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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Math\Geometry\Shape\D2 |
| 8 | * @copyright Dennis Eichhorn |
| 9 | * @license OMS License 2.0 |
| 10 | * @version 1.0.0 |
| 11 | * @link https://jingga.app |
| 12 | */ |
| 13 | declare(strict_types=1); |
| 14 | |
| 15 | namespace phpOMS\Math\Geometry\Shape\D2; |
| 16 | |
| 17 | /** |
| 18 | * Polygon class. |
| 19 | * |
| 20 | * @package phpOMS\Math\Geometry\Shape\D2 |
| 21 | * @license OMS License 2.0 |
| 22 | * @link https://jingga.app |
| 23 | * @since 1.0.0 |
| 24 | */ |
| 25 | final class Polygon implements D2ShapeInterface |
| 26 | { |
| 27 | /** |
| 28 | * Epsilon for float comparison. |
| 29 | * |
| 30 | * @var float |
| 31 | * @since 1.0.0 |
| 32 | */ |
| 33 | public const EPSILON = 4.88e-04; |
| 34 | |
| 35 | /** |
| 36 | * Coordinates. |
| 37 | * |
| 38 | * These coordinates define the polygon |
| 39 | * |
| 40 | * @var array<int, array{x:int|float, y:int|float}> |
| 41 | * @since 1.0.0 |
| 42 | */ |
| 43 | private array $coord = []; |
| 44 | |
| 45 | /** |
| 46 | * Constructor. |
| 47 | * |
| 48 | * @param array<int, array{x:int|float, y:int|float}> $coord 2 Dimensional coordinate array where the indices are x and y |
| 49 | * |
| 50 | * @example Polygon([['x' => 1, 'y' => 2], ['x' => ...], ...]) |
| 51 | * |
| 52 | * @since 1.0.0 |
| 53 | */ |
| 54 | public function __construct(array $coord) |
| 55 | { |
| 56 | $this->coord = $coord; |
| 57 | } |
| 58 | |
| 59 | /** |
| 60 | * Point polygon relative position |
| 61 | * |
| 62 | * @param array{x:int|float, y:int|float} $point Point location |
| 63 | * |
| 64 | * @return int -1 inside polygon 0 on vertice 1 outside |
| 65 | * |
| 66 | * @since 1.0.0 |
| 67 | */ |
| 68 | public function pointInPolygon(array $point) : int |
| 69 | { |
| 70 | $coord = $this->coord; |
| 71 | $coord[] = $this->coord[0]; |
| 72 | |
| 73 | return self::isPointInPolygon($point, $coord); |
| 74 | } |
| 75 | |
| 76 | /** |
| 77 | * Point polygon relative position |
| 78 | * |
| 79 | * @param array{x:int|float, y:int|float} $point Point location |
| 80 | * @param array<int, array{x:int|float, y:int|float}> $polygon Polygon definition |
| 81 | * |
| 82 | * @return int -1 inside polygon 0 on vertice 1 outside |
| 83 | * |
| 84 | * @link http://erich.realtimerendering.com/ptinpoly/ |
| 85 | * @since 1.0.0 |
| 86 | */ |
| 87 | public static function isPointInPolygon(array $point, array $polygon) : int |
| 88 | { |
| 89 | $length = \count($polygon); |
| 90 | |
| 91 | // Polygon has to start and end with same point |
| 92 | if ($polygon[0]['x'] !== $polygon[$length - 1]['x'] || $polygon[0]['y'] !== $polygon[$length - 1]['y']) { |
| 93 | $polygon[] = $polygon[0]; |
| 94 | } |
| 95 | |
| 96 | // On vertex? |
| 97 | if (self::isOnVertex($point, $polygon)) { |
| 98 | return 0; |
| 99 | } |
| 100 | |
| 101 | // Inside or ontop? |
| 102 | $countIntersect = 0; |
| 103 | $polygonCount = \count($polygon); |
| 104 | |
| 105 | for ($i = 1; $i < $polygonCount; ++$i) { |
