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 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
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 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
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 * See the License for the specific language governing permissions and
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package org.apache.commons.math3.geometry.spherical.twod;

import java.util.List;

import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
import org.apache.commons.math3.geometry.spherical.oned.Arc;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;

Spherical polygons boundary edge.
See Also:
getBoundaryLoops.getBoundaryLoops()
Vertex
Since:
3.3/** Spherical polygons boundary edge.
 * @see SphericalPolygonsSet#getBoundaryLoops()
 * @see Vertex
 * @since 3.3
 */
public class Edge {

    
Start vertex. /** Start vertex. */
    private final Vertex start;

    
End vertex. /** End vertex. */
    private Vertex end;

    
Length of the arc. /** Length of the arc. */
    private final double length;

    
Circle supporting the edge. /** Circle supporting the edge. */
    private final Circle circle;

    
Build an edge not contained in any node yet.
Params:
start – start vertex
end – end vertex
length – length of the arc (it can be greater than \( \pi \))
circle – circle supporting the edge/** Build an edge not contained in any node yet.
     * @param start start vertex
     * @param end end vertex
     * @param length length of the arc (it can be greater than \( \pi \))
     * @param circle circle supporting the edge
     */
    Edge(final Vertex start, final Vertex end, final double length, final Circle circle) {

        this.start  = start;
        this.end    = end;
        this.length = length;
        this.circle = circle;

        // connect the vertices back to the edge
        start.setOutgoing(this);
        end.setIncoming(this);

    }

    
Get start vertex.
Returns:
start vertex/** Get start vertex.
     * @return start vertex
     */
    public Vertex getStart() {
        return start;
    }

    
Get end vertex.
Returns:
end vertex/** Get end vertex.
     * @return end vertex
     */
    public Vertex getEnd() {
        return end;
    }

    
Get the length of the arc.
Returns:
length of the arc (can be greater than \( \pi \))/** Get the length of the arc.
     * @return length of the arc (can be greater than \( \pi \))
     */
    public double getLength() {
        return length;
    }

    
Get the circle supporting this edge.
Returns:
circle supporting this edge/** Get the circle supporting this edge.
     * @return circle supporting this edge
     */
    public Circle getCircle() {
        return circle;
    }

    
Get an intermediate point.
 The angle along the edge should normally be between 0 and getLength() in order to remain within edge limits. However, there are no checks on the value of the angle, so user can rebuild the full circle on which an edge is defined if they want. 
Params:
alpha – angle along the edge, counted from getStart()
Returns:
an intermediate point/** Get an intermediate point.
     * <p>
     * The angle along the edge should normally be between 0 and {@link #getLength()}
     * in order to remain within edge limits. However, there are no checks on the
     * value of the angle, so user can rebuild the full circle on which an edge is
     * defined if they want.
     * </p>
     * @param alpha angle along the edge, counted from {@link #getStart()}
     * @return an intermediate point
     */
    public Vector3D getPointAt(final double alpha) {
        return circle.getPointAt(alpha + circle.getPhase(start.getLocation().getVector()));
    }

    
Connect the instance with a following edge.
Params:
next – edge following the instance/** Connect the instance with a following edge.
     * @param next edge following the instance
     */
    void setNextEdge(final Edge next) {
        end = next.getStart();
        end.setIncoming(this);
        end.bindWith(getCircle());
    }

    
Split the edge.

Once split, this edge is not referenced anymore by the vertices,
it is replaced by the two or three sub-edges and intermediate splitting
vertices are introduced to connect these sub-edges together.

Params:
splitCircle – circle splitting the edge in several parts
outsideList – list where to put parts that are outside of the split circle
insideList – list where to put parts that are inside the split circle/** Split the edge.
     * <p>
     * Once split, this edge is not referenced anymore by the vertices,
     * it is replaced by the two or three sub-edges and intermediate splitting
     * vertices are introduced to connect these sub-edges together.
     * </p>
     * @param splitCircle circle splitting the edge in several parts
     * @param outsideList list where to put parts that are outside of the split circle
     * @param insideList list where to put parts that are inside the split circle
     */
    void split(final Circle splitCircle,
                       final List<Edge> outsideList, final List<Edge> insideList) {

