EllipsoidTessellator.java
/* Copyright 2002-2024 CS GROUP
* Licensed to CS GROUP (CS) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* CS 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,
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package org.orekit.models.earth.tessellation;
import java.util.ArrayList;
import java.util.Collection;
import java.util.IdentityHashMap;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Queue;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.geometry.partitioning.BSPTree;
import org.hipparchus.geometry.partitioning.Hyperplane;
import org.hipparchus.geometry.partitioning.RegionFactory;
import org.hipparchus.geometry.partitioning.SubHyperplane;
import org.hipparchus.geometry.spherical.oned.ArcsSet;
import org.hipparchus.geometry.spherical.twod.Circle;
import org.hipparchus.geometry.spherical.twod.S2Point;
import org.hipparchus.geometry.spherical.twod.Sphere2D;
import org.hipparchus.geometry.spherical.twod.SphericalPolygonsSet;
import org.hipparchus.geometry.spherical.twod.SubCircle;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathUtils;
import org.orekit.bodies.GeodeticPoint;
import org.orekit.bodies.OneAxisEllipsoid;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitInternalError;
/** Class used to tessellate an interest zone on an ellipsoid in either
* {@link Tile tiles} or grids of {@link GeodeticPoint geodetic points}.
* <p>
* This class is typically used for Earth Observation missions, in order to
* create tiles or grids that may be used as the basis of visibility event
* detectors. Tiles are used when surface-related elements are needed, the
* tiles created completely cover the zone of interest. Grids are used when
* point-related elements are needed, the points created lie entirely within
* the zone of interest.
* </p>
* <p>
* One should note that as tessellation essentially creates a 2 dimensional
* almost Cartesian map, it can never perfectly fulfill geometrical dimensions
* because neither sphere nor ellipsoid are developable surfaces. This implies
* that the tesselation will always be distorted, and distortion increases as
* the size of the zone to be tessellated increases.
* </p>
* @author Luc Maisonobe
* @since 7.1
*/
public class EllipsoidTessellator {
/** Safety limit to avoid infinite loops during tesselation due to numerical noise.
* @since 10.3.1
*/
private static final int MAX_ITER = 1000;
/** Number of segments tiles sides are split into for tiles fine positioning. */
private final int quantization;
/** Aiming used for orienting tiles. */
private final TileAiming aiming;
/** Underlying ellipsoid. */
private final OneAxisEllipsoid ellipsoid;
/** Simple constructor.
* <p>
* The {@code quantization} parameter is used internally to adjust points positioning.
* For example when quantization is set to 4, a complete tile that has 4 corner points
* separated by the tile lengths will really be computed on a grid containing 25 points
* (5 rows of 5 points, as each side will be split in 4 segments, hence will have 5
* points). This quantization allows rough adjustment to balance margins around the
* zone of interest and improves geometric accuracy as the along and across directions
* are readjusted at each points.
* </p>
* <p>
* It is recommended to use at least 2 as the quantization parameter for tiling. The
* rationale is that using only 1 for quantization would imply all points used are tiles
* vertices, and hence would lead small zones to generate 4 tiles with a shared vertex
* inside the zone and the 4 tiles covering the four quadrants at North-West, North-East,
* South-East and South-West. A quantization value of at least 2 allows to shift the
* tiles so the center point is an inside point rather than a tile vertex, hence allowing
* a single tile to cover the small zone. A value even greater like 4 or 8 would allow even
* finer positioning to balance the tiles margins around the zone.
* </p>
* @param ellipsoid underlying ellipsoid
* @param aiming aiming used for orienting tiles
* @param quantization number of segments tiles sides are split into for tiles fine positioning
*/
public EllipsoidTessellator(final OneAxisEllipsoid ellipsoid, final TileAiming aiming,
final int quantization) {
this.ellipsoid = ellipsoid;
this.aiming = aiming;
this.quantization = quantization;
}
/** Tessellate a zone of interest into tiles.
* <p>
* The created tiles will completely cover the zone of interest.