| 106 | $vertex1 = $polygon[$i - 1]; |
| 107 | $vertex2 = $polygon[$i]; |
| 108 | |
| 109 | if (\abs($vertex1['y'] - $vertex2['y']) < self::EPSILON |
| 110 | && \abs($vertex1['y'] - $point['y']) < self::EPSILON |
| 111 | && $point['x'] > \min($vertex1['x'], $vertex2['x']) |
| 112 | && $point['x'] < \max($vertex1['x'], $vertex2['x']) |
| 113 | ) { |
| 114 | return 0; // boundary |
| 115 | } |
| 116 | |
| 117 | if ($point['y'] > \min($vertex1['y'], $vertex2['y']) |
| 118 | && $point['y'] <= \max($vertex1['y'], $vertex2['y']) |
| 119 | && $point['x'] <= \max($vertex1['x'], $vertex2['x']) |
| 120 | && \abs($vertex1['y'] - $vertex2['y']) >= self::EPSILON |
| 121 | ) { |
| 122 | $xinters = ($point['y'] - $vertex1['y']) * ($vertex2['x'] - $vertex1['x']) / ($vertex2['y'] - $vertex1['y']) + $vertex1['x']; |
| 123 | |
| 124 | if (\abs($xinters - $point['x']) < self::EPSILON) { |
| 125 | return 0; // boundary |
| 126 | } |
| 127 | |
| 128 | if (\abs($vertex1['x'] - $vertex2['x']) < self::EPSILON || $point['x'] < $xinters) { |
| 129 | ++$countIntersect; |
| 130 | } |
| 131 | } |
| 132 | } |
| 133 | |
| 134 | if ($countIntersect % 2 !== 0) { |
| 135 | return -1; |
| 136 | } |
| 137 | |
| 138 | return 1; |
| 139 | } |
| 140 | |
| 141 | /** |
| 142 | * Is point on vertex? |
| 143 | * |
| 144 | * @param array{x:int|float, y:int|float} $point Point location |
| 145 | * @param array<int, array{x:int|float, y:int|float}> $polygon Polygon definition |
| 146 | * |
| 147 | * @return bool |
| 148 | * |
| 149 | * @since 1.0.0 |
| 150 | */ |
| 151 | private static function isOnVertex(array $point, array $polygon) : bool |
| 152 | { |
| 153 | foreach ($polygon as $vertex) { |
| 154 | if (\abs($point['x'] - $vertex['x']) < self::EPSILON && \abs($point['y'] - $vertex['y']) < self::EPSILON) { |
| 155 | return true; |
| 156 | } |
| 157 | } |
| 158 | |
| 159 | return false; |
| 160 | } |
| 161 | |
| 162 | /** |
| 163 | * Get interior angle sum |
| 164 | * |
| 165 | * @return int |
| 166 | * |
| 167 | * @since 1.0.0 |
| 168 | */ |
| 169 | public function getInteriorAngleSum() : int |
| 170 | { |
| 171 | return (\count($this->coord) - 2) * 180; |
| 172 | } |
| 173 | |
| 174 | /** |
| 175 | * Get exterior angle sum |
| 176 | * |
| 177 | * @return int |
| 178 | * |
| 179 | * @since 1.0.0 |
| 180 | */ |
| 181 | public function getExteriorAngleSum() : int |
| 182 | { |
| 183 | return 360; |
| 184 | } |
| 185 | |
| 186 | /** |
| 187 | * Get surface area |
| 188 | * |
| 189 | * @return float |
| 190 | * |
| 191 | * @since 1.0.0 |
| 192 | */ |
| 193 | public function getSurface() : float |
| 194 | { |
| 195 | return \abs($this->getSignedSurface()); |
| 196 | } |
| 197 | |
| 198 | /** |
| 199 | * Get signed surface area |
| 200 | * |
| 201 | * @return float |
| 202 | * |
| 203 | * @since 1.0.0 |
| 204 | */ |
| 205 | private function getSignedSurface() : float |
| 206 | { |
| 207 | $count = \count($this->coord); |
| 208 | $surface = 0; |
| 209 | |
| 210 | for ($i = 0; $i < $count - 1; ++$i) { |
