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Diffstat (limited to 'src/main/java/org/apache/commons/math3/geometry/spherical/oned/ArcsSet.java')
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diff --git a/src/main/java/org/apache/commons/math3/geometry/spherical/oned/ArcsSet.java b/src/main/java/org/apache/commons/math3/geometry/spherical/oned/ArcsSet.java new file mode 100644 index 0000000..0a00aa7 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/geometry/spherical/oned/ArcsSet.java @@ -0,0 +1,955 @@ +/* + * 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.oned; + +import java.util.ArrayList; +import java.util.Collection; +import java.util.Iterator; +import java.util.List; +import java.util.NoSuchElementException; + +import org.apache.commons.math3.exception.MathIllegalArgumentException; +import org.apache.commons.math3.exception.MathInternalError; +import org.apache.commons.math3.exception.NumberIsTooLargeException; +import org.apache.commons.math3.exception.util.LocalizedFormats; +import org.apache.commons.math3.geometry.Point; +import org.apache.commons.math3.geometry.partitioning.AbstractRegion; +import org.apache.commons.math3.geometry.partitioning.BSPTree; +import org.apache.commons.math3.geometry.partitioning.BoundaryProjection; +import org.apache.commons.math3.geometry.partitioning.Side; +import org.apache.commons.math3.geometry.partitioning.SubHyperplane; +import org.apache.commons.math3.util.FastMath; +import org.apache.commons.math3.util.MathUtils; +import org.apache.commons.math3.util.Precision; + +/** This class represents a region of a circle: a set of arcs. + * <p> + * Note that due to the wrapping around \(2 \pi\), barycenter is + * ill-defined here. It was defined only in order to fulfill + * the requirements of the {@link + * org.apache.commons.math3.geometry.partitioning.Region Region} + * interface, but its use is discouraged. + * </p> + * @since 3.3 + */ +public class ArcsSet extends AbstractRegion<Sphere1D, Sphere1D> implements Iterable<double[]> { + + /** Build an arcs set representing the whole circle. + * @param tolerance tolerance below which close sub-arcs are merged together + */ + public ArcsSet(final double tolerance) { + super(tolerance); + } + + /** Build an arcs set corresponding to a single arc. + * <p> + * If either {@code lower} is equals to {@code upper} or + * the interval exceeds \( 2 \pi \), the arc is considered + * to be the full circle and its initial defining boundaries + * will be forgotten. {@code lower} is not allowed to be greater + * than {@code upper} (an exception is thrown in this case). + * </p> + * @param lower lower bound of the arc + * @param upper upper bound of the arc + * @param tolerance tolerance below which close sub-arcs are merged together + * @exception NumberIsTooLargeException if lower is greater than upper + */ + public ArcsSet(final double lower, final double upper, final double tolerance) + throws NumberIsTooLargeException { + super(buildTree(lower, upper, tolerance), tolerance); + } + + /** Build an arcs set from an inside/outside BSP tree. + * <p>The leaf nodes of the BSP tree <em>must</em> have a + * {@code Boolean} attribute representing the inside status of + * the corresponding cell (true for inside cells, false for outside + * cells). In order to avoid building too many small objects, it is + * recommended to use the predefined constants + * {@code Boolean.TRUE} and {@code Boolean.FALSE}</p> + * @param tree inside/outside BSP tree representing the arcs set + * @param tolerance tolerance below which close sub-arcs are merged together + * @exception InconsistentStateAt2PiWrapping if the tree leaf nodes are not + * consistent across the \( 0, 2 \pi \) crossing + */ + public ArcsSet(final BSPTree<Sphere1D> tree, final double tolerance) + throws InconsistentStateAt2PiWrapping { + super(tree, tolerance); + check2PiConsistency(); + } + + /** Build an arcs set from a Boundary REPresentation (B-rep). + * <p>The boundary is provided as a collection of {@link + * SubHyperplane sub-hyperplanes}. Each sub-hyperplane has the + * interior part of the region on its minus side and the exterior on + * its plus side.