', 12);
$svg .= DrawText(($Cx + $Dx) / 2 + 5, ($Cy + $Dy) / 2 - 5, '$' . $top . '$', 12);
$svg .= DrawText(($Dx + $Ax) / 2 - 15, ($Dy + $Ay) / 2 - 5, '$' . round2($side) . '$', 12);
} elseif ($progress == 1) {
// Arcs
$svg .= DrawArc($Ax, $Ay, $Bx, $By, $Dx, $Dy, $radius, 0, 0, NULL, 'red');
$svg .= DrawArc($Bx, $By, $Cx, $Cy, $Ax, $Ay, $radius, 0, 0, NULL, 'red');
$svg .= DrawArc($Ax, $Ay, $Bx, $By, $Dx, $Dy, $radius + 3, 0, 0, NULL, 'red');
$svg .= DrawArc($Bx, $By, $Cx, $Cy, $Ax, $Ay, $radius + 3, 0, 0, NULL, 'red');
$svg .= DrawArc($Cx, $Cy, $Dx, $Dy, $Bx, $By, $radius, 0, 0, NULL, 'blue');
$svg .= DrawArc($Dx, $Dy, $Ax, $Ay, $Cx, $Cy, $radius, 0, 0, NULL, 'blue');
// Lengths
$svg .= DrawText(($Ax + $Bx) / 2, ($Ay + $By) / 2 + 17, '$' . $bottom . '$', 12);
$svg .= DrawText(($Bx + $Cx) / 2 + 15, ($By + $Cy) / 2 - 5, '$' . round2($side) . '$', 12);
$svg .= DrawText(($Cx + $Dx) / 2 + 5, ($Cy + $Dy) / 2 - 5, '$' . $top . '$', 12);
$svg .= DrawText(($Dx + $Ax) / 2 - 15, ($Dy + $Ay) / 2 - 5, '$' . round2($side) . '$', 12);
} elseif ($progress == 2) {
// Height
$svg .= DrawPath($Dx, $Dy, $Ex, $Ey, $color1 = 'blue', $width = 1, $color2 = 'white', $dasharray1 = 5, $dasharray2 = 3);
$svg .= DrawPath($Cx, $Cy, $Fx, $Fy, $color1 = 'blue', $width = 1, $color2 = 'white', $dasharray1 = 5, $dasharray2 = 3);
$svg .= DrawLine($Ex, $Ey, $Fx, $Fy, 'red', 3);
$svg .= DrawText($Ex, $Ey + 20, '$E$', 12);
$svg .= DrawText($Fx, $Fy + 20, '$F$', 12);
// Lengths
$svg .= DrawText(($Ax + $Bx) / 2, ($Ay + $By) / 2 + 17, '$' . $top . '$', 12);
$svg .= DrawText(($Bx + $Cx) / 2 + 15, ($By + $Cy) / 2 - 5, '$' . round2($side) . '$', 12);
$svg .= DrawText(($Cx + $Dx) / 2 + 5, ($Cy + $Dy) / 2 - 5, '$' . $top . '$', 12);
$svg .= DrawText(($Dx + $Ax) / 2 - 15, ($Dy + $Ay) / 2 - 5, '$' . round2($side) . '$', 12);
} elseif ($progress == 3) {
// Height
$svg .= DrawPath($Dx, $Dy, $Ex, $Ey, $color1 = 'black', $width = 1, $color2 = 'white', $dasharray1 = 5, $dasharray2 = 3);
$svg .= DrawPath($Cx, $Cy, $Fx, $Fy, $color1 = 'blue', $width = 1, $color2 = 'white', $dasharray1 = 5, $dasharray2 = 3);
$svg .= DrawLine($Ax, $Ay, $Ex, $Ey, 'red', 3);
$svg .= DrawText($Ex, $Ey + 20, '$E$', 12);
$svg .= DrawText($Fx, $Fy + 20, '$F$', 12);
// AE length
$ae = ($bottom - $top) / 2;
// Lengths
$svg .= DrawText(($Ax + $Ex) / 2 - 5, ($Ay + $Ey) / 2 + 17, '$' . round2($ae) . '$', 12, 'red');