* </p>
* <p>
* The distance between a vertex at a tile corner and the vertex at the same corner
* in the next vertex are computed by subtracting the overlap width (resp. overlap length)
* from the full width (resp. full length). If for example the full width is specified to
* be 55 km and the overlap in width is specified to be +5 km, successive tiles would span
* as follows:
* </p>
* <ul>
* <li>tile 1 covering from 0 km to 55 km</li>
* <li>tile 2 covering from 50 km to 105 km</li>
* <li>tile 3 covering from 100 km to 155 km</li>
* <li>...</li>
* </ul>
* <p>
* In order to achieve the same 50 km step but using a 5 km gap instead of an overlap, one would
* need to specify the full width to be 45 km and the overlap to be -5 km. With these settings,
* successive tiles would span as follows:
* </p>
* <ul>
* <li>tile 1 covering from 0 km to 45 km</li>
* <li>tile 2 covering from 50 km to 95 km</li>
* <li>tile 3 covering from 100 km to 155 km</li>
* <li>...</li>
* </ul>
* @param zone zone of interest to tessellate
* @param fullWidth full tiles width as a distance on surface, including overlap (in meters)
* @param fullLength full tiles length as a distance on surface, including overlap (in meters)
* @param widthOverlap overlap between adjacent tiles (in meters), if negative the tiles
* will have a gap between each other instead of an overlap
* @param lengthOverlap overlap between adjacent tiles (in meters), if negative the tiles
* will have a gap between each other instead of an overlap
* @param truncateLastWidth if true, the first tiles strip will be started as close as
* possible to the zone of interest, and the last tiles strip will have its width reduced
* to also remain close to the zone of interest; if false all tiles strip will have the
* same {@code fullWidth} and they will be balanced around zone of interest
* @param truncateLastLength if true, the first tile in each strip will be started as close as
* possible to the zone of interest, and the last tile in each strip will have its length reduced
* to also remain close to the zone of interest; if false all tiles in each strip will have the
* same {@code fullLength} and they will be balanced around zone of interest
* @return a list of lists of tiles covering the zone of interest,
* each sub-list corresponding to a part not connected to the other
* parts (for example for islands)
*/
public List<List<Tile>> tessellate(final SphericalPolygonsSet zone,
final double fullWidth, final double fullLength,
final double widthOverlap, final double lengthOverlap,
final boolean truncateLastWidth, final boolean truncateLastLength) {
final double splitWidth = (fullWidth - widthOverlap) / quantization;
final double splitLength = (fullLength - lengthOverlap) / quantization;
final Map<Mesh, List<Tile>> map = new IdentityHashMap<Mesh, List<Tile>>();
final RegionFactory<Sphere2D> factory = new RegionFactory<Sphere2D>();
SphericalPolygonsSet remaining = (SphericalPolygonsSet) zone.copySelf();
S2Point inside = getInsidePoint(remaining);
int count = 0;
while (inside != null) {
if (++count > MAX_ITER) {
throw new OrekitException(LocalizedCoreFormats.MAX_COUNT_EXCEEDED, MAX_ITER);
}
// find a mesh covering at least one connected part of the zone
final List<Mesh.Node> mergingSeeds = new ArrayList<Mesh.Node>();
Mesh mesh = new Mesh(ellipsoid, zone, aiming, splitLength, splitWidth, inside);
mergingSeeds.add(mesh.getNode(0, 0));
List<Tile> tiles = null;
while (!mergingSeeds.isEmpty()) {
// expand the mesh around the seed
neighborExpandMesh(mesh, mergingSeeds, zone);
// extract the tiles from the mesh
// this further expands the mesh so tiles dimensions are multiples of quantization,
// hence it must be performed here before checking meshes independence
tiles = extractTiles(mesh, zone, lengthOverlap, widthOverlap, truncateLastWidth, truncateLastLength);
// check the mesh is independent from existing meshes
mergingSeeds.clear();
for (final Map.Entry<Mesh, List<Tile>> entry : map.entrySet()) {
if (!factory.intersection(mesh.getCoverage(), entry.getKey().getCoverage()).isEmpty()) {
// the meshes are not independent, they intersect each other!
