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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.euclidean.twod;
import java.awt.geom.AffineTransform;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.geometry.Point;
import org.apache.commons.math3.geometry.Vector;
import org.apache.commons.math3.geometry.euclidean.oned.Euclidean1D;
import org.apache.commons.math3.geometry.euclidean.oned.IntervalsSet;
import org.apache.commons.math3.geometry.euclidean.oned.OrientedPoint;
import org.apache.commons.math3.geometry.euclidean.oned.Vector1D;
import org.apache.commons.math3.geometry.partitioning.Embedding;
import org.apache.commons.math3.geometry.partitioning.Hyperplane;
import org.apache.commons.math3.geometry.partitioning.SubHyperplane;
import org.apache.commons.math3.geometry.partitioning.Transform;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.MathUtils;
/** This class represents an oriented line in the 2D plane.
* An oriented line can be defined either by prolongating a line
* segment between two points past these points, or by one point and
* an angular direction (in trigonometric orientation).
* Since it is oriented the two half planes at its two sides are
* unambiguously identified as a left half plane and a right half
* plane. This can be used to identify the interior and the exterior
* in a simple way by local properties only when part of a line is
* used to define part of a polygon boundary.
* A line can also be used to completely define a reference frame
* in the plane. It is sufficient to select one specific point in the
* line (the orthogonal projection of the original reference frame on
* the line) and to use the unit vector in the line direction and the
* orthogonal vector oriented from left half plane to right half
* plane. We define two coordinates by the process, the
* abscissa along the line, and the offset across
* the line. All points of the plane are uniquely identified by these
* two coordinates. The line is the set of points at zero offset, the
* left half plane is the set of points with negative offsets and the
* right half plane is the set of points with positive offsets.
* @since 3.0
*/
public class Line implements Hyperplane, Embedding {
/** Default value for tolerance. */
private static final double DEFAULT_TOLERANCE = 1.0e-10;
/** Angle with respect to the abscissa axis. */
private double angle;
/** Cosine of the line angle. */
private double cos;
/** Sine of the line angle. */
private double sin;
/** Offset of the frame origin. */
private double originOffset;
/** Tolerance below which points are considered identical. */
private final double tolerance;
/** Reverse line. */
private Line reverse;
/** Build a line from two points.
* The line is oriented from p1 to p2
* @param p1 first point
* @param p2 second point
* @param tolerance tolerance below which points are considered identical
* @since 3.3
*/
public Line(final Vector2D p1, final Vector2D p2, final double tolerance) {
reset(p1, p2);
this.tolerance = tolerance;
}
/** Build a line from a point and an angle.
* @param p point belonging to the line
* @param angle angle of the line with respect to abscissa axis
* @param tolerance tolerance below which points are considered identical
* @since 3.3
*/
public Line(final Vector2D p, final double angle, final double tolerance) {
reset(p, angle);
this.tolerance = tolerance;
}
/** Build a line from its internal characteristics.
* @param angle angle of the line with respect to abscissa axis
* @param cos cosine of the angle
* @param sin sine of the angle
* @param originOffset offset of the origin
* @param tolerance tolerance below which points are considered identical
* @since 3.3
*/
private Line(final double angle, final double cos, final double sin,
final double originOffset, final double tolerance) {
this.angle = angle;
this.cos = cos;
this.sin = sin;
this.originOffset = originOffset;
this.tolerance = tolerance;
this.reverse = null;
}
/** Build a line from two points.
* The line is oriented from p1 to p2
* @param p1 first point
* @param p2 second point
* @deprecated as of 3.3, replaced with {@link #Line(Vector2D, Vector2D, double)}
*/
@Deprecated
public Line(final Vector2D p1, final Vector2D p2) {
this(p1, p2, DEFAULT_TOLERANCE);
}
/** Build a line from a point and an angle.
* @param p point belonging to the line
* @param angle angle of the line with respect to abscissa axis
* @deprecated as of 3.3, replaced with {@link #Line(Vector2D, double, double)}
*/
@Deprecated
public Line(final Vector2D p, final double angle) {
this(p, angle, DEFAULT_TOLERANCE);
}
/** Copy constructor.
* The created instance is completely independent from the
* original instance, it is a deep copy.
* @param line line to copy
*/
public Line(final Line line) {
angle = MathUtils.normalizeAngle(line.angle, FastMath.PI);
cos = line.cos;
sin = line.sin;
originOffset = line.originOffset;
tolerance = line.tolerance;
reverse = null;
}
/** {@inheritDoc} */
public Line copySelf() {
return new Line(this);
}
/** Reset the instance as if built from two points.