$svg .= DrawText(($Ax + $Bx) / 2, ($Ay + $By) / 2 + 17, '$' . $top . '$', 12);
$svg .= DrawText(($Bx + $Cx) / 2 + 15, ($By + $Cy) / 2 - 5, '$' . round2($side) . '$', 12);
$svg .= DrawText(($Cx + $Dx) / 2 + 5, ($Cy + $Dy) / 2 - 5, '$' . $top . '$', 12);
$svg .= DrawText(($Dx + $Ax) / 2 - 15, ($Dy + $Ay) / 2 - 5, '$' . round2($side) . '$', 12);
} elseif ($progress == 4) {
// Height
$svg .= DrawPath($Dx, $Dy, $Ex, $Ey, $color1 = 'black', $width = 1, $color2 = 'white', $dasharray1 = 5, $dasharray2 = 3);
$svg .= DrawPath($Cx, $Cy, $Fx, $Fy, $color1 = 'blue', $width = 1, $color2 = 'white', $dasharray1 = 5, $dasharray2 = 3);
$svg .= DrawLine($Ax, $Ay, $Ex, $Ey, 'red', 3);
$svg .= DrawLine($Ax, $Ay, $Dx, $Dy, 'red', 3);
$svg .= DrawText($Ex, $Ey + 20, '$E$', 12);
$svg .= DrawText($Fx, $Fy + 20, '$F$', 12);
// AE length
$ae = ($bottom - $top) / 2;
// Arc
$svg .= DrawArc($Ax, $Ay, $Bx, $By, $Dx, $Dy, $radius, +10, 0, '$\\color{red}{\\alpha}$', 'red');
// Lengths
$svg .= DrawText(($Ax + $Ex) / 2 - 5, ($Ay + $Ey) / 2 + 17, '$' . round2($ae) . '$', 12, 'red');
$svg .= DrawText(($Ax + $Bx) / 2, ($Ay + $By) / 2 + 17, '$' . $top . '$', 12);
$svg .= DrawText(($Bx + $Cx) / 2 + 15, ($By + $Cy) / 2 - 5, '$' . round2($side) . '$', 12);
$svg .= DrawText(($Cx + $Dx) / 2 + 5, ($Cy + $Dy) / 2 - 5, '$' . $top . '$', 12);
$svg .= DrawText(($Dx + $Ax) / 2 - 15, ($Dy + $Ay) / 2 - 5, '$' . round2($side) . '$', 12);
}
$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 $svg;
}
function Side($a, $b, $c, $option = 0)
{
$width = 250;
$height = 250;
$paddingX_top = 20;
$paddingX_bottom = 70;
$paddingY = 50;
$Ax = $paddingX_top;
$Ay = $paddingY;
$Bx = $paddingX_bottom;
$By = $height - $paddingY;
$Cx = $width - $Bx;
$Cy = $By;
$Dx = $width - $Ax;
$Dy = $Ay;
$Ex = $paddingX_bottom;
$Ey = $Ay;
$Fx = $width - $Ex;
$Fy = $Ay;
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
// Sides
$svg .= DrawLine($Ax, $Ay, $Bx, $By, 'black', 2);
$svg .= DrawLine($Bx, $By, $Cx, $Cy, 'black', 2);
$svg .= DrawLine($Cx, $Cy, $Dx, $Dy, 'black', 2);
$svg .= DrawLine($Dx, $Dy, $Ax, $Ay, 'black', 2);
if ($option == 0) {
// Nodes
$svg .= DrawText(($Ax + $Bx) / 2 - 13, ($Ay + $By) / 2 + 7, '$' . $c . '$', 12);
$svg .= DrawText(($Bx + $Cx) / 2 - 3, ($By + $Cy) / 2 + 20, '$' . $b . '$', 12);
$svg .= DrawText(($Cx + $Dx) / 2 + 10, ($Cy + $Dy) / 2 + 7, '$' . $c . '$', 12);
$svg .= DrawText(($Dx + $Ax) / 2 - 2, ($Dy + $Ay) / 2 - 10, '$' . $a . '$', 12);