</p> + * <p>The boundary elements can be in any order, and can form + * several non-connected sets (like for example polygons with holes + * or a set of disjoints polyhedrons considered as a whole). In + * fact, the elements do not even need to be connected together + * (their topological connections are not used here). However, if the + * boundary does not really separate an inside open from an outside + * open (open having here its topological meaning), then subsequent + * calls to the {@link + * org.apache.commons.math3.geometry.partitioning.Region#checkPoint(org.apache.commons.math3.geometry.Point) + * checkPoint} method will not be meaningful anymore.</p> + * <p>If the boundary is empty, the region will represent the whole + * space.</p> + * @param boundary collection of boundary elements + * @param tolerance tolerance below which close sub-arcs are merged together + * @exception InconsistentStateAt2PiWrapping if the tree leaf nodes are not + * consistent across the \( 0, 2 \pi \) crossing + */ + public ArcsSet(final Collection<SubHyperplane<Sphere1D>> boundary, final double tolerance) + throws InconsistentStateAt2PiWrapping { + super(boundary, tolerance); + check2PiConsistency(); + } + + /** Build an inside/outside tree representing a single arc. + * @param lower lower angular bound of the arc + * @param upper upper angular bound of the arc + * @param tolerance tolerance below which close sub-arcs are merged together + * @return the built tree + * @exception NumberIsTooLargeException if lower is greater than upper + */ + private static BSPTree<Sphere1D> buildTree(final double lower, final double upper, + final double tolerance) + throws NumberIsTooLargeException { + + if (Precision.equals(lower, upper, 0) || (upper - lower) >= MathUtils.TWO_PI) { + // the tree must cover the whole circle + return new BSPTree<Sphere1D>(Boolean.TRUE); + } else if (lower > upper) { + throw new NumberIsTooLargeException(LocalizedFormats.ENDPOINTS_NOT_AN_INTERVAL, + lower, upper, true); + } + + // this is a regular arc, covering only part of the circle + final double normalizedLower = MathUtils.normalizeAngle(lower, FastMath.PI); + final double normalizedUpper = normalizedLower + (upper - lower); + final SubHyperplane<Sphere1D> lowerCut = + new LimitAngle(new S1Point(normalizedLower), false, tolerance).wholeHyperplane(); + + if (normalizedUpper <= MathUtils.TWO_PI) { + // simple arc starting after 0 and ending before 2 \pi + final SubHyperplane<Sphere1D> upperCut = + new LimitAngle(new S1Point(normalizedUpper), true, tolerance).wholeHyperplane(); + return new BSPTree<Sphere1D>(lowerCut, + new BSPTree<Sphere1D>(Boolean.FALSE), + new BSPTree<Sphere1D>(upperCut, + new BSPTree<Sphere1D>(Boolean.FALSE), + new BSPTree<Sphere1D>(Boolean.TRUE), + null), + null); + } else { + // arc wrapping around 2 \pi + final SubHyperplane<Sphere1D> upperCut = + new LimitAngle(new S1Point(normalizedUpper - MathUtils.TWO_PI), true, tolerance).wholeHyperplane(); + return new BSPTree<Sphere1D>(lowerCut, + new BSPTree<Sphere1D>(upperCut, + new BSPTree<Sphere1D>(Boolean.FALSE), + new BSPTree<Sphere1D>(Boolean.TRUE), + null), + new BSPTree<Sphere1D>(Boolean.TRUE), + null); + } + + } + + /** Check consistency. + * @exception InconsistentStateAt2PiWrapping if the tree leaf nodes are not + * consistent across the \( 0, 2 \pi \) crossing + */ + private void check2PiConsistency() throws InconsistentStateAt2PiWrapping { + + // start search at the tree root + BSPTree<Sphere1D> root = getTree(false); + if (root.getCut() == null) { + return; + } + + // find the inside/outside state before the smallest internal node + final Boolean stateBefore = (Boolean) getFirstLeaf(root).getAttribute(); + + // find the inside/outside state after the largest internal node + final Boolean stateAfter = (Boolean) getLastLeaf(root).getAttribute(); + + if (stateBefore ^ stateAfter) { + throw new InconsistentStateAt2PiWrapping(); + } + + } + + /** Get the first leaf node of a tree. + * @param root tree root + * @return first leaf node (i.e. node corresponding to the region just after 0.0 radians) + */ + private BSPTree<Sphere1D> getFirstLeaf(final BSPTree<Sphere1D> root) { + + if (root.getCut() == null) { + return root; + } + + // find the smallest internal node + BSPTree<Sphere1D> smallest = null; + for (BSPTree<Sphere1D> n = root; n != null; n = previousInternalNode(n)) { + smallest = n; + } + + return leafBefore(smallest); + + } + + /** Get the last leaf node of a tree. + * @param root tree root + * @return last leaf node (i.e. node corresponding to the region just before \( 2 \pi \) radians) + */ + private BSPTree<Sphere1D> getLastLeaf(final BSPTree<Sphere1D> root) { + + if (root.getCut() == null) { + return root; + } + + // find the largest internal node + BSPTree<Sphere1D> largest = null; + for (BSPTree<Sphere1D> n = root; n != null; n = nextInternalNode(n)) { + largest = n; + } + + return leafAfter(largest); + + } + + /** Get the node corresponding to the first arc start. + * @return smallest internal node (i.e. first after 0.0 radians, in trigonometric direction), + * or null if there are no internal nodes (i.e. the set is either empty or covers the full circle) + */ + private BSPTree<Sphere1D> getFirstArcStart() { + + // start search at the tree root + BSPTree<Sphere1D> node = getTree(false); + if (node.getCut() == null) { + return null; + } + + // walk tree until we find the smallest internal node + node = getFirstLeaf(node).getParent(); + + // walk tree until we find an arc start + while (node != null && !isArcStart(node)) { + node = nextInternalNode(node); + } + + return node; + + } + + /** Check if an internal node corresponds to the start angle of an arc. + * @param node internal node to check + * @return true if the node corresponds to the start angle of an arc + */ + private boolean isArcStart(final BSPTree<Sphere1D> node) { + + if ((Boolean) leafBefore(node).getAttribute()) { + // it has an inside cell before it, it may end an arc but not start it + return false; + } + + if (!(Boolean) leafAfter(node).getAttribute()) { + // it has an outside cell after it, it is a dummy cut away from real arcs + return false; + } + + // the cell has an outside before and an inside after it + // it is the start of an arc + return true; + + } + + /** Check if an internal node corresponds to the end angle of an arc. + * @param node internal node to check + * @return true if the node corresponds to the end angle of an arc + */ + private boolean isArcEnd(final BSPTree<Sphere1D> node) { + + if (!(Boolean) leafBefore(node).getAttribute()) { + // it has an outside cell before it, it may start an arc but not end it + return false; + } + + if ((Boolean) leafAfter(node).getAttribute()) { + // it has an inside cell after it, it is a dummy cut in the middle of an arc + return false; + } + + // the cell has an inside before and an outside after it + // it is the end of an arc + return true; + + } + + /** Get the next internal node. + * @param node current internal node + * @return next internal node in trigonometric order, or null + * if this is the last internal node + */ + private BSPTree<Sphere1D> nextInternalNode(BSPTree<Sphere1D> node) { + + if (childAfter(node).getCut() != null) { + // the next node is in the sub-tree + return leafAfter(node).getParent(); + } + + // there is nothing left deeper in the tree, we backtrack + while (isAfterParent(node)) { + node = node.getParent(); + } + return node.getParent(); + + } + + /** Get the previous internal node. + * @param node current internal node + * @return previous internal node in trigonometric order, or null + * if this is the first internal node + */ + private BSPTree<Sphere1D> previousInternalNode(BSPTree<Sphere1D> node) { + + if (childBefore(node).getCut() != null) { + // the next node is in the sub-tree + return leafBefore(node).getParent(); + } + + // there is nothing left deeper in the tree, we backtrack + while (isBeforeParent(node)) { + node = node.getParent(); + } + return node.getParent(); + + } + + /** Find the leaf node just before an internal node. + * @param node internal node at which the sub-tree starts + * @return leaf node just before the internal node + */ + private BSPTree<Sphere1D> leafBefore(BSPTree<Sphere1D> node) { + + node = childBefore(node); + while (node.getCut() != null) { + node = childAfter(node); + } + + return node; + + } + + /** Find the leaf node just after an internal node. + * @param node internal node at which the sub-tree starts + * @return leaf node just after the internal node + */ + private BSPTree<Sphere1D> leafAfter(BSPTree<Sphere1D> node) { + + node = childAfter(node); + while (node.getCut() != null) { + node = childBefore(node); + } + + return node; + + } + + /** Check if a node is the child before its parent in trigonometric order. + * @param node child node considered + * @return true is the node has a parent end is before it in trigonometric order + */ + private boolean isBeforeParent(final BSPTree<Sphere1D> node) { + final BSPTree<Sphere1D> parent = node.getParent(); + if (parent == null) { + return false; + } else { + return node == childBefore(parent); + } + } + + /** Check if a node is the child after its parent in trigonometric order. + * @param node child node considered + * @return true is the node has a parent end is after it in trigonometric order + */ + private boolean isAfterParent(final BSPTree<Sphere1D> node) { + final BSPTree<Sphere1D> parent = node.getParent(); + if (parent == null) { + return false; + } else { + return node == childAfter(parent); + } + } + + /** Find the child node just before an internal node. + * @param node internal node at which the sub-tree starts + * @return child node just before the internal node + */ + private BSPTree<Sphere1D> childBefore(BSPTree<Sphere1D> node) { + if (isDirect(node)) { + // smaller angles are on minus side, larger angles are on plus side + return node.getMinus(); + } else { + // smaller angles are on plus side, larger angles are on minus side + return node.getPlus(); + } + } + + /** Find the child node just after an internal node. + * @param node internal node at which the sub-tree starts + * @return child node just after the internal node + */ + private BSPTree<Sphere1D> childAfter(BSPTree<Sphere1D> node) { + if (isDirect(node)) { + // smaller angles are on minus side, larger angles are on plus side + return node.getPlus(); + } else { + // smaller angles are on plus side, larger angles are on minus side + return node.getMinus(); + } + } + + /** Check if an internal node has a direct limit angle. + * @param node internal node to check + * @return true if the limit angle is direct + */ + private boolean isDirect(final BSPTree<Sphere1D> node) { + return ((LimitAngle) node.getCut().getHyperplane()).isDirect(); + } + + /** Get the limit angle of an internal node. + * @param node internal node to check + * @return limit angle + */ + private double getAngle(final BSPTree<Sphere1D> node) { + return ((LimitAngle) node.getCut().getHyperplane()).getLocation().getAlpha(); + } + + /** {@inheritDoc} */ + @Override + public ArcsSet buildNew(final BSPTree<Sphere1D> tree) { + return new ArcsSet(tree, getTolerance()); + } + + /** {@inheritDoc} */ + @Override + protected void computeGeometricalProperties() { + if (getTree(false).getCut() == null) { + setBarycenter(S1Point.NaN); + setSize(((Boolean) getTree(false).getAttribute()) ? MathUtils.TWO_PI : 0); + } else { + double size = 0.0; + double sum = 0.0; + for (final double[] a : this) { + final double length = a[1] - a[0]; + size += length; + sum += length * (a[0] + a[1]); + } + setSize(size); + if (Precision.equals(size, MathUtils.TWO_PI, 0)) { + setBarycenter(S1Point.NaN); + } else if (size >= Precision.SAFE_MIN) { + setBarycenter(new S1Point(sum / (2 * size))); + } else { + final LimitAngle limit = (LimitAngle) getTree(false).getCut().getHyperplane(); + setBarycenter(limit.getLocation()); + } + } + } + + /** {@inheritDoc} + * @since 3.3 + */ + @Override + public BoundaryProjection<Sphere1D> projectToBoundary(final Point<Sphere1D> point) { + + // get position of test point + final double alpha = ((S1Point) point).getAlpha(); + + boolean wrapFirst = false; + double first = Double.NaN; + double previous = Double.NaN; + for (final double[] a : this) { + + if (Double.isNaN(first)) { + // remember the first angle in case we need it later + first = a[0]; + } + + if (!wrapFirst) { + if (alpha < a[0]) { + // the test point lies between the previous and the current arcs + // offset will be positive + if (Double.isNaN(previous)) { + // we need to wrap around the circle + wrapFirst = true; + } else { + final double previousOffset = alpha - previous; + final double currentOffset = a[0] - alpha; + if (previousOffset < currentOffset) { + return new BoundaryProjection<Sphere1D>(point, new S1Point(previous), previousOffset); + } else { + return new