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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* 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
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.geometry.spherical.twod;
import java.util.ArrayList;
import java.util.List;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
import org.apache.commons.math3.geometry.partitioning.BSPTree;
import org.apache.commons.math3.geometry.partitioning.BSPTreeVisitor;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;
/** Visitor computing geometrical properties.
* @since 3.3
*/
class PropertiesComputer implements BSPTreeVisitor<Sphere2D> {
/** Tolerance below which points are consider to be identical. */
private final double tolerance;
/** Summed area. */
private double summedArea;
/** Summed barycenter. */
private Vector3D summedBarycenter;
/** List of points strictly inside convex cells. */
private final List<Vector3D> convexCellsInsidePoints;
/** Simple constructor.
* @param tolerance below which points are consider to be identical
*/
PropertiesComputer(final double tolerance) {
this.tolerance = tolerance;
this.summedArea = 0;
this.summedBarycenter = Vector3D.ZERO;
this.convexCellsInsidePoints = new ArrayList<Vector3D>();
}
/** {@inheritDoc} */
public Order visitOrder(final BSPTree<Sphere2D> node) {
return Order.MINUS_SUB_PLUS;
}
/** {@inheritDoc} */
public void visitInternalNode(final BSPTree<Sphere2D> node) {
// nothing to do here
}
/** {@inheritDoc} */
public void visitLeafNode(final BSPTree<Sphere2D> node) {
if ((Boolean) node.getAttribute()) {
// transform this inside leaf cell into a simple convex polygon
final SphericalPolygonsSet convex =
new SphericalPolygonsSet(node.pruneAroundConvexCell(Boolean.TRUE,
Boolean.FALSE,
null),
tolerance);
// extract the start of the single loop boundary of the convex cell
final List<Vertex> boundary = convex.getBoundaryLoops();
if (boundary.size() != 1) {
// this should never happen
throw new MathInternalError();
}
// compute the geometrical properties of the convex cell
final double area = convexCellArea(boundary.get(0));
final Vector3D barycenter = convexCellBarycenter(boundary.get(0));
convexCellsInsidePoints.add(barycenter);
// add the cell contribution to the global properties
summedArea += area;
summedBarycenter = new Vector3D(1, summedBarycenter, area, barycenter);
}
}
/** Compute convex cell area.
* @param start start vertex of the convex cell boundary
* @return area
*/
private double convexCellArea(final Vertex start) {
int n = 0;
double sum = 0;
// loop around the cell
for (Edge e = start.getOutgoing(); n == 0 || e.getStart() != start; e = e.getEnd().getOutgoing()) {
// find path interior angle at vertex
final Vector3D previousPole = e.getCircle().getPole();
final Vector3D nextPole = e.getEnd().getOutgoing().getCircle().getPole();
final Vector3D point = e.getEnd().getLocation().getVector();
double alpha = FastMath.atan2(Vector3D.dotProduct(nextPole, Vector3D.crossProduct(point, previousPole)),
-Vector3D.dotProduct(nextPole, previousPole));
if (alpha < 0) {
alpha += MathUtils.TWO_PI;
}
sum += alpha;
n++;
}
// compute area using extended Girard theorem
// see Spherical Trigonometry: For the Use of Colleges and Schools by I. Todhunter
// article 99 in chapter VIII Area Of a Spherical Triangle. Spherical Excess.
// book available from project Gutenberg at http://www.gutenberg.org/ebooks/19770
return sum - (n - 2) * FastMath.PI;
}
/** Compute convex cell barycenter.
* @param start start vertex of the convex cell boundary
* @return barycenter
*/
private Vector3D convexCellBarycenter(final Vertex start) {
int n = 0;
Vector3D sumB = Vector3D.ZERO;
// loop around the cell
for (Edge e = start.getOutgoing(); n == 0 || e.getStart() != start; e = e.getEnd().getOutgoing()) {
sumB = new Vector3D(1, sumB, e.getLength(), e.getCircle().getPole());
n++;
}
return sumB.normalize();
}
/** Get the area.
* @return area
*/
public double getArea() {
return summedArea;
}
/** Get the barycenter.
* @return barycenter
*/
public S2Point getBarycenter() {
if (summedBarycenter.getNormSq() == 0) {
return S2Point.NaN;
} else {
return new S2Point(summedBarycenter);
}
}
/** Get the points strictly inside convex cells.
* @return points strictly inside convex cells
*/
public List<Vector3D> getConvexCellsInsidePoints() {
return convexCellsInsidePoints;
}
}
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