// merge the two meshes together
mesh = mergeMeshes(mesh, entry.getKey(), mergingSeeds);
map.remove(entry.getKey());
break;
}
}
}
// remove the part of the zone covered by the mesh
remaining = (SphericalPolygonsSet) factory.difference(remaining, mesh.getCoverage());
inside = getInsidePoint(remaining);
map.put(mesh, tiles);
}
// concatenate the lists from the independent meshes
final List<List<Tile>> tilesLists = new ArrayList<List<Tile>>(map.size());
for (final Map.Entry<Mesh, List<Tile>> entry : map.entrySet()) {
tilesLists.add(entry.getValue());
}
return tilesLists;
}
/** Sample a zone of interest into a grid sample of {@link GeodeticPoint geodetic points}.
* <p>
* The created points will be entirely within the zone of interest.
* </p>
* @param zone zone of interest to sample
* @param width grid sample cells width as a distance on surface (in meters)
* @param length grid sample cells length as a distance on surface (in meters)
* @return a list of lists of points sampling the zone of interest,
* each sub-list corresponding to a part not connected to the other
* parts (for example for islands)
*/
public List<List<GeodeticPoint>> sample(final SphericalPolygonsSet zone,
final double width, final double length) {
final double splitWidth = width / quantization;
final double splitLength = length / quantization;
final Map<Mesh, List<GeodeticPoint>> map = new IdentityHashMap<Mesh, List<GeodeticPoint>>();
final RegionFactory<Sphere2D> factory = new RegionFactory<Sphere2D>();
SphericalPolygonsSet remaining = (SphericalPolygonsSet) zone.copySelf();
S2Point inside = getInsidePoint(remaining);
int count = 0;
while (inside != null) {
if (++count > MAX_ITER) {
throw new OrekitException(LocalizedCoreFormats.MAX_COUNT_EXCEEDED, MAX_ITER);
}
// find a mesh covering at least one connected part of the zone
final List<Mesh.Node> mergingSeeds = new ArrayList<Mesh.Node>();
Mesh mesh = new Mesh(ellipsoid, zone, aiming, splitLength, splitWidth, inside);
mergingSeeds.add(mesh.getNode(0, 0));
List<GeodeticPoint> sample = null;
while (!mergingSeeds.isEmpty()) {
// expand the mesh around the seed
neighborExpandMesh(mesh, mergingSeeds, zone);
// extract the sample from the mesh
// this further expands the mesh so sample cells dimensions are multiples of quantization,
// hence it must be performed here before checking meshes independence
sample = extractSample(mesh, zone);
// check the mesh is independent from existing meshes
mergingSeeds.clear();
for (final Map.Entry<Mesh, List<GeodeticPoint>> entry : map.entrySet()) {
if (!factory.intersection(mesh.getCoverage(), entry.getKey().getCoverage()).isEmpty()) {
// the meshes are not independent, they intersect each other!
// merge the two meshes together
mesh = mergeMeshes(mesh, entry.getKey(), mergingSeeds);
map.remove(entry.getKey());
break;
}
}
}
// remove the part of the zone covered by the mesh
remaining = (SphericalPolygonsSet) factory.difference(remaining, mesh.getCoverage());
inside = getInsidePoint(remaining);
map.put(mesh, sample);
}
// concatenate the lists from the independent meshes
final List<List<GeodeticPoint>> sampleLists = new ArrayList<List<GeodeticPoint>>(map.size());
for (final Map.Entry<Mesh, List<GeodeticPoint>> entry : map.entrySet()) {
sampleLists.add(entry.getValue());
}
return sampleLists;
}
/** Get an inside point from a zone of interest.
* @param zone zone to mesh
* @return a point inside the zone or null if zone is empty or too thin
*/
private S2Point getInsidePoint(final SphericalPolygonsSet zone) {
final InsideFinder finder = new InsideFinder(zone);
zone.getTree(false).visit(finder);
return finder.getInsidePoint();
}
/** Expand a mesh so it surrounds at least one connected part of a zone.