} elseif ($option == 1) {
// Nodes
$svg .= DrawText(($Ax + $Bx) / 2 - 13, ($Ay + $By) / 2 + 7, '$' . $c . '$', 12);
$svg .= DrawText(($Bx + $Cx) / 2 - 3, ($By + $Cy) / 2 + 20, '$' . $b . '$', 12);
$svg .= DrawText(($Cx + $Dx) / 2 + 10, ($Cy + $Dy) / 2 + 7, '$' . $c . '$', 12);
$svg .= DrawText(($Dx + $Ax) / 2 - 2, ($Dy + $Ay) / 2 - 10, '$' . $b . '$', 12);
$svg .= DrawText(($Ex + $Ax) / 2 - 2, ($Ey + $Ay) / 2 - 10, '$' . strval(($a - $b) / 2) . '$', 12);
$svg .= DrawText(($Fx + $Dx) / 2 - 2, ($Fy + $Dy) / 2 - 10, '$' . strval(($a - $b) / 2) . '$', 12);
// Extra edges
$svg .= DrawPath($Bx, $By, $Ex, $Ey, $color1 = 'black', $width = 1, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
$svg .= DrawPath($Cx, $Cy, $Fx, $Fy, $color1 = 'black', $width = 1, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
} elseif ($option == 2) {
$svg .= DrawLine($Ax, $Ay, $Bx, $By, 'blue', 2);
$svg .= DrawLine($Bx, $By, $Ex, $Ey, 'blue', 2);
$svg .= DrawLine($Ex, $Ey, $Ax, $Ay, 'blue', 2);
$svg .= DrawText(($Ax + $Bx) / 2 - 13, ($Ay + $By) / 2 + 7, '$' . $c . '$', 12, 'blue');
$svg .= DrawText(($Bx + $Ex) / 2 + 10, ($By + $Ey) / 2 + 7, '$x$', 12, 'blue');
$svg .= DrawText(($Ex + $Ax) / 2 - 2, ($Ey + $Ay) / 2 - 10, '$' . strval(($a - $b) / 2) . '$', 12, 'blue');
}
$svg .= '</svg></div>';
return $svg;
}
function Pyramid($pyramid_base, $pyramid_side, $progress = 0)
{
$sides = 4;
// sides of pyramid
$height = 150;
// height of pyramid
$radius = 150;
// radius of base circle
$alfa0 = 15;
// starting angle of nodes
$visible = [1, 0, 1, 1];
// ids of visible edges
$perspective = 0.4;
// 0 (view from side) ... 1 (view from top)
$padding_y = 20;
$padding_x = 20;
$canvas_width = 2 * $padding_y + 2 * $radius;
$canvas_height = 2 * $padding_x + $height + $perspective * $radius;
$svg = '<div class="img-question text-center">
<svg width="' . $canvas_width . '" height="' . $canvas_height . '">';
// $svg .= '<rect width="'.$canvas_width.'" height="'.$canvas_height.'" fill="black" fill-opacity="0.2" />';
$center_x = $canvas_width / 2;
$center_y_top = $padding_y;
$center_x = $canvas_width / 2;
$center_y_bottom = $center_y_top + $height;
$node_top = [$center_x, $center_y_top];
for ($i = 0; $i < $sides; $i++) {
$alfa = $alfa0 + $i * 360 / $sides;
// Calculate bottom nodes
list($Px, $Py) = Rotate($center_x, $center_y_bottom, $center_x + $radius, $center_y_bottom, $alfa);
$Py = $center_y_bottom + $perspective * ($Py - $center_y_bottom);