BoundaryProjection<Sphere1D>(point, new S1Point(a[0]), currentOffset); + } + } + } else if (alpha <= a[1]) { + // the test point lies within the current arc + // offset will be negative + final double offset0 = a[0] - alpha; + final double offset1 = alpha - a[1]; + if (offset0 < offset1) { + return new BoundaryProjection<Sphere1D>(point, new S1Point(a[1]), offset1); + } else { + return new BoundaryProjection<Sphere1D>(point, new S1Point(a[0]), offset0); + } + } + } + previous = a[1]; + } + + if (Double.isNaN(previous)) { + + // there are no points at all in the arcs set + return new BoundaryProjection<Sphere1D>(point, null, MathUtils.TWO_PI); + + } else { + + // the test point if before first arc and after last arc, + // somewhere around the 0/2 \pi crossing + if (wrapFirst) { + // the test point is between 0 and first + final double previousOffset = alpha - (previous - MathUtils.TWO_PI); + final double currentOffset = first - alpha; + if (previousOffset < currentOffset) { + return new BoundaryProjection<Sphere1D>(point, new S1Point(previous), previousOffset); + } else { + return new BoundaryProjection<Sphere1D>(point, new S1Point(first), currentOffset); + } + } else { + // the test point is between last and 2\pi + final double previousOffset = alpha - previous; + final double currentOffset = first + MathUtils.TWO_PI - alpha; + if (previousOffset < currentOffset) { + return new BoundaryProjection<Sphere1D>(point, new S1Point(previous), previousOffset); + } else { + return new BoundaryProjection<Sphere1D>(point, new S1Point(first), currentOffset); + } + } + + } + + } + + /** Build an ordered list of arcs representing the instance. + * <p>This method builds this arcs set as an ordered list of + * {@link Arc Arc} elements. An empty tree will build an empty list + * while a tree representing the whole circle will build a one + * element list with bounds set to \( 0 and 2 \pi \).</p> + * @return a new ordered list containing {@link Arc Arc} elements + */ + public List<Arc> asList() { + final List<Arc> list = new ArrayList<Arc>(); + for (final double[] a : this) { + list.add(new Arc(a[0], a[1], getTolerance())); + } + return list; + } + + /** {@inheritDoc} + * <p> + * The iterator returns the limit angles pairs of sub-arcs in trigonometric order. + * </p> + * <p> + * The iterator does <em>not</em> support the optional {@code remove} operation. + * </p> + */ + public Iterator<double[]> iterator() { + return new SubArcsIterator(); + } + + /** Local iterator for sub-arcs. */ + private class SubArcsIterator implements Iterator<double[]> { + + /** Start of the first arc. */ + private final BSPTree<Sphere1D> firstStart; + + /** Current node. */ + private BSPTree<Sphere1D> current; + + /** Sub-arc no yet returned. */ + private double[] pending; + + /** Simple constructor. + */ + SubArcsIterator() { + + firstStart = getFirstArcStart(); + current = firstStart; + + if (firstStart == null) { + // all the leaf tree nodes share the same inside/outside status + if ((Boolean) getFirstLeaf(getTree(false)).getAttribute()) { + // it is an inside node, it represents the full circle + pending = new double[] { + 0, MathUtils.TWO_PI + }; + } else { + pending = null; + } + } else { + selectPending(); + } + } + + /** Walk the tree to select the pending sub-arc. + */ + private void selectPending() { + + // look for the start of the arc + BSPTree<Sphere1D> start = current; + while (start != null && !isArcStart(start)) { + start = nextInternalNode(start); + } + + if (start == null) { + // we have exhausted the iterator + current = null; + pending = null; + return; + } + + // look for the end of the arc + BSPTree<Sphere1D> end = start; + while (end != null && !isArcEnd(end)) { + end = nextInternalNode(end); + } + + if (end != null) { + + // we have identified the arc + pending = new double[] { + getAngle(start), getAngle(end) + }; + + // prepare search for next arc + current = end; + + } else { + + // the final arc wraps around 2\pi, its end is before the first start + end = firstStart; + while (end != null && !isArcEnd(end)) { + end = previousInternalNode(end); + } + if (end == null) { + // this should never happen + throw new MathInternalError(); + } + + // we have identified the last arc + pending = new