* <p>
* This part of mesh expansion is neighbors based. It includes the seed
* node neighbors, and their neighbors, and the neighbors of their
* neighbors until the path-connected sub-parts of the zone these nodes
* belong to are completely surrounded by the mesh taxicab boundary.
* </p>
* @param mesh mesh to expand
* @param seeds seed nodes (already in the mesh) from which to start expansion
* @param zone zone to mesh
*/
private void neighborExpandMesh(final Mesh mesh, final Collection<Mesh.Node> seeds,
final SphericalPolygonsSet zone) {
// mesh expansion loop
boolean expanding = true;
final Queue<Mesh.Node> newNodes = new LinkedList<Mesh.Node>();
newNodes.addAll(seeds);
int count = 0;
while (expanding) {
if (++count > MAX_ITER) {
throw new OrekitException(LocalizedCoreFormats.MAX_COUNT_EXCEEDED, MAX_ITER);
}
// first expansion step: set up the mesh so that all its
// inside nodes are completely surrounded by at least
// one layer of outside nodes
while (!newNodes.isEmpty()) {
// retrieve an active node
final Mesh.Node node = newNodes.remove();
if (node.isInside()) {
// the node is inside the zone, the mesh must contain its 8 neighbors
addAllNeighborsIfNeeded(node, mesh, newNodes);
}
}
// second expansion step: check if the loop of outside nodes
// completely surrounds the zone, i.e. there are no peaks
// pointing out of the loop between two nodes
expanding = false;
final List<Mesh.Node> boundary = mesh.getTaxicabBoundary(false);
if (boundary.size() > 1) {
Mesh.Node previous = boundary.get(boundary.size() - 1);
for (final Mesh.Node node : boundary) {
if (meetInside(previous.getS2P(), node.getS2P(), zone)) {
// part of the mesh boundary is still inside the zone!
// the mesh must be expanded again
addAllNeighborsIfNeeded(previous, mesh, newNodes);
addAllNeighborsIfNeeded(node, mesh, newNodes);
expanding = true;
}
previous = node;
}
}
}
}
/** Extract tiles from a mesh.
* @param mesh mesh from which tiles should be extracted
* @param zone zone covered by the mesh
* @param lengthOverlap overlap between adjacent tiles
* @param widthOverlap overlap between adjacent tiles
* @param truncateLastWidth true if we can reduce last tile width
* @param truncateLastLength true if we can reduce last tile length
* @return extracted tiles
*/
private List<Tile> extractTiles(final Mesh mesh, final SphericalPolygonsSet zone,
final double lengthOverlap, final double widthOverlap,
final boolean truncateLastWidth, final boolean truncateLastLength) {
final List<Tile> tiles = new ArrayList<Tile>();
final List<RangePair> rangePairs = new ArrayList<RangePair>();
final int minAcross = mesh.getMinAcrossIndex();
final int maxAcross = mesh.getMaxAcrossIndex();
for (Range acrossPair : nodesIndices(minAcross, maxAcross, truncateLastWidth)) {
int minAlong = mesh.getMaxAlongIndex() + 1;
int maxAlong = mesh.getMinAlongIndex() - 1;
for (int c = acrossPair.lower; c <= acrossPair.upper; ++c) {
minAlong = FastMath.min(minAlong, mesh.getMinAlongIndex(c));
maxAlong = FastMath.max(maxAlong, mesh.getMaxAlongIndex(c));
}
for (Range alongPair : nodesIndices(minAlong, maxAlong, truncateLastLength)) {
// get the base vertex nodes
final Mesh.Node node0 = mesh.addNode(alongPair.lower, acrossPair.lower);
final Mesh.Node node1 = mesh.addNode(alongPair.upper, acrossPair.lower);
final Mesh.Node node2 = mesh.addNode(alongPair.upper, acrossPair.upper);
final Mesh.Node node3 = mesh.addNode(alongPair.lower, acrossPair.upper);
// apply tile overlap
