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Reducing a Map Path Using Douglas-Peucker Algorithm

Implementing Douglas-Peucker In PHP: Part 2

The final class we need to implement is the ShapeReducer class.

As mentioned earlier in this article, this algorithm is recursive (meaning it calls itself until complete), and we need to determine the orthogonal distance for a point from the (imaginary) line joining two other points.

Thus, we need to implement three methods:

  1. The entry point for the reducer
  2. The recursive function
  3. A function to determine orthogonal distance

Rather than breaking down every line of code, I've included a number of comments in the following listing, which shows the code for the ShapeReducer class.

Listing 3 The ShapeReducer class, used to reduce the number of points in a shape (ShapeReducer.php)
    class ShapeReducer
         * Reduce the number of points in a shape using the Douglas-Peucker algorithm
         * @param   Shape   $shape      The shape to reduce
         * @param   float   $tolerance  The tolerance to decide whether or not
         *                              to keep a point, in geographic
         *                              coordinate system degrees
         * @return  Shape   The reduced shape
        public function reduceWithTolerance($shape, $tolerance)
            // if a shape has 2 or less points it cannot be reduced
            if ($tolerance <= 0 || count($shape->points()) < 3) {
                return $shape;
            $points = $shape->points();
            $newShape = new Shape(); // the new shape to return
            // automatically add the first and last point to the returned shape
            $newShape->addPoint($points[count($points) - 1]);
            // the first and last points in the original shape are
            // used as the entry point to the algorithm.
                $shape,             // original shape
                $newShape,          // reduced shape
                $tolerance,         // tolerance
                0,                  // index of first point
                count($points) - 1  // index of last point
            // all done, return the reduced shape
            return $newShape;
         * Reduce the points in $shape between the specified first and last
         * index. Add the shapes to keep to $newShape
         * @param   Shape   $shape      The original shape
         * @param   Shape   $newShape   The reduced (output) shape
         * @param   float   $tolerance  The tolerance to determine if a point is kept
         * @param   int     $firstIdx   The index in original shape's point of
         *                              the starting point for this line segment
         * @param   int     $lastIdx    The index in original shape's point of
         *                              the ending point for this line segment
        public function douglasPeuckerReduction(Shape $shape, Shape $newShape, $tolerance, $firstIdx, $lastIdx)
            if ($lastIdx <= $firstIdx + 1) {
                // overlapping indexes, just return
            // retrieve all points for subsequent processing
            $points = $shape->points();
            // loop over the points between the first and last points
            // and find the point that is the furthest away
            $maxDistance = 0.0;
            $indexFarthest = 0;
            $firstPoint = $points[$firstIdx];
            $lastPoint = $points[$lastIdx];
            for ($idx = $firstIdx + 1; $idx < $lastIdx; $idx++) {
                $point = $points[$idx];
                $distance = $this->orthogonalDistance($point, $firstPoint, $lastPoint);
                // only keep the point with the greatest distance
                if ($distance > $maxDistance) {
                    $maxDistance = $distance;
                    $indexFarthest = $idx;
            // if the point that is furthest away is within the tolerance,
            // it is simply discarded. Otherwise, it's added to the reduced
            // shape and the algorithm continues
            if ($maxDistance > $tolerance) {
                // reduce the shape between the starting point to newly found point
                $this->douglasPeuckerReduction($shape, $newShape, $tolerance, $firstIdx, $indexFarthest);
                // reduce the shape between the newly found point and the finishing point
                $this->douglasPeuckerReduction($shape, $newShape, $tolerance, $indexFarthest, $lastIdx);
         * Calculate the orthogonal distance from the line joining the
         * $lineStart and $lineEnd points from $point
         * @param   ShapePoint  $point      The point the distance is being calculated for
         * @param   ShapePoint  $lineStart  The point that starts the line
         * @param   ShapePoint  $lineEnd    The point that ends the line
         * @return  float   The distance in geographic coordinate system degrees
        public function orthogonalDistance($point, $lineStart, $lineEnd)
            $area = abs(
                    $lineStart->lat * $lineEnd->lng
                  + $lineEnd->lat * $point->lng
                  + $point->lat * $lineStart->lng
                  - $lineEnd->lat * $lineStart->lng
                  - $point->lat * $lineEnd->lng
                  - $lineStart->lat * $point->lng
                ) / 2
            $bottom = sqrt(pow($lineStart->lat - $lineEnd->lat, 2) + pow($lineStart->lng - $lineEnd->lng, 2));
            return $area / $bottom * 2.0;

In the next section I'll show you how to use the three PHP classes we've just created.

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