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<?php |
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/** |
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* PHPCoord. |
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* |
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* @author Doug Wright |
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*/ |
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declare(strict_types=1); |
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namespace PHPCoord\CoordinateOperation; |
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use function assert; |
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use function count; |
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use function max; |
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use function min; |
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trait BiquadraticInterpolation |
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{ |
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protected float $startX; |
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protected float $endX; |
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protected float $startY; |
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protected float $endY; |
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protected int $numberOfColumns; |
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protected int $numberOfRows; |
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protected float $columnGridInterval; |
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protected float $rowGridInterval; |
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public function interpolate( |
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float $x, |
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float $y |
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): array { |
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$corners = $this->getCorners($x, $y); |
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$dx = $corners['lowerRight']->getX() === $corners['lowerLeft']->getX() ? 0 : (($x - $corners['lowerLeft']->getX()) / $this->columnGridInterval); |
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$dy = $corners['upperLeft']->getY() === $corners['lowerLeft']->getY() ? 0 : (($y - $corners['lowerLeft']->getY()) / $this->rowGridInterval); |
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$interpolations = []; |
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for ($i = 0, $count = count($corners['lowerLeft']->getValues()); $i < $count; ++$i) { |
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//Interpolate value at lower row |
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$y0 = $this->interpolateQuadratic($dx, $corners['lowerLeft']->getValues()[$i], $corners['lowerCentre']->getValues()[$i], $corners['lowerRight']->getValues()[$i]); |
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//Interpolate value at middle row |
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$y1 = $this->interpolateQuadratic($dx, $corners['middleLeft']->getValues()[$i], $corners['middleCentre']->getValues()[$i], $corners['middleRight']->getValues()[$i]); |
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//Interpolate value at upper row |
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$y2 = $this->interpolateQuadratic($dx, $corners['upperLeft']->getValues()[$i], $corners['upperCentre']->getValues()[$i], $corners['upperRight']->getValues()[$i]); |
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//Interpolate between rows |
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$xy = $this->interpolateQuadratic($dy, $y0, $y1, $y2); |
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$interpolations[] = $xy; |
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} |
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return $interpolations; |
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} |
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/** |
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* Quadratic interpolation at point p, where p is between 0 and 2. |
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* Converted from NOAA FORTRAN implementation, this function apparently uses Newton-Gregory forward polynomial. |
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*/ |
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private function interpolateQuadratic(float $p, float $valueAt0, float $valueAt1, float $valueAt2): float |
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{ |
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assert($p >= 0 && $p <= 2); |
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$difference1 = $valueAt1 - $valueAt0; |
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$difference2 = $valueAt2 - $valueAt1; |
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$differenceDifferences = $difference2 - $difference1; |
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return $valueAt0 + $p * $difference1 + $p / 2 * ($p - 1) * $differenceDifferences; |
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} |
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/** |
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* @return GridValues[] |
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*/ |
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private function getCorners(float $x, float $y): array |
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{ |
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// Method: |
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// Fit a 3x3 window over the random point. The closest |
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// 2x2 points will surround the point. But based on which |
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// quadrant of that 2x2 cell in which the point falls, the |
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// 3x3 window could extend NW, NE, SW or SE from the 2x2 cell. |
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// Find which column should be LEAST when fitting |
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// a 3x3 window around $longitude. |
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$xIndex = (int) (($x - $this->startX) / $this->columnGridInterval - 0.5); |
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// Find which row should be LEAST when fitting |
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// a 3x3 window around $latitude. |
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$yIndex = (int) (($y - $this->startY) / $this->rowGridInterval - 0.5); |
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$xIndex = min(max($xIndex, 0), $this->numberOfColumns - 3); |
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$yIndex = min(max($yIndex, 0), $this->numberOfRows - 3); |
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return [ |
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'lowerLeft' => $this->getRecord($xIndex, $yIndex), |
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'lowerCentre' => $this->getRecord($xIndex + 1, $yIndex), |
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'lowerRight' => $this->getRecord($xIndex + 2, $yIndex), |
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'middleLeft' => $this->getRecord($xIndex, $yIndex + 1), |
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'middleCentre' => $this->getRecord($xIndex + 1, $yIndex + 1), |
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'middleRight' => $this->getRecord($xIndex + 2, $yIndex + 1), |
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'upperLeft' => $this->getRecord($xIndex, $yIndex + 2), |
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'upperCentre' => $this->getRecord($xIndex + 1, $yIndex + 2), |
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'upperRight' => $this->getRecord($xIndex + 2, $yIndex + 2), |
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]; |
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} |
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} |
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dvdoug /
PHPCoord
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