final S2Point s2p0 = node0.move(new Vector3D(-0.5 * lengthOverlap, node0.getAlong(),
-0.5 * widthOverlap, node0.getAcross()));
final S2Point s2p1 = node1.move(new Vector3D(+0.5 * lengthOverlap, node1.getAlong(),
-0.5 * widthOverlap, node1.getAcross()));
final S2Point s2p2 = node2.move(new Vector3D(+0.5 * lengthOverlap, node2.getAlong(),
+0.5 * widthOverlap, node2.getAcross()));
final S2Point s2p3 = node3.move(new Vector3D(-0.5 * lengthOverlap, node2.getAlong(),
+0.5 * widthOverlap, node2.getAcross()));
// create a quadrilateral region corresponding to the candidate tile
final SphericalPolygonsSet quadrilateral =
new SphericalPolygonsSet(zone.getTolerance(), s2p0, s2p1, s2p2, s2p3);
if (!new RegionFactory<Sphere2D>().intersection(zone.copySelf(), quadrilateral).isEmpty()) {
// the tile does cover part of the zone, it contributes to the tessellation
tiles.add(new Tile(toGeodetic(s2p0), toGeodetic(s2p1), toGeodetic(s2p2), toGeodetic(s2p3)));
rangePairs.add(new RangePair(acrossPair, alongPair));
}
}
}
// ensure the taxicab boundary follows the built tile sides
// this is done outside of the previous loop in order
// to avoid one tile changing the min/max indices of the
// neighboring tile as they share some nodes that will be enabled here
for (final RangePair rangePair : rangePairs) {
for (int c = rangePair.across.lower; c < rangePair.across.upper; ++c) {
mesh.addNode(rangePair.along.lower, c + 1).setEnabled();
mesh.addNode(rangePair.along.upper, c).setEnabled();
}
for (int l = rangePair.along.lower; l < rangePair.along.upper; ++l) {
mesh.addNode(l, rangePair.across.lower).setEnabled();
mesh.addNode(l + 1, rangePair.across.upper).setEnabled();
}
}
return tiles;
}
/** Extract a sample of points from a mesh.
* @param mesh mesh from which grid should be extracted
* @param zone zone covered by the mesh
* @return extracted grid
*/
private List<GeodeticPoint> extractSample(final Mesh mesh, final SphericalPolygonsSet zone) {
// find how to select sample points taking quantization into account
// to have the largest possible number of points while still
// being inside the zone of interest
int selectedAcrossModulus = -1;
int selectedAlongModulus = -1;
int selectedCount = -1;
for (int acrossModulus = 0; acrossModulus < quantization; ++acrossModulus) {
for (int alongModulus = 0; alongModulus < quantization; ++alongModulus) {
// count how many points would be selected for the current modulus
int count = 0;
for (int across = mesh.getMinAcrossIndex() + acrossModulus;
across <= mesh.getMaxAcrossIndex();
across += quantization) {
for (int along = mesh.getMinAlongIndex() + alongModulus;
along <= mesh.getMaxAlongIndex();
along += quantization) {
final Mesh.Node node = mesh.getNode(along, across);
if (node != null && node.isInside()) {
++count;
}
}
}
if (count > selectedCount) {
// current modulus are better than the selected ones
selectedAcrossModulus = acrossModulus;
selectedAlongModulus = alongModulus;
selectedCount = count;
}
}
}
// extract the sample points
final List<GeodeticPoint> sample = new ArrayList<GeodeticPoint>(selectedCount);
for (int across = mesh.getMinAcrossIndex() + selectedAcrossModulus;
across <= mesh.getMaxAcrossIndex();
across += quantization) {
for (int along = mesh.getMinAlongIndex() + selectedAlongModulus;
along <= mesh.getMaxAlongIndex();
along += quantization) {
final Mesh.Node node = mesh.getNode(along, across);
if (node != null && node.isInside()) {
sample.add(toGeodetic(node.getS2P()));
}
}
}
return sample;
}
/** Merge two meshes together.
