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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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.threed;
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.Vector1D;
import org.apache.commons.math3.geometry.partitioning.Embedding;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;
/** The class represent lines in a three dimensional space.
* Each oriented line is intrinsically associated with an abscissa
* which is a coordinate on the line. The point at abscissa 0 is the
* orthogonal projection of the origin on the line, another equivalent
* way to express this is to say that it is the point of the line
* which is closest to the origin. Abscissa increases in the line
* direction.
* @since 3.0
*/
public class Line implements Embedding {
/** Default value for tolerance. */
private static final double DEFAULT_TOLERANCE = 1.0e-10;
/** Line direction. */
private Vector3D direction;
/** Line point closest to the origin. */
private Vector3D zero;
/** Tolerance below which points are considered identical. */
private final double tolerance;
/** Build a line from two points.
* @param p1 first point belonging to the line (this can be any point)
* @param p2 second point belonging to the line (this can be any point, different from p1)
* @param tolerance tolerance below which points are considered identical
* @exception MathIllegalArgumentException if the points are equal
* @since 3.3
*/
public Line(final Vector3D p1, final Vector3D p2, final double tolerance)
throws MathIllegalArgumentException {
reset(p1, p2);
this.tolerance = 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) {
this.direction = line.direction;
this.zero = line.zero;
this.tolerance = line.tolerance;
}
/** Build a line from two points.
* @param p1 first point belonging to the line (this can be any point)
* @param p2 second point belonging to the line (this can be any point, different from p1)
* @exception MathIllegalArgumentException if the points are equal
* @deprecated as of 3.3, replaced with {@link #Line(Vector3D, Vector3D, double)}
*/
@Deprecated
public Line(final Vector3D p1, final Vector3D p2) throws MathIllegalArgumentException {
this(p1, p2, DEFAULT_TOLERANCE);
}
/** Reset the instance as if built from two points.
* @param p1 first point belonging to the line (this can be any point)
* @param p2 second point belonging to the line (this can be any point, different from p1)
* @exception MathIllegalArgumentException if the points are equal
*/
public void reset(final Vector3D p1, final Vector3D p2) throws MathIllegalArgumentException {
final Vector3D delta = p2.subtract(p1);
final double norm2 = delta.getNormSq();
if (norm2 == 0.0) {
throw new MathIllegalArgumentException(LocalizedFormats.ZERO_NORM);
}
this.direction = new Vector3D(1.0 / FastMath.sqrt(norm2), delta);
zero = new Vector3D(1.0, p1, -p1.dotProduct(delta) / norm2, delta);
}
/** Get the tolerance below which points are considered identical.
* @return tolerance below which points are considered identical
* @since 3.3
*/
public double getTolerance() {
return tolerance;
}
/** Get a line with reversed direction.
* @return a new instance, with reversed direction
*/
public Line revert() {
final Line reverted = new Line(this);
reverted.direction = reverted.direction.negate();
return reverted;
}
/** Get the normalized direction vector.
* @return normalized direction vector
*/
public Vector3D getDirection() {
return direction;
}
/** Get the line point closest to the origin.
* @return line point closest to the origin
*/
public Vector3D getOrigin() {
return zero;
}
/** Get the abscissa of a point with respect to the line.
* The abscissa is 0 if the projection of the point and the
* projection of the frame origin on the line are the same
* point.
* @param point point to check
* @return abscissa of the point
*/
public double getAbscissa(final Vector3D point) {
return point.subtract(zero).dotProduct(direction);
}
/** Get one point from the line.
* @param abscissa desired abscissa for the point
* @return one point belonging to the line, at specified abscissa
*/
public Vector3D pointAt(final double abscissa) {
return new Vector3D(1.0, zero, abscissa, direction);
}
/** 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 Vector3D toSpace(Vector vector) {
return toSpace((Point) vector);
}
/** {@inheritDoc}
* @see #getAbscissa(Vector3D)
*/
public Vector1D toSubSpace(final Point point) {
return new Vector1D(getAbscissa((Vector3D) point));
}
/** {@inheritDoc}
* @see #pointAt(double)
*/
public Vector3D toSpace(final Point point) {
return pointAt(((Vector1D) point).getX());
}
/** Check if the instance is similar to another line.
* Lines are considered similar if they contain the same
* points. This does not mean they are equal since they can have
* opposite directions.
* @param line line to which instance should be compared
* @return true if the lines are similar
*/
public boolean isSimilarTo(final Line line) {
final double angle = Vector3D.angle(direction, line.direction);
return ((angle < tolerance) || (angle > (FastMath.PI - tolerance))) && contains(line.zero);
}
/** Check if the instance contains a point.
* @param p point to check
* @return true if p belongs to the line
*/
public boolean contains(final Vector3D p) {
return distance(p) < tolerance;
}
/** Compute the distance between the instance and a point.
* @param p to check
* @return distance between the instance and the point
*/
public double distance(final Vector3D p) {
final Vector3D d = p.subtract(zero);
final Vector3D n = new Vector3D(1.0, d, -d.dotProduct(direction), direction);
return n.getNorm();
}
/** Compute the shortest distance between the instance and another line.
* @param line line to check against the instance
* @return shortest distance between the instance and the line
*/
public double distance(final Line line) {
final Vector3D normal = Vector3D.crossProduct(direction, line.direction);
final double n = normal.getNorm();
if (n < Precision.SAFE_MIN) {
// lines are parallel
return distance(line.zero);
}
// signed separation of the two parallel planes that contains the lines
final double offset = line.zero.subtract(zero).dotProduct(normal) / n;
return FastMath.abs(offset);
}
/** Compute the point of the instance closest to another line.
* @param line line to check against the instance
* @return point of the instance closest to another line
*/
public Vector3D closestPoint(final Line line) {
final double cos = direction.dotProduct(line.direction);
final double n = 1 - cos * cos;
if (n < Precision.EPSILON) {
// the lines are parallel
return zero;
}
final Vector3D delta0 = line.zero.subtract(zero);
final double a = delta0.dotProduct(direction);
final double b = delta0.dotProduct(line.direction);
return new Vector3D(1, zero, (a - b * cos) / n, direction);
}
/** Get the intersection point of the instance and another line.
* @param line other line
* @return intersection point of the instance and the other line
* or null if there are no intersection points
*/
public Vector3D intersection(final Line line) {
final Vector3D closest = closestPoint(line);
return line.contains(closest) ? closest : null;
}
/** Build a sub-line covering the whole line.
* @return a sub-line covering the whole line
*/
public SubLine wholeLine() {
return new SubLine(this, new IntervalsSet(tolerance));
}
}