        // get the inside arc, synchronizing its phase with the edge itself
        final double edgeStart        = circle.getPhase(start.getLocation().getVector());
        final Arc    arc              = circle.getInsideArc(splitCircle);
        final double arcRelativeStart = MathUtils.normalizeAngle(arc.getInf(), edgeStart + FastMath.PI) - edgeStart;
        final double arcRelativeEnd   = arcRelativeStart + arc.getSize();
        final double unwrappedEnd     = arcRelativeEnd - MathUtils.TWO_PI;

        // build the sub-edges
        final double tolerance = circle.getTolerance();
        Vertex previousVertex = start;
        if (unwrappedEnd >= length - tolerance) {

            // the edge is entirely contained inside the circle
            // we don't split anything
            insideList.add(this);

        } else {

            // there are at least some parts of the edge that should be outside
            // (even is they are later be filtered out as being too small)
            double alreadyManagedLength = 0;
            if (unwrappedEnd >= 0) {
                // the start of the edge is inside the circle
                previousVertex = addSubEdge(previousVertex,
                                            new Vertex(new S2Point(circle.getPointAt(edgeStart + unwrappedEnd))),
                                            unwrappedEnd, insideList, splitCircle);
                alreadyManagedLength = unwrappedEnd;
            }

            if (arcRelativeStart >= length - tolerance) {
                // the edge ends while still outside of the circle
                if (unwrappedEnd >= 0) {
                    previousVertex = addSubEdge(previousVertex, end,
                                                length - alreadyManagedLength, outsideList, splitCircle);
                } else {
                    // the edge is entirely outside of the circle
                    // we don't split anything
                    outsideList.add(this);
                }
            } else {
                // the edge is long enough to enter inside the circle
                previousVertex = addSubEdge(previousVertex,
                                            new Vertex(new S2Point(circle.getPointAt(edgeStart + arcRelativeStart))),
                                            arcRelativeStart - alreadyManagedLength, outsideList, splitCircle);
                alreadyManagedLength = arcRelativeStart;

                if (arcRelativeEnd >= length - tolerance) {
                    // the edge ends while still inside of the circle
                    previousVertex = addSubEdge(previousVertex, end,
                                                length - alreadyManagedLength, insideList, splitCircle);
                } else {
                    // the edge is long enough to exit outside of the circle
                    previousVertex = addSubEdge(previousVertex,
                                                new Vertex(new S2Point(circle.getPointAt(edgeStart + arcRelativeStart))),
                                                arcRelativeStart - alreadyManagedLength, insideList, splitCircle);
                    alreadyManagedLength = arcRelativeStart;
                    previousVertex = addSubEdge(previousVertex, end,
                                                length - alreadyManagedLength, outsideList, splitCircle);
                }
            }

        }

    }

    
Add a sub-edge to a list if long enough.
 If the length of the sub-edge to add is smaller than the Circle.getTolerance() tolerance of the support circle, it will be ignored. 
Params:
subStart – start of the sub-edge
subEnd – end of the sub-edge
subLength – length of the sub-edge
splitCircle – circle splitting the edge in several parts
list – list where to put the sub-edge
Returns:
end vertex of the edge (subEnd if the edge was long enough and really added, subStart if the edge was too small and therefore ignored)/** Add a sub-edge to a list if long enough.
     * <p>
     * If the length of the sub-edge to add is smaller than the {@link Circle#getTolerance()}
     * tolerance of the support circle, it will be ignored.
     * </p>
     * @param subStart start of the sub-edge
     * @param subEnd end of the sub-edge
     * @param subLength length of the sub-edge
     * @param splitCircle circle splitting the edge in several parts
     * @param list list where to put the sub-edge
     * @return end vertex of the edge ({@code subEnd} if the edge was long enough and really
     * added, {@code subStart} if the edge was too small and therefore ignored)
     */
    private Vertex addSubEdge(final Vertex subStart, final Vertex subEnd, final double subLength,
                              final List<Edge> list, final Circle splitCircle) {

        if (subLength <= circle.getTolerance()) {
            // the edge is too short, we ignore it
            return subStart;
        }

        // really add the edge
        subEnd.bindWith(splitCircle);
        final Edge edge = new Edge(subStart, subEnd, subLength, circle);
        list.add(edge);
        return subEnd;

    }

}