* @param mesh1 first mesh
* @param mesh2 second mesh
* @param mergingSeeds collection where to put the nodes created during the merge
* @return merged mesh (really one of the instances)
*/
private Mesh mergeMeshes(final Mesh mesh1, final Mesh mesh2,
final Collection<Mesh.Node> mergingSeeds) {
// select the way merge will be performed
final Mesh larger;
final Mesh smaller;
if (mesh1.getNumberOfNodes() >= mesh2.getNumberOfNodes()) {
// the larger new mesh should absorb the smaller existing mesh
larger = mesh1;
smaller = mesh2;
} else {
// the larger existing mesh should absorb the smaller new mesh
larger = mesh2;
smaller = mesh1;
}
// prepare seed nodes for next iteration
for (final Mesh.Node insideNode : smaller.getInsideNodes()) {
// beware we cannot reuse the node itself as the two meshes are not aligned!
// we have to create new nodes around the previous location
Mesh.Node node = larger.getClosestExistingNode(insideNode.getV());
while (estimateAlongMotion(node, insideNode.getV()) > +mesh1.getAlongGap()) {
// the node is before desired index in the along direction
// we need to create intermediates nodes up to the desired index
node = larger.addNode(node.getAlongIndex() + 1, node.getAcrossIndex());
}
while (estimateAlongMotion(node, insideNode.getV()) < -mesh1.getAlongGap()) {
// the node is after desired index in the along direction
// we need to create intermediates nodes up to the desired index
node = larger.addNode(node.getAlongIndex() - 1, node.getAcrossIndex());
}
while (estimateAcrossMotion(node, insideNode.getV()) > +mesh1.getAcrossGap()) {
// the node is before desired index in the across direction
// we need to create intermediates nodes up to the desired index
node = larger.addNode(node.getAlongIndex(), node.getAcrossIndex() + 1);
}
while (estimateAcrossMotion(node, insideNode.getV()) < -mesh1.getAcrossGap()) {
// the node is after desired index in the across direction
// we need to create intermediates nodes up to the desired index
node = larger.addNode(node.getAlongIndex(), node.getAcrossIndex() - 1);
}
// now we are close to the inside node,
// make sure the four surrounding nodes are available
final int otherAlong = (estimateAlongMotion(node, insideNode.getV()) < 0.0) ?
node.getAlongIndex() - 1 : node.getAlongIndex() + 1;
final int otherAcross = (estimateAcrossMotion(node, insideNode.getV()) < 0.0) ?
node.getAcrossIndex() - 1 : node.getAcrossIndex() + 1;
addNode(node.getAlongIndex(), node.getAcrossIndex(), larger, mergingSeeds);
addNode(node.getAlongIndex(), otherAcross, larger, mergingSeeds);
addNode(otherAlong, node.getAcrossIndex(), larger, mergingSeeds);
addNode(otherAlong, otherAcross, larger, mergingSeeds);
}
return larger;
}
/** Ensure all 8 neighbors of a node are in the mesh.
* @param base base node
* @param mesh complete mesh containing nodes
* @param newNodes queue where new node must be put
*/
private void addAllNeighborsIfNeeded(final Mesh.Node base, final Mesh mesh,
final Collection<Mesh.Node> newNodes) {
addNode(base.getAlongIndex() - 1, base.getAcrossIndex() - 1, mesh, newNodes);
addNode(base.getAlongIndex() - 1, base.getAcrossIndex(), mesh, newNodes);
addNode(base.getAlongIndex() - 1, base.getAcrossIndex() + 1, mesh, newNodes);
addNode(base.getAlongIndex(), base.getAcrossIndex() - 1, mesh, newNodes);
addNode(base.getAlongIndex(), base.getAcrossIndex() + 1, mesh, newNodes);
addNode(base.getAlongIndex() + 1, base.getAcrossIndex() - 1, mesh, newNodes);
addNode(base.getAlongIndex() + 1, base.getAcrossIndex(), mesh, newNodes);
addNode(base.getAlongIndex() + 1, base.getAcrossIndex() + 1, mesh, newNodes);
}
/** Add a node to a mesh if not already present.
