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Geometric primitives for spherical space.
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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.geometry.spherical.oned;
import java.util.Collections;
import java.util.List;
import java.util.Objects;
import org.apache.commons.geometry.core.RegionLocation;
import org.apache.commons.geometry.core.Transform;
import org.apache.commons.geometry.core.partitioning.AbstractHyperplane;
import org.apache.commons.geometry.core.partitioning.Hyperplane;
import org.apache.commons.geometry.core.partitioning.HyperplaneConvexSubset;
import org.apache.commons.geometry.core.partitioning.HyperplaneLocation;
import org.apache.commons.geometry.core.partitioning.Split;
import org.apache.commons.numbers.core.Precision;
/** Class representing an oriented point in 1-dimensional spherical space,
* meaning an azimuth angle and a direction (increasing or decreasing angles)
* along the circle.
*
* Hyperplanes split the spaces they are embedded in into three distinct parts:
* the hyperplane itself, a plus side and a minus side. However, since spherical
* space wraps around, a single oriented point is not sufficient to partition the space;
* any point could be classified as being on the plus or minus side of a hyperplane
* depending on the direction that the circle is traversed. The approach taken in this
* class to address this issue is to (1) define a second, implicit cut point at {@code 0pi} and
* (2) define the domain of hyperplane points (for partitioning purposes) to be the
* range {@code [0, 2pi)}. Each hyperplane then splits the space into the intervals
* {@code [0, x]} and {@code [x, 2pi)}, where {@code x} is the location of the hyperplane.
* One way to visualize this is to picture the circle as a cake that has already been
* cut at {@code 0pi}. Each hyperplane then specifies the location of the second
* cut of the cake, with the plus and minus sides being the pieces thus cut.
*
*
* Note that with the hyperplane partitioning rules described above, the hyperplane
* at {@code 0pi} is unique in that it has the entire space on one side (minus the hyperplane
* itself) and no points whatsoever on the other. This is very different from hyperplanes in
* Euclidean space, which always have infinitely many points on both sides.
*
* Instances of this class are guaranteed to be immutable.
* @see CutAngles
*/
public final class CutAngle extends AbstractHyperplane {
/** Hyperplane location as a point. */
private final Point1S point;
/** Hyperplane direction. */
private final boolean positiveFacing;
/** Simple constructor.
* @param point location of the hyperplane
* @param positiveFacing if true, the hyperplane will point in a positive angular
* direction; otherwise, it will point in a negative direction
* @param precision precision context used to compare floating point values
*/
CutAngle(final Point1S point, final boolean positiveFacing,
final Precision.DoubleEquivalence precision) {
super(precision);
this.point = point;
this.positiveFacing = positiveFacing;
}
/** Get the location of the hyperplane as a point.
* @return the hyperplane location as a point
* @see #getAzimuth()
*/
public Point1S getPoint() {
return point;
}
/** Get the location of the hyperplane as a single value. This is
* equivalent to {@code cutAngle.getPoint().getAzimuth()}.
* @return the location of the hyperplane as a single value.
* @see #getPoint()
* @see Point1S#getAzimuth()
*/
public double getAzimuth() {
return point.getAzimuth();
}
/** Get the location of the hyperplane as a single value, normalized
* to the range {@code [0, 2pi)}. This is equivalent to
* {@code cutAngle.getPoint().getNormalizedAzimuth()}.
* @return the location of the hyperplane, normalized to the range
* {@code [0, 2pi)}
* @see #getPoint()
* @see Point1S#getNormalizedAzimuth()
*/
public double getNormalizedAzimuth() {
return point.getNormalizedAzimuth();
}
/** Return true if the hyperplane is oriented with its plus
* side pointing toward increasing angles.
* @return true if the hyperplane is facing in the direction
* of increasing angles
*/
public boolean isPositiveFacing() {
return positiveFacing;
}
/** Return true if this instance should be considered equivalent to the argument, using the
* given precision context for comparison.
* The instances are considered equivalent if they
*
* - have equivalent point locations (points separated by multiples of 2pi are
* considered equivalent) and
*
- point in the same direction.
*
* @param other point to compare with
* @param precision precision context to use for the comparison
* @return true if this instance should be considered equivalent to the argument
* @see Point1S#eq(Point1S, Precision.DoubleEquivalence)
*/
public boolean eq(final CutAngle other, final Precision.DoubleEquivalence precision) {
return point.eq(other.point, precision) &&
positiveFacing == other.positiveFacing;
}
/** {@inheritDoc} */
@Override
public double offset(final Point1S pt) {
final double dist = pt.getNormalizedAzimuth() - this.point.getNormalizedAzimuth();
return positiveFacing ? +dist : -dist;
}
/** {@inheritDoc} */
@Override
public HyperplaneLocation classify(final Point1S pt) {
final Precision.DoubleEquivalence precision = getPrecision();
final Point1S compPt = Point1S.ZERO.eq(pt, precision) ?