* The line is oriented from p1 to p2
* @param p1 first point
* @param p2 second point
*/
public void reset(final Vector2D p1, final Vector2D p2) {
unlinkReverse();
final double dx = p2.getX() - p1.getX();
final double dy = p2.getY() - p1.getY();
final double d = FastMath.hypot(dx, dy);
if (d == 0.0) {
angle = 0.0;
cos = 1.0;
sin = 0.0;
originOffset = p1.getY();
} else {
angle = FastMath.PI + FastMath.atan2(-dy, -dx);
cos = dx / d;
sin = dy / d;
originOffset = MathArrays.linearCombination(p2.getX(), p1.getY(), -p1.getX(), p2.getY()) / d;
}
}
/** Reset the instance as if built from a line and an angle.
* @param p point belonging to the line
* @param alpha angle of the line with respect to abscissa axis
*/
public void reset(final Vector2D p, final double alpha) {
unlinkReverse();
this.angle = MathUtils.normalizeAngle(alpha, FastMath.PI);
cos = FastMath.cos(this.angle);
sin = FastMath.sin(this.angle);
originOffset = MathArrays.linearCombination(cos, p.getY(), -sin, p.getX());
}
/** Revert the instance.
*/
public void revertSelf() {
unlinkReverse();
if (angle < FastMath.PI) {
angle += FastMath.PI;
} else {
angle -= FastMath.PI;
}
cos = -cos;
sin = -sin;
originOffset = -originOffset;
}
/** Unset the link between an instance and its reverse.
*/
private void unlinkReverse() {
if (reverse != null) {
reverse.reverse = null;
}
reverse = null;
}
/** Get the reverse of the instance.
* Get a line with reversed orientation with respect to the
* instance.
*
* As long as neither the instance nor its reverse are modified
* (i.e. as long as none of the {@link #reset(Vector2D, Vector2D)},
* {@link #reset(Vector2D, double)}, {@link #revertSelf()},
* {@link #setAngle(double)} or {@link #setOriginOffset(double)}
* methods are called), then the line and its reverse remain linked
* together so that {@code line.getReverse().getReverse() == line}.
* When one of the line is modified, the link is deleted as both
* instance becomes independent.
*
* @return a new line, with orientation opposite to the instance orientation
*/
public Line getReverse() {
if (reverse == null) {
reverse = new Line((angle < FastMath.PI) ? (angle + FastMath.PI) : (angle - FastMath.PI),
-cos, -sin, -originOffset, tolerance);
reverse.reverse = this;
}
return reverse;
}
/** Transform a space point into a sub-space point.
* @param vector n-dimension point of the space
* @return (n-1)-dimension point of the sub-space corresponding to
* the specified space point
*/
public Vector1D toSubSpace(Vector vector) {
return toSubSpace((Point) vector);
}
/** Transform a sub-space point into a space point.
* @param vector (n-1)-dimension point of the sub-space
* @return n-dimension point of the space corresponding to the
* specified sub-space point
*/
public Vector2D toSpace(Vector vector) {
return toSpace((Point) vector);
}
/** {@inheritDoc} */
public Vector1D toSubSpace(final Point point) {
Vector2D p2 = (Vector2D) point;
return new Vector1D(MathArrays.linearCombination(cos, p2.getX(), sin, p2.getY()));
}
/** {@inheritDoc} */
public Vector2D toSpace(final Point point) {
final double abscissa = ((Vector1D) point).getX();
return new Vector2D(MathArrays.linearCombination(abscissa, cos, -originOffset, sin),
MathArrays.linearCombination(abscissa, sin, originOffset, cos));
}
/** Get the intersection point of the instance and another line.
* @param other other line
* @return intersection point of the instance and the other line
* or null if there are no intersection points
*/
public Vector2D intersection(final Line other) {
final double d = MathArrays.linearCombination(sin, other.cos, -other.sin, cos);
if (FastMath.abs(d) < tolerance) {
return null;
}
return new Vector2D(MathArrays.linearCombination(cos, other.originOffset, -other.cos, originOffset) / d,
MathArrays.linearCombination(sin, other.originOffset, -other.sin, originOffset) / d);
}
/** {@inheritDoc}
* @since 3.3
*/
public Point project(Point point) {
return toSpace(toSubSpace(point));
}
/** {@inheritDoc}
* @since 3.3
*/
public double getTolerance() {
return tolerance;
}
/** {@inheritDoc} */
public SubLine wholeHyperplane() {
return new SubLine(this, new IntervalsSet(tolerance));
}
/** Build a region covering the whole space.
* @return a region containing the instance (really a {@link
* PolygonsSet PolygonsSet} instance)
*/
public PolygonsSet wholeSpace() {
return new PolygonsSet(tolerance);
}
/** Get the offset (oriented distance) of a parallel line.