* @param alongIndex index in the along direction
* @param acrossIndex index in the across direction
* @param mesh complete mesh containing nodes
* @param newNodes queue where new node must be put
*/
private void addNode(final int alongIndex, final int acrossIndex,
final Mesh mesh, final Collection<Mesh.Node> newNodes) {
final Mesh.Node node = mesh.addNode(alongIndex, acrossIndex);
if (!node.isEnabled()) {
// enable the node
node.setEnabled();
newNodes.add(node);
}
}
/** Convert a point on the unit 2-sphere to geodetic coordinates.
* @param point point on the unit 2-sphere
* @return geodetic point (arbitrarily set at altitude 0)
*/
protected GeodeticPoint toGeodetic(final S2Point point) {
return new GeodeticPoint(0.5 * FastMath.PI - point.getPhi(), point.getTheta(), 0.0);
}
/** Build a simple zone (connected zone without holes).
* <p>
* In order to build more complex zones (not connected or with
* holes), the user should directly call Hipparchus
* {@link SphericalPolygonsSet} constructors and
* {@link RegionFactory region factory} if set operations
* are needed (union, intersection, difference ...).
* </p>
* <p>
* Take care that the vertices boundary points must be given <em>counterclockwise</em>.
* Using the wrong order defines the complementary of the real zone,
* and will often result in tessellation failure as the zone is too
* wide.
* </p>
* @param tolerance angular separation below which points are considered
* equal (typically 1.0e-10)
* @param points vertices of the boundary, in <em>counterclockwise</em>
* order, each point being a two-elements arrays with latitude at index 0
* and longitude at index 1
* @return a zone defined on the unit 2-sphere
*/
public static SphericalPolygonsSet buildSimpleZone(final double tolerance,
final double[]... points) {
final S2Point[] vertices = new S2Point[points.length];
for (int i = 0; i < points.length; ++i) {
vertices[i] = new S2Point(points[i][1], 0.5 * FastMath.PI - points[i][0]);
}
return new SphericalPolygonsSet(tolerance, vertices);
}
/** Build a simple zone (connected zone without holes).
* <p>
* In order to build more complex zones (not connected or with
* holes), the user should directly call Hipparchus
* {@link SphericalPolygonsSet} constructors and
* {@link RegionFactory region factory} if set operations
* are needed (union, intersection, difference ...).
* </p>
* <p>
* Take care that the vertices boundary points must be given <em>counterclockwise</em>.
* Using the wrong order defines the complementary of the real zone,
* and will often result in tessellation failure as the zone is too
* wide.
* </p>
* @param tolerance angular separation below which points are considered
* equal (typically 1.0e-10)
* @param points vertices of the boundary, in <em>counterclockwise</em>
* order
* @return a zone defined on the unit 2-sphere
*/
public static SphericalPolygonsSet buildSimpleZone(final double tolerance,
final GeodeticPoint... points) {
final S2Point[] vertices = new S2Point[points.length];
for (int i = 0; i < points.length; ++i) {
vertices[i] = new S2Point(points[i].getLongitude(),
0.5 * FastMath.PI - points[i].getLatitude());
}
return new SphericalPolygonsSet(tolerance, vertices);
}
/** Estimate an approximate motion in the along direction.
* @param start node at start of motion
* @param end desired point at end of motion
* @return approximate motion in the along direction
*/
private double estimateAlongMotion(final Mesh.Node start, final Vector3D end) {
return Vector3D.dotProduct(start.getAlong(), end.subtract(start.getV()));
}
/** Estimate an approximate motion in the across direction.
* @param start node at start of motion
* @param end desired point at end of motion
* @return approximate motion in the across direction
*/
private double estimateAcrossMotion(final Mesh.Node start, final Vector3D end) {
return Vector3D.dotProduct(start.getAcross(), end.subtract(start.getV()));
}
/** Check if an arc meets the inside of a zone.
