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The Hipparchus geometry module
/*
* 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.
*/
/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.geometry.euclidean.threed;
import org.hipparchus.RealFieldElement;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.util.FastMath;
import org.hipparchus.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.
* @param the type of the field elements
*/
public class FieldLine> {
/** Line direction. */
private FieldVector3D direction;
/** Line point closest to the origin. */
private FieldVector3D 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
*/
public FieldLine(final FieldVector3D p1, final FieldVector3D 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 FieldLine(final FieldLine line) {
this.direction = line.direction;
this.zero = line.zero;
this.tolerance = line.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 FieldVector3D p1, final FieldVector3D p2)
throws MathIllegalArgumentException {
final FieldVector3D delta = p2.subtract(p1);
final T norm2 = delta.getNormSq();
if (norm2.getReal() == 0.0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.ZERO_NORM);
}
this.direction = new FieldVector3D<>(norm2.sqrt().reciprocal(), delta);
zero = new FieldVector3D<>(norm2.getField().getOne(), p1,
p1.dotProduct(delta).negate().divide(norm2), delta);
}
/** Get the tolerance below which points are considered identical.
* @return tolerance below which points are considered identical
*/
public double getTolerance() {
return tolerance;
}
/** Get a line with reversed direction.
* @return a new instance, with reversed direction
*/
public FieldLine revert() {
final FieldLine reverted = new FieldLine<>(this);
reverted.direction = reverted.direction.negate();
return reverted;
}
/** Get the normalized direction vector.
* @return normalized direction vector
*/
public FieldVector3D getDirection() {
return direction;
}
/** Get the line point closest to the origin.
* @return line point closest to the origin
*/
public FieldVector3D 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 T getAbscissa(final FieldVector3D point) {
return point.subtract(zero).dotProduct(direction);
}
/** 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 T getAbscissa(final Vector3D point) {
return zero.subtract(point).dotProduct(direction).negate();
}
/** Get one point from the line.
* @param abscissa desired abscissa for the point
* @return one point belonging to the line, at specified abscissa
*/
public FieldVector3D pointAt(final T abscissa) {
return new FieldVector3D(abscissa.getField().getOne(), zero,
abscissa, 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 FieldVector3D pointAt(final double abscissa) {
return new FieldVector3D(1, zero, abscissa, direction);
}
/** 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 FieldLine line) {
final double angle = FieldVector3D.angle(direction, line.direction).getReal();
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 FieldVector3D p) {
return distance(p).getReal() < tolerance;
}
/** 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).getReal() < tolerance;
}
/** Compute the distance between the instance and a point.
* @param p to check
* @return distance between the instance and the point
*/
public T distance(final FieldVector3D p) {
final FieldVector3D d = p.subtract(zero);
final FieldVector3D n = new FieldVector3D<>(zero.getX().getField().getOne(), d,
d.dotProduct(direction).negate(), direction);
return n.getNorm();
}
/** Compute the distance between the instance and a point.
* @param p to check
* @return distance between the instance and the point
*/
public T distance(final Vector3D p) {
final FieldVector3D d = zero.subtract(p).negate();
final FieldVector3D n = new FieldVector3D<>(zero.getX().getField().getOne(), d,
d.dotProduct(direction).negate(), 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 T distance(final FieldLine line) {
final FieldVector3D normal = FieldVector3D.crossProduct(direction, line.direction);
final T n = normal.getNorm();
if (n.getReal() < Precision.SAFE_MIN) {
// lines are parallel
return distance(line.zero);
}
// signed separation of the two parallel planes that contains the lines
final T offset = line.zero.subtract(zero).dotProduct(normal).divide(n);
return offset.abs();
}
/** 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 FieldVector3D closestPoint(final FieldLine line) {
final T cos = direction.dotProduct(line.direction);
final T n = cos.multiply(cos).subtract(1).negate();
if (n.getReal() < Precision.EPSILON) {
// the lines are parallel
return zero;
}
final FieldVector3D delta0 = line.zero.subtract(zero);
final T a = delta0.dotProduct(direction);
final T b = delta0.dotProduct(line.direction);
return new FieldVector3D(a.getField().getOne(), zero,
a.subtract(b.multiply(cos)).divide(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 FieldVector3D intersection(final FieldLine line) {
final FieldVector3D closest = closestPoint(line);
return line.contains(closest) ? closest : null;
}
}
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