* This method should be called only for parallel lines otherwise
* the result is not meaningful.
* The offset is 0 if both lines are the same, it is
* positive if the line is on the right side of the instance and
* negative if it is on the left side, according to its natural
* orientation.
* @param line line to check
* @return offset of the line
*/
public double getOffset(final Line line) {
return originOffset +
(MathArrays.linearCombination(cos, line.cos, sin, line.sin) > 0 ? -line.originOffset : line.originOffset);
}
/** Get the offset (oriented distance) of a vector.
* @param vector vector to check
* @return offset of the vector
*/
public double getOffset(Vector vector) {
return getOffset((Point) vector);
}
/** {@inheritDoc} */
public double getOffset(final Point point) {
Vector2D p2 = (Vector2D) point;
return MathArrays.linearCombination(sin, p2.getX(), -cos, p2.getY(), 1.0, originOffset);
}
/** {@inheritDoc} */
public boolean sameOrientationAs(final Hyperplane other) {
final Line otherL = (Line) other;
return MathArrays.linearCombination(sin, otherL.sin, cos, otherL.cos) >= 0.0;
}
/** Get one point from the plane.
* @param abscissa desired abscissa for the point
* @param offset desired offset for the point
* @return one point in the plane, with given abscissa and offset
* relative to the line
*/
public Vector2D getPointAt(final Vector1D abscissa, final double offset) {
final double x = abscissa.getX();
final double dOffset = offset - originOffset;
return new Vector2D(MathArrays.linearCombination(x, cos, dOffset, sin),
MathArrays.linearCombination(x, sin, -dOffset, cos));
}
/** Check if the line contains a point.
* @param p point to check
* @return true if p belongs to the line
*/
public boolean contains(final Vector2D p) {
return FastMath.abs(getOffset(p)) < tolerance;
}
/** Compute the distance between the instance and a point.
* This is a shortcut for invoking FastMath.abs(getOffset(p)),
* and provides consistency with what is in the
* org.apache.commons.math3.geometry.euclidean.threed.Line class.
*
* @param p to check
* @return distance between the instance and the point
* @since 3.1
*/
public double distance(final Vector2D p) {
return FastMath.abs(getOffset(p));
}
/** Check the instance is parallel to another line.
* @param line other line to check
* @return true if the instance is parallel to the other line
* (they can have either the same or opposite orientations)
*/
public boolean isParallelTo(final Line line) {
return FastMath.abs(MathArrays.linearCombination(sin, line.cos, -cos, line.sin)) < tolerance;
}
/** Translate the line to force it passing by a point.
* @param p point by which the line should pass
*/
public void translateToPoint(final Vector2D p) {
originOffset = MathArrays.linearCombination(cos, p.getY(), -sin, p.getX());
}
/** Get the angle of the line.
* @return the angle of the line with respect to the abscissa axis
*/
public double getAngle() {
return MathUtils.normalizeAngle(angle, FastMath.PI);
}
/** Set the angle of the line.
* @param angle new angle of the line with respect to the abscissa axis
*/
public void setAngle(final double angle) {
unlinkReverse();
this.angle = MathUtils.normalizeAngle(angle, FastMath.PI);
cos = FastMath.cos(this.angle);
sin = FastMath.sin(this.angle);
}
/** Get the offset of the origin.
* @return the offset of the origin
*/
public double getOriginOffset() {
return originOffset;
}
/** Set the offset of the origin.
* @param offset offset of the origin
*/
public void setOriginOffset(final double offset) {
unlinkReverse();
originOffset = offset;
}
/** Get a {@link org.apache.commons.math3.geometry.partitioning.Transform
* Transform} embedding an affine transform.
* @param transform affine transform to embed (must be inversible
* otherwise the {@link
* org.apache.commons.math3.geometry.partitioning.Transform#apply(Hyperplane)
* apply(Hyperplane)} method would work only for some lines, and
* fail for other ones)
* @return a new transform that can be applied to either {@link
* Vector2D Vector2D}, {@link Line Line} or {@link
* org.apache.commons.math3.geometry.partitioning.SubHyperplane
* SubHyperplane} instances
* @exception MathIllegalArgumentException if the transform is non invertible
* @deprecated as of 3.6, replaced with {@link #getTransform(double, double, double, double, double, double)}
*/
@Deprecated
public static Transform getTransform(final AffineTransform transform)
throws MathIllegalArgumentException {
final double[] m = new double[6];
transform.getMatrix(m);
return new LineTransform(m[0], m[1], m[2], m[3], m[4], m[5]);
}
/** Get a {@link org.apache.commons.math3.geometry.partitioning.Transform
* Transform} embedding an affine transform.