* @param s1 first point
* @param s2 second point
* @param zone zone to check arc against
* @return true if the arc meets the inside of the zone
*/
private boolean meetInside(final S2Point s1, final S2Point s2,
final SphericalPolygonsSet zone) {
final Circle circle = new Circle(s1, s2, zone.getTolerance());
final double alpha1 = circle.toSubSpace(s1).getAlpha();
final double alpha2 = MathUtils.normalizeAngle(circle.toSubSpace(s2).getAlpha(),
alpha1 + FastMath.PI);
final SubCircle sub = new SubCircle(circle,
new ArcsSet(alpha1, alpha2, zone.getTolerance()));
return recurseMeetInside(zone.getTree(false), sub);
}
/** Check if an arc meets the inside of a zone.
* <p>
* This method is heavily based on the Characterization class from
* Hipparchus library, also distributed under the terms
* of the Apache Software License V2.
* </p>
* @param node spherical zone node
* @param sub arc to characterize
* @return true if the arc meets the inside of the zone
*/
private boolean recurseMeetInside(final BSPTree<Sphere2D> node, final SubHyperplane<Sphere2D> sub) {
if (node.getCut() == null) {
// we have reached a leaf node
if (sub.isEmpty()) {
return false;
} else {
return (Boolean) node.getAttribute();
}
} else {
final Hyperplane<Sphere2D> hyperplane = node.getCut().getHyperplane();
final SubHyperplane.SplitSubHyperplane<Sphere2D> split = sub.split(hyperplane);
switch (split.getSide()) {
case PLUS:
return recurseMeetInside(node.getPlus(), sub);
case MINUS:
return recurseMeetInside(node.getMinus(), sub);
case BOTH:
if (recurseMeetInside(node.getPlus(), split.getPlus())) {
return true;
} else {
return recurseMeetInside(node.getMinus(), split.getMinus());
}
default:
// this should not happen
throw new OrekitInternalError(null);
}
}
}
/** Get an iterator over mesh nodes indices.
* @param minIndex minimum node index
* @param maxIndex maximum node index
* @param truncateLast true if we can reduce last tile
* @return iterator over mesh nodes indices
*/
private Iterable<Range> nodesIndices(final int minIndex, final int maxIndex, final boolean truncateLast) {
final int first;
if (truncateLast) {
// truncate last tile rather than balance tiles around the zone of interest
first = minIndex;
} else {
// balance tiles around the zone of interest rather than truncate last tile
// number of tiles needed to cover the full indices range
final int range = maxIndex - minIndex;
final int nbTiles = (range + quantization - 1) / quantization;
// extra nodes that must be added to complete the tiles
final int extraNodes = nbTiles * quantization - range;
// balance the extra nodes before min index and after maxIndex
final int extraBefore = (extraNodes + 1) / 2;
first = minIndex - extraBefore;
}
return new Iterable<Range>() {
/** {@inheritDoc} */
@Override
public Iterator<Range> iterator() {
return new Iterator<Range>() {
private int nextLower = first;
/** {@inheritDoc} */
@Override
public boolean hasNext() {
return nextLower < maxIndex;
}
/** {@inheritDoc} */
@Override
public Range next() {
if (nextLower >= maxIndex) {
throw new NoSuchElementException();
}
final int lower = nextLower;
nextLower += quantization;
if (truncateLast && nextLower > maxIndex && lower < maxIndex) {
// truncate last tile
nextLower = maxIndex;
}
return new Range(lower, nextLower);
}
/** {@inheritDoc} */
@Override
public void remove() {
throw new UnsupportedOperationException();
}
};
}
};
}
/** Local class for a range of indices to be used for building a tile. */
private static class Range {
/** Lower index. */
private final int lower;
/** Upper index. */
private final int upper;
/** Simple constructor.
* @param lower lower index
* @param upper upper index
*/
Range(final int lower, final int upper) {
this.lower = lower;
this.upper = upper;
}
}
/** Local class for a pair of ranges of indices to be used for building a tile. */
private static class RangePair {
/** Across range. */
private final Range across;
/** Along range. */
private final Range along;
/** Simple constructor.
* @param across across range
* @param along along range
*/
RangePair(final Range across, final Range along) {
this.across = across;
this.along = along;
}
}
}