$nodes_bottom[] = [$Px, $Py];
// Draw bottom edges
if ($i > 0) {
if ($visible[$i] && $visible[$i - 1]) {
$svg .= DrawLine($nodes_bottom[$i - 1][0], $nodes_bottom[$i - 1][1], $Px, $Py, 'black', 2);
} else {
$svg .= DrawPath($nodes_bottom[$i - 1][0], $nodes_bottom[$i - 1][1], $Px, $Py, 'black', 1, 'none', 5, 5);
}
}
if ($i == $sides - 1) {
if ($visible[$i] && $visible[0]) {
$svg .= DrawLine($nodes_bottom[0][0], $nodes_bottom[0][1], $Px, $Py, 'black', 2);
} else {
$svg .= DrawPath($nodes_bottom[0][0], $nodes_bottom[0][1], $Px, $Py, 'black', 1, 'none', 5, 5);
}
}
// Draw sides
if ($visible[$i]) {
$svg .= DrawLine($node_top[0], $node_top[1], $Px, $Py, 'black', 2);
} else {
$svg .= DrawPath($node_top[0], $node_top[1], $Px, $Py, 'black', 1, 'none', 5, 5);
}
}
$b = $nodes_bottom;
$t = $node_top;
if ($progress == 1) {
// Draw labels
$svg .= DrawText(($b[0][0] + $t[0]) / 2 + 20, ($b[0][1] + $t[1]) / 2 - 5, '$' . $pyramid_side . '$', 13);
// side
$svg .= DrawText(($b[2][0] + $b[3][0]) / 2 - 10, ($b[2][1] + $b[3][1]) / 2 + 25, '$' . $pyramid_base . '$', 13);
// base
$svg .= DrawText($b[3][0] / 4 + $b[0][0] / 4 * 3 + 10, $b[3][1] / 4 + $b[0][1] / 4 * 3 + 25, '$\\frac{' . $pyramid_base . '}{2}$', 13);
// base/2
$svg .= DrawText(($t[0] + ($b[3][0] + $b[0][0]) / 2) / 2 - 10, ($t[1] + ($b[3][1] + $b[0][1]) / 2) / 2 + 20, '$m_{\\triangle}$', 13);
// m_triangle
// Draw side
$points = [$b[0], $t, [($b[3][0] + $b[0][0]) / 2, ($b[3][1] + $b[0][1]) / 2]];
$svg .= DrawPolygon($points, $stroke = 'black', $strokewidth = 2, $fill = 'blue', $opacity = 0.5);
} elseif ($progress == 2) {
$b = $nodes_bottom;
$t = $node_top;
// Draw labels
$svg .= DrawText(($b[2][0] + $b[3][0]) / 2 - 10, ($b[2][1] + $b[3][1]) / 2 + 25, '$' . $pyramid_base . '$', 13);
// base
$svg .= DrawText(($center_x + $b[3][0]) / 2, ($center_y_bottom + $b[3][1]) / 2, '$\\frac{' . $pyramid_base . '}{2}$', 13);
// base/2
$svg .= DrawText(($t[0] + ($b[3][0] + $b[0][0]) / 2) / 2 + 30, ($t[1] + ($b[3][1] + $b[0][1]) / 2) / 2 + 10, '$m_{\\triangle}$', 13);
// m_triangle
$svg .= DrawText($center_x - 20, ($center_y_bottom + $center_y_top) / 2 + 10, '$m$', 13);
// m
// Draw side
$points = [$t, [($b[3][0] + $b[0][0]) / 2, ($b[3][1] + $b[0][1]) / 2], [$center_x, $center_y_bottom]];
$svg .= DrawPolygon($points, $stroke = 'black', $strokewidth = 2, $fill = 'blue', $opacity = 0.5);
}
$svg .= '</svg></div>';
return $svg;
}