double[] { + getAngle(start), getAngle(end) + MathUtils.TWO_PI + }; + + // there won't be any other arcs + current = null; + + } + + } + + /** {@inheritDoc} */ + public boolean hasNext() { + return pending != null; + } + + /** {@inheritDoc} */ + public double[] next() { + if (pending == null) { + throw new NoSuchElementException(); + } + final double[] next = pending; + selectPending(); + return next; + } + + /** {@inheritDoc} */ + public void remove() { + throw new UnsupportedOperationException(); + } + + } + + /** Compute the relative position of the instance with respect + * to an arc. + * <p> + * The {@link Side#MINUS} side of the arc is the one covered by the arc. + * </p> + * @param arc arc to check instance against + * @return one of {@link Side#PLUS}, {@link Side#MINUS}, {@link Side#BOTH} + * or {@link Side#HYPER} + * @deprecated as of 3.6, replaced with {@link #split(Arc)}.{@link Split#getSide()} + */ + @Deprecated + public Side side(final Arc arc) { + return split(arc).getSide(); + } + + /** Split the instance in two parts by an arc. + * @param arc splitting arc + * @return an object containing both the part of the instance + * on the plus side of the arc and the part of the + * instance on the minus side of the arc + */ + public Split split(final Arc arc) { + + final List<Double> minus = new ArrayList<Double>(); + final List<Double> plus = new ArrayList<Double>(); + + final double reference = FastMath.PI + arc.getInf(); + final double arcLength = arc.getSup() - arc.getInf(); + + for (final double[] a : this) { + final double syncedStart = MathUtils.normalizeAngle(a[0], reference) - arc.getInf(); + final double arcOffset = a[0] - syncedStart; + final double syncedEnd = a[1] - arcOffset; + if (syncedStart < arcLength) { + // the start point a[0] is in the minus part of the arc + minus.add(a[0]); + if (syncedEnd > arcLength) { + // the end point a[1] is past the end of the arc + // so we leave the minus part and enter the plus part + final double minusToPlus = arcLength + arcOffset; + minus.add(minusToPlus); + plus.add(minusToPlus); + if (syncedEnd > MathUtils.TWO_PI) { + // in fact the end point a[1] goes far enough that we + // leave the plus part of the arc and enter the minus part again + final double plusToMinus = MathUtils.TWO_PI + arcOffset; + plus.add(plusToMinus); + minus.add(plusToMinus); + minus.add(a[1]); + } else { + // the end point a[1] is in the plus part of the arc + plus.add(a[1]); + } + } else { + // the end point a[1] is in the minus part of the arc + minus.add(a[1]); + } + } else { + // the start point a[0] is in the plus part of the arc + plus.add(a[0]); + if (syncedEnd > MathUtils.TWO_PI) { + // the end point a[1] wraps around to the start of the arc + // so we leave the plus part and enter the minus part + final double plusToMinus = MathUtils.TWO_PI + arcOffset; + plus.add(plusToMinus); + minus.add(plusToMinus); + if (syncedEnd > MathUtils.TWO_PI + arcLength) { + // in fact the end point a[1] goes far enough that we + // leave the minus part of the arc and enter the plus part again + final double minusToPlus = MathUtils.TWO_PI + arcLength + arcOffset; + minus.add(minusToPlus); + plus.add(minusToPlus); + plus.add(a[1]); + } else { + // the end point a[1] is in the minus part of the arc + minus.add(a[1]); + } + } else { + // the end point a[1] is in the plus part of the arc + plus.add(a[1]); + } + } + } + + return new Split(createSplitPart(plus), createSplitPart(minus)); + + } + + /** Add an arc limit to a BSP tree under construction. + * @param tree BSP tree under construction + * @param alpha arc limit + * @param isStart if true, the limit is the start of an arc + */ + private void addArcLimit(final BSPTree<Sphere1D> tree, final double alpha, final boolean isStart) { + + final LimitAngle limit = new LimitAngle(new S1Point(alpha), !isStart, getTolerance()); + final BSPTree<Sphere1D> node = tree.getCell(limit.getLocation(), getTolerance()); + if (node.getCut() != null) { + // this should never happen + throw new MathInternalError(); + } + + node.insertCut(limit); + node.setAttribute(null); + node.getPlus().setAttribute(Boolean.FALSE); + node.getMinus().setAttribute(Boolean.TRUE); + + } + + /** Create a split part. + * <p> + * As per construction, the list of limit angles is known to