* @param cXX transform factor between input abscissa and output abscissa
* @param cYX transform factor between input abscissa and output ordinate
* @param cXY transform factor between input ordinate and output abscissa
* @param cYY transform factor between input ordinate and output ordinate
* @param cX1 transform addendum for output abscissa
* @param cY1 transform addendum for output ordinate
* @return a new transform that can be applied to either {@link
* Vector2D Vector2D}, {@link Line Line} or {@link
* org.apache.commons.math3.geometry.partitioning.SubHyperplane
* SubHyperplane} instances
* @exception MathIllegalArgumentException if the transform is non invertible
* @since 3.6
*/
public static Transform getTransform(final double cXX,
final double cYX,
final double cXY,
final double cYY,
final double cX1,
final double cY1)
throws MathIllegalArgumentException {
return new LineTransform(cXX, cYX, cXY, cYY, cX1, cY1);
}
/** Class embedding an affine transform.
* This class is used in order to apply an affine transform to a
* line. Using a specific object allow to perform some computations
* on the transform only once even if the same transform is to be
* applied to a large number of lines (for example to a large
* polygon)./
*/
private static class LineTransform implements Transform {
/** Transform factor between input abscissa and output abscissa. */
private double cXX;
/** Transform factor between input abscissa and output ordinate. */
private double cYX;
/** Transform factor between input ordinate and output abscissa. */
private double cXY;
/** Transform factor between input ordinate and output ordinate. */
private double cYY;
/** Transform addendum for output abscissa. */
private double cX1;
/** Transform addendum for output ordinate. */
private double cY1;
/** cXY * cY1 - cYY * cX1. */
private double c1Y;
/** cXX * cY1 - cYX * cX1. */
private double c1X;
/** cXX * cYY - cYX * cXY. */
private double c11;
/** Build an affine line transform from a n {@code AffineTransform}.
* @param cXX transform factor between input abscissa and output abscissa
* @param cYX transform factor between input abscissa and output ordinate
* @param cXY transform factor between input ordinate and output abscissa
* @param cYY transform factor between input ordinate and output ordinate
* @param cX1 transform addendum for output abscissa
* @param cY1 transform addendum for output ordinate
* @exception MathIllegalArgumentException if the transform is non invertible
* @since 3.6
*/
LineTransform(final double cXX, final double cYX, final double cXY,
final double cYY, final double cX1, final double cY1)
throws MathIllegalArgumentException {
this.cXX = cXX;
this.cYX = cYX;
this.cXY = cXY;
this.cYY = cYY;
this.cX1 = cX1;
this.cY1 = cY1;
c1Y = MathArrays.linearCombination(cXY, cY1, -cYY, cX1);
c1X = MathArrays.linearCombination(cXX, cY1, -cYX, cX1);
c11 = MathArrays.linearCombination(cXX, cYY, -cYX, cXY);
if (FastMath.abs(c11) < 1.0e-20) {
throw new MathIllegalArgumentException(LocalizedFormats.NON_INVERTIBLE_TRANSFORM);
}
}
/** {@inheritDoc} */
public Vector2D apply(final Point point) {
final Vector2D p2D = (Vector2D) point;
final double x = p2D.getX();
final double y = p2D.getY();
return new Vector2D(MathArrays.linearCombination(cXX, x, cXY, y, cX1, 1),
MathArrays.linearCombination(cYX, x, cYY, y, cY1, 1));
}
/** {@inheritDoc} */
public Line apply(final Hyperplane hyperplane) {
final Line line = (Line) hyperplane;
final double rOffset = MathArrays.linearCombination(c1X, line.cos, c1Y, line.sin, c11, line.originOffset);
final double rCos = MathArrays.linearCombination(cXX, line.cos, cXY, line.sin);
final double rSin = MathArrays.linearCombination(cYX, line.cos, cYY, line.sin);
final double inv = 1.0 / FastMath.sqrt(rSin * rSin + rCos * rCos);
return new Line(FastMath.PI + FastMath.atan2(-rSin, -rCos),
inv * rCos, inv * rSin,
inv * rOffset, line.tolerance);
}
/** {@inheritDoc} */
public SubHyperplane apply(final SubHyperplane sub,
final Hyperplane original,
final Hyperplane transformed) {
final OrientedPoint op = (OrientedPoint) sub.getHyperplane();
final Line originalLine = (Line) original;
final Line transformedLine = (Line) transformed;
final Vector1D newLoc =
transformedLine.toSubSpace(apply(originalLine.toSpace(op.getLocation())));
return new OrientedPoint(newLoc, op.isDirect(), originalLine.tolerance).wholeHyperplane();
}
}
}