Point1S.ZERO :
pt;
final double offsetValue = offset(compPt);
final double cmp = precision.signum(offsetValue);
if (cmp > 0) {
return HyperplaneLocation.PLUS;
} else if (cmp < 0) {
return HyperplaneLocation.MINUS;
}
return HyperplaneLocation.ON;
}
/** {@inheritDoc} */
@Override
public Point1S project(final Point1S pt) {
return this.point;
}
/** {@inheritDoc} */
@Override
public CutAngle reverse() {
return new CutAngle(point, !positiveFacing, getPrecision());
}
/** {@inheritDoc} */
@Override
public CutAngle transform(final Transform transform) {
final Point1S tPoint = transform.apply(point);
final boolean tPositiveFacing = transform.preservesOrientation() == positiveFacing;
return CutAngles.fromPointAndDirection(tPoint, tPositiveFacing, getPrecision());
}
/** {@inheritDoc} */
@Override
public boolean similarOrientation(final Hyperplane other) {
return positiveFacing == ((CutAngle) other).positiveFacing;
}
/** {@inheritDoc}
*
* Since there are no subspaces in spherical 1D space, this method effectively returns a stub implementation
* of {@link HyperplaneConvexSubset}, the main purpose of which is to support the proper functioning
* of the partitioning code.
*/
@Override
public HyperplaneConvexSubset span() {
return new CutAngleConvexSubset(this);
}
/** {@inheritDoc} */
@Override
public int hashCode() {
return Objects.hash(point, positiveFacing, getPrecision());
}
/** {@inheritDoc} */
@Override
public boolean equals(final Object obj) {
if (this == obj) {
return true;
} else if (!(obj instanceof CutAngle)) {
return false;
}
final CutAngle other = (CutAngle) obj;
return Objects.equals(getPrecision(), other.getPrecision()) &&
Objects.equals(point, other.point) &&
positiveFacing == other.positiveFacing;
}
/** {@inheritDoc} */
@Override
public String toString() {
final StringBuilder sb = new StringBuilder();
sb.append(this.getClass().getSimpleName())
.append("[point= ")
.append(point)
.append(", positiveFacing= ")
.append(isPositiveFacing())
.append(']');
return sb.toString();
}
/** {@link HyperplaneConvexSubset} implementation for spherical 1D space. Since there are no subspaces in 1D,
* this is effectively a stub implementation, its main use being to allow for the correct functioning of
* partitioning code.
*/
private static final class CutAngleConvexSubset implements HyperplaneConvexSubset {
/** The hyperplane containing for this instance. */
private final CutAngle hyperplane;
/** Simple constructor.
* @param hyperplane containing hyperplane instance
*/
CutAngleConvexSubset(final CutAngle hyperplane) {
this.hyperplane = hyperplane;
}
/** {@inheritDoc} */
@Override
public CutAngle getHyperplane() {
return hyperplane;
}
/** {@inheritDoc}
*
* This method always returns {@code false}.
*/
@Override
public boolean isFull() {
return false;
}
/** {@inheritDoc}
*
* This method always returns {@code false}.
*/
@Override
public boolean isEmpty() {
return false;
}
/** {@inheritDoc}
*
* This method always returns {@code false}.
*/
@Override
public boolean isInfinite() {
return false;
}
/** {@inheritDoc}
*
* This method always returns {@code true}.
*/
@Override
public boolean isFinite() {
return true;
}
/** {@inheritDoc}
*
* This method always returns {@code 0}.
*/
@Override
public double getSize() {
return 0;
}
/** {@inheritDoc}
*
* This method returns the point for the underlying hyperplane.
*/
@Override
public Point1S getCentroid() {
return hyperplane.getPoint();
}
/** {@inheritDoc}
*
* This method returns {@link RegionLocation#BOUNDARY} if the
* point is on the hyperplane and {@link RegionLocation#OUTSIDE}
* otherwise.
*/
@Override
public RegionLocation classify(final Point1S point) {
if (hyperplane.contains(point)) {
return RegionLocation.BOUNDARY;
}
return RegionLocation.OUTSIDE;
}
/** {@inheritDoc} */
@Override
public Point1S closest(final Point1S point) {
return hyperplane.project(point);
}
/** {@inheritDoc} */
@Override
public Split split(final Hyperplane splitter) {
final HyperplaneLocation side = splitter.classify(hyperplane.getPoint());
CutAngleConvexSubset minus = null;
CutAngleConvexSubset plus = null;
if (side == HyperplaneLocation.MINUS) {
minus = this;
} else if (side == HyperplaneLocation.PLUS) {
plus = this;
}
return new Split<>(minus, plus);
}
/** {@inheritDoc} */
@Override
public List toConvex() {
return Collections.singletonList(this);
}
/** {@inheritDoc} */
@Override
public CutAngleConvexSubset transform(final Transform transform) {
return new CutAngleConvexSubset(getHyperplane().transform(transform));
}
/** {@inheritDoc} */
@Override
public CutAngleConvexSubset reverse() {
return new CutAngleConvexSubset(hyperplane.reverse());
}
/** {@inheritDoc} */
@Override
public String toString() {
final StringBuilder sb = new StringBuilder();
sb.append(this.getClass().getSimpleName())
.append("[hyperplane= ")
.append(hyperplane)
.append(']');
return sb.toString();
}
}
}