have + * an even number of entries, with start angles at even indices and + * end angles at odd indices. + * </p> + * @param limits limit angles of the split part + * @return split part (may be null) + */ + private ArcsSet createSplitPart(final List<Double> limits) { + if (limits.isEmpty()) { + return null; + } else { + + // collapse close limit angles + for (int i = 0; i < limits.size(); ++i) { + final int j = (i + 1) % limits.size(); + final double lA = limits.get(i); + final double lB = MathUtils.normalizeAngle(limits.get(j), lA); + if (FastMath.abs(lB - lA) <= getTolerance()) { + // the two limits are too close to each other, we remove both of them + if (j > 0) { + // regular case, the two entries are consecutive ones + limits.remove(j); + limits.remove(i); + i = i - 1; + } else { + // special case, i the the last entry and j is the first entry + // we have wrapped around list end + final double lEnd = limits.remove(limits.size() - 1); + final double lStart = limits.remove(0); + if (limits.isEmpty()) { + // the ends were the only limits, is it a full circle or an empty circle? + if (lEnd - lStart > FastMath.PI) { + // it was full circle + return new ArcsSet(new BSPTree<Sphere1D>(Boolean.TRUE), getTolerance()); + } else { + // it was an empty circle + return null; + } + } else { + // we have removed the first interval start, so our list + // currently starts with an interval end, which is wrong + // we need to move this interval end to the end of the list + limits.add(limits.remove(0) + MathUtils.TWO_PI); + } + } + } + } + + // build the tree by adding all angular sectors + BSPTree<Sphere1D> tree = new BSPTree<Sphere1D>(Boolean.FALSE); + for (int i = 0; i < limits.size() - 1; i += 2) { + addArcLimit(tree, limits.get(i), true); + addArcLimit(tree, limits.get(i + 1), false); + } + + if (tree.getCut() == null) { + // we did not insert anything + return null; + } + + return new ArcsSet(tree, getTolerance()); + + } + } + + /** Class holding the results of the {@link #split split} method. + */ + public static class Split { + + /** Part of the arcs set on the plus side of the splitting arc. */ + private final ArcsSet plus; + + /** Part of the arcs set on the minus side of the splitting arc. */ + private final ArcsSet minus; + + /** Build a Split from its parts. + * @param plus part of the arcs set on the plus side of the + * splitting arc + * @param minus part of the arcs set on the minus side of the + * splitting arc + */ + private Split(final ArcsSet plus, final ArcsSet minus) { + this.plus = plus; + this.minus = minus; + } + + /** Get the part of the arcs set on the plus side of the splitting arc. + * @return part of the arcs set on the plus side of the splitting arc + */ + public ArcsSet getPlus() { + return plus; + } + + /** Get the part of the arcs set on the minus side of the splitting arc. + * @return part of the arcs set on the minus side of the splitting arc + */ + public ArcsSet getMinus() { + return minus; + } + + /** Get the side of the split arc with respect to its splitter. + * @return {@link Side#PLUS} if only {@link #getPlus()} returns non-null, + * {@link Side#MINUS} if only {@link #getMinus()} returns non-null, + * {@link Side#BOTH} if both {@link #getPlus()} and {@link #getMinus()} + * return non-null or {@link Side#HYPER} if both {@link #getPlus()} and + * {@link #getMinus()} return null + * @since 3.6 + */ + public Side getSide() { + if (plus != null) { + if (minus != null) { + return Side.BOTH; + } else { + return Side.PLUS; + } + } else if (minus != null) { + return Side.MINUS; + } else { + return Side.HYPER; + } + } + + } + + /** Specialized exception for inconsistent BSP tree state inconsistency. + * <p> + * This exception is thrown at {@link ArcsSet} construction time when the + * {@link org.apache.commons.math3.geometry.partitioning.Region.Location inside/outside} + * state is not consistent at the 0, \(2 \pi \) crossing. + * </p> + */ + public static class InconsistentStateAt2PiWrapping extends MathIllegalArgumentException { + + /** Serializable UID. */ + private static final long serialVersionUID = 20140107L; + + /** Simple constructor. + */ + public InconsistentStateAt2PiWrapping() { + super(LocalizedFormats.INCONSISTENT_STATE_AT_2_PI_WRAPPING); + } + + } + +} |