function Vectors($angle, $size, $option = 0)
{
$width = 400;
$height = 250;
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
$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, 120);
$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, 50);
$svg .= DrawVector($Ax, $Ay, $Bx, $By, 'black', 10, 2, 10);
$svg .= DrawVector($Ax, $Ay, $Cx, $Cy, 'black', 10, 2, 10);
$svg .= DrawText(($Ax + $Bx) / 2, ($Ay + $By) / 2 + 30, '$' . $size . '$', 12);
$svg .= DrawText(($Ax + $Cx) / 2 - 23, ($Ay + $Cy) / 2, '$' . $size . '$', 12);
$svg .= DrawText($Ax + 20, $Ay - 15, '$' . $angle . '°$', 12);
if ($option) {
$svg .= DrawVector($Cx, $Cy, $Bx, $By, 'black', 10, 2, 10);
$svg .= DrawText(($Bx + $Cx) / 2 + 40, ($By + $Cy) / 2 - 10, '$\\overrightarrow{AB}-\\overrightarrow{AC}$', 12, 'black');
}
$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 $svg;
}
function Coordinates3($Px, $Py, $Qx, $Qy, $type = 'node')
{
if ($type == 'center') {
$Cx = ($Px + $Qx) / 2;
$Cy = ($Py + $Qy) / 2;
list($C1x, $C1y) = Rotate($Cx, $Cy, $Px, $Py, 45);
list($Rx, $Ry) = LinePoint($Cx, $Cy, $C1x, $C1y, 0.5);
} else {
$length = Length($Px, $Py, $Qx, $Qy);
list($Rx, $Ry) = LinePoint($Px, $Py, $Qx, $Qy, $length + 0.5);
}
return array($Rx, $Ry);
}
function Bottom($a, $option = 0)
{
$width = 250;
$height = 250;
$centerX = $width / 2;
$centerY = $height / 2;
$radius = 100;
$svg = '<div class="img-question text-center">
<svg width="' . $width . '" height="' . $height . '">';
for ($i = 0; $i < 6; $i++) {
$alfa = $i * 60;
// Rotate point
list($Px, $Py) = Rotate($centerX, $centerY, $centerX + $radius, $centerY, $alfa);
$points[] = [$Px, $Py];
// Draw side
if ($i > 0) {
$svg .= DrawLine($points[$i - 1][0], $points[$i - 1][1], $Px, $Py, 'black', 2);
$side_x = ($points[$i - 1][0] + $Px) / 2;
$side_y = ($points[$i - 1][1] + $Py) / 2;
// Node
list($Ex, $Ey) = LinePoint($centerX, $centerY, $side_x, $side_y, $radius);
$svg .= DrawText($Ex, $Ey + 7, '$' . $a . '$', 12);
}
if ($i == 5) {
$svg .= DrawLine($points[0][0], $points[0][1], $Px, $Py, 'black', 2);
$side_x = ($points[0][0] + $Px) / 2;
$side_y = ($points[0][1] + $Py) / 2;
// Node
list($Ex, $Ey) = LinePoint($centerX, $centerY, $side_x, $side_y, $radius);
$svg .= DrawText($Ex, $Ey + 7, '$' . $a . '$', 12);
}
// Draw edge
$svg .= DrawPath($centerX, $centerY, $Px, $Py, $color1 = 'black', $width = 1, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
if ($option == 1) {
$A = $points[4];
$B = $points[5];
$svg .= DrawLine($A[0], $A[1], $B[0], $B[1], 'blue', 2);
$svg .= DrawLine($A[0], $A[1], $centerX, $centerY, 'blue', 2);
$svg .= DrawLine($B[0], $B[1], $centerX, $centerY, 'blue', 2);
$svg .= DrawPath($centerX, $centerY, ($A[0] + $B[0]) / 2, ($A[1] + $B[1]) / 2, $color1 = 'black', $width = 1, $color2 = 'none', $dasharray1 = 5, $dasharray2 = 5);
}
$svg .= '</svg></div>';
return $svg;
}
function Triangle($Ax, $Ay, $Bx, $By, $alpha, $beta)
{
// Rotate AB vector around A with alpha
list($BBx, $BBy) = Rotate($Ax, $Ay, $Bx, $By, $alpha);
// Rotate AB vector around B with -beta
list($AAx, $AAy) = Rotate($Bx, $By, $Ax, $Ay, -$beta);
list($Px, $Py) = IntersectLines($Ax, $Ay, $BBx, $BBy, $Bx, $By, $AAx, $AAy);
return array($Px, $Py);
}
function Pyramid($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 $svg;
}
function LabelCoordinates($P, $Q, $type = 'node')
{
if ($type == 'center') {
$C[0] = ($P[0] + $Q[0]) / 2;
$C[1] = ($P[1] + $Q[1]) / 2;
list($C1[0], $C1[1]) = Rotate($C[0], $C[1], $P[0], $P[1], -45);
list($R[0], $R[1]) = LinePoint($C[0], $C[1], $C1[0], $C1[1], 0.7);
} elseif ($type == 'minus') {
$length = Length($P[0], $P[1], $Q[0], $Q[1]);
list($R[0], $R[1]) = LinePoint($P[0], $P[1], $Q[0], $Q[1], $length - 0.7);
} else {
$length = Length($P[0], $P[1], $Q[0], $Q[1]);
list($R[0], $R[1]) = LinePoint($P[0], $P[1], $Q[0], $Q[1], $length + 0.7);
}
return $R;
}
