Transform envelopes (bounding boxes)

The transformation of envelopes (or bounding boxes) is a much more difficult task than transforming the four corners of a rectangle. The rectangle straight lines in source CRS may become curves in the target CRS with minimum and maximum values that are not located in any corner. The calculation is also more complicated if the envelope contains a pole or crosses the anti-meridian. Apache SIS handles those complexities in convenience static methods. This is demonstrated by comparing the result of using Apache SIS methods with the result of transforming the four corners. The latter naive approach has an error of 40 kilometres in this example.

While the example below uses a two-dimensional envelope, the same Apache SIS methods can transform efficiently N-dimensional envelopes.

Direct dependencies

Maven coordinates Module info org.apache.sis.referencing

Code example

Note that all geographic coordinates below express latitude before longitude.

import org.opengis.geometry.Envelope;
import org.opengis.referencing.operation.CoordinateOperation;
import org.opengis.referencing.operation.TransformException;
import org.opengis.util.FactoryException;
import org.apache.sis.referencing.CRS;
import org.apache.sis.referencing.CommonCRS;
import org.apache.sis.geometry.Envelopes;
import org.apache.sis.geometry.GeneralEnvelope;
import org.apache.sis.geometry.DirectPosition2D;

public class TransformEnvelopes {
     * Demo entry point.
     * @param  args  ignored.
     * @throws FactoryException   if an error occurred while creating a Coordinate Reference System (CRS).
     * @throws TransformException if an error occurred while transforming coordinates to the target CRS.
    public static void main(String[] args) throws FactoryException, TransformException {
        CoordinateReferenceSystem sourceCRS = CommonCRS.WGS84.geographic();
        CoordinateReferenceSystem targetCRS = CommonCRS.WGS84.universal(90, 0);  // Polar stereographic.

        GeneralEnvelope bbox = new GeneralEnvelope(sourceCRS);
        bbox.setRange(0,  84, 88);             // Latitudes.
        bbox.setRange(1, -20, 50);             // Longitudes.

        Envelope transformed = Envelopes.transform(bbox, targetCRS);
        Envelope corners = transformCorners(bbox, CRS.findOperation(sourceCRS, targetCRS, null));

        System.out.println("Source:  " + bbox);
        System.out.println("Result:  " + transformed);
        System.out.println("Corners: " + corners);
        System.out.println("Errors on Y axis: "
                + (corners.getMinimum(1) - transformed.getMinimum(1)) + " metres.");

     * Transforms the 4 corners of a two-dimensional envelope. This is not recommended.
     * This method is provided only for demonstrating that this approach is not sufficient.
     * @param  bbox       the bounding box to transform.
     * @param  operation  the coordinate operation to use for transforming corners.
     * @return the result of transforming the 4 corners of the provided bounding box.
     * @throws TransformException if a coordinate cannot be converted.
    private static Envelope transformCorners(Envelope bbox, CoordinateOperation operation) throws TransformException {
        double[] corners = {
            bbox.getMinimum(0), bbox.getMinimum(1),
            bbox.getMaximum(0), bbox.getMinimum(1),
            bbox.getMaximum(0), bbox.getMaximum(1),
            bbox.getMinimum(0), bbox.getMaximum(1)
        operation.getMathTransform().transform(corners, 0, corners, 0, 4);
        GeneralEnvelope result = new GeneralEnvelope(operation.getTargetCRS());
        for (int i=0; i<result.getDimension(); i++) {
            result.setRange(i, corners[i], corners[i]);
        for (int i=0; i<corners.length;) {
            result.add(new DirectPosition2D(corners[i++], corners[i++]));
        return result;


Source:  BOX(84 -20, 88 50)
Result:  BOX(1771965.695226812 1333272.44494046, 2510743.0524805877 1857256.625440407)
Corners: BOX(1771965.695226812 1373480.89677463, 2510743.0524805877 1857256.625440407)
Errors on Y axis: 40208.451834172476 metres.