| 211 | $surface += $this->coord[$i]['x'] * $this->coord[$i + 1]['y'] - $this->coord[$i + 1]['x'] * $this->coord[$i]['y']; |
| 212 | } |
| 213 | |
| 214 | $surface += $this->coord[$count - 1]['x'] * $this->coord[0]['y'] - $this->coord[0]['x'] * $this->coord[$count - 1]['y']; |
| 215 | |
| 216 | return $surface / 2; |
| 217 | } |
| 218 | |
| 219 | /** |
| 220 | * Get perimeter |
| 221 | * |
| 222 | * @return float |
| 223 | * |
| 224 | * @since 1.0.0 |
| 225 | */ |
| 226 | public function getPerimeter() : float |
| 227 | { |
| 228 | $count = \count($this->coord); |
| 229 | $perimeter = \sqrt(($this->coord[0]['x'] - $this->coord[$count - 1]['x']) ** 2 + ($this->coord[0]['y'] - $this->coord[$count - 1]['y']) ** 2); |
| 230 | |
| 231 | for ($i = 0; $i < $count - 1; ++$i) { |
| 232 | $perimeter += \sqrt(($this->coord[$i + 1]['x'] - $this->coord[$i]['x']) ** 2 + ($this->coord[$i + 1]['y'] - $this->coord[$i]['y']) ** 2); |
| 233 | } |
| 234 | |
| 235 | return $perimeter; |
| 236 | } |
| 237 | |
| 238 | /** |
| 239 | * Get barycenter |
| 240 | * |
| 241 | * @return array{x:int|float, y:int|float} |
| 242 | * |
| 243 | * @since 1.0.0 |
| 244 | */ |
| 245 | public function getBarycenter() : array |
| 246 | { |
| 247 | $barycenter = ['x' => 0, 'y' => 0]; |
| 248 | $count = \count($this->coord); |
| 249 | |
| 250 | for ($i = 0; $i < $count - 1; ++$i) { |
| 251 | $mult = ($this->coord[$i]['x'] * $this->coord[$i + 1]['y'] - $this->coord[$i + 1]['x'] * $this->coord[$i]['y']); |
| 252 | $barycenter['x'] += ($this->coord[$i]['x'] + $this->coord[$i + 1]['x']) * $mult; |
| 253 | $barycenter['y'] += ($this->coord[$i]['y'] + $this->coord[$i + 1]['y']) * $mult; |
| 254 | } |
| 255 | |
| 256 | $mult = ($this->coord[$count - 1]['x'] * $this->coord[0]['y'] - $this->coord[0]['x'] * $this->coord[$count - 1]['y']); |
| 257 | $barycenter['x'] += ($this->coord[$count - 1]['x'] + $this->coord[0]['x']) * $mult; |
| 258 | $barycenter['y'] += ($this->coord[$count - 1]['y'] + $this->coord[0]['y']) * $mult; |
| 259 | |
| 260 | $surface = $this->getSignedSurface(); |
| 261 | |
| 262 | $barycenter['x'] = 1 / (6 * $surface) * $barycenter['x']; |
| 263 | $barycenter['y'] = 1 / (6 * $surface) * $barycenter['y']; |
| 264 | |
| 265 | return $barycenter; |
| 266 | } |
| 267 | |
| 268 | /** |
| 269 | * Get area by side length |
| 270 | * |
| 271 | * @param float $length Side length |
| 272 | * @param int $sides Number of sides |
| 273 | * |
| 274 | * @return float |
| 275 | * |
| 276 | * @since 1.0.0 |
| 277 | */ |
| 278 | public static function getRegularAreaByLength(float $length, int $sides) : float |
| 279 | { |
| 280 | return $length ** 2 * $sides / (4 * \tan(\M_PI / $sides)); |
| 281 | } |
| 282 | |
| 283 | /** |
| 284 | * Get area by radius |
| 285 | * |
| 286 | * @param float $r Radius |
| 287 | * @param int $sides Number of sides |
| 288 | * |
| 289 | * @return float |
| 290 | * |
| 291 | * @since 1.0.0 |
| 292 | */ |
| 293 | public static function getRegularAreaByRadius(float $r, int $sides) : float |
| 294 | { |
| 295 | return $r ** 2 * $sides * \tan(\M_PI / $sides); |
| 296 | } |
| 297 | } |