/*
* 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 peasy.org.apache.commons.math.geometry;
import java.io.Serializable;
/**
* This class implements vectors in a three-dimensional space.
* <p>
* Instance of this class are guaranteed to be immutable.
* </p>
*
* @version $Revision: 627998 $ $Date: 2008-02-15 03:24:50 -0700 (Fri, 15 Feb
* 2008) $
* @since 1.2
*/
public class Vector3D implements Serializable {
/** First canonical vector (coordinates: 1, 0, 0). */
public static final Vector3D plusI = new Vector3D(1, 0, 0);
/** Opposite of the first canonical vector (coordinates: -1, 0, 0). */
public static final Vector3D minusI = new Vector3D(-1, 0, 0);
/** Second canonical vector (coordinates: 0, 1, 0). */
public static final Vector3D plusJ = new Vector3D(0, 1, 0);
/** Opposite of the second canonical vector (coordinates: 0, -1, 0). */
public static final Vector3D minusJ = new Vector3D(0, -1, 0);
/** Third canonical vector (coordinates: 0, 0, 1). */
public static final Vector3D plusK = new Vector3D(0, 0, 1);
/** Opposite of the third canonical vector (coordinates: 0, 0, -1). */
public static final Vector3D minusK = new Vector3D(0, 0, -1);
/** Null vector (coordinates: 0, 0, 0). */
public static final Vector3D zero = new Vector3D(0, 0, 0);
/**
* Simple constructor. Build a null vector.
*/
public Vector3D() {
x = 0;
y = 0;
z = 0;
}
/**
* Simple constructor. Build a vector from its coordinates
*
* @param x
* abscissa
* @param y
* ordinate
* @param z
* height
* @see #getX()
* @see #getY()
* @see #getZ()
*/
public Vector3D(final double x, final double y, final double z) {
this.x = x;
this.y = y;
this.z = z;
}
/**
* Simple constructor. Build a vector from its azimuthal coordinates
*
* @param alpha
* azimuth (α) around Z (0 is +X, π/2 is +Y, π is -X
* and 3π/2 is -Y)
* @param delta
* elevation (δ) above (XY) plane, from -π/2 to +π/2
* @see #getAlpha()
* @see #getDelta()
*/
public Vector3D(final double alpha, final double delta) {
final double cosDelta = Math.cos(delta);
this.x = Math.cos(alpha) * cosDelta;
this.y = Math.sin(alpha) * cosDelta;
this.z = Math.sin(delta);
}
/**
* Multiplicative constructor Build a vector from another one and a scale
* factor. The vector built will be a * u
*
* @param a
* scale factor
* @param u
* base (unscaled) vector
*/
public Vector3D(final double a, final Vector3D u) {
this.x = a * u.x;
this.y = a * u.y;
this.z = a * u.z;
}
/**
* Linear constructor Build a vector from two other ones and corresponding
* scale factors. The vector built will be a1 * u1 + a2 * u2
*
* @param a1
* first scale factor
* @param u1
* first base (unscaled) vector
* @param a2
* second scale factor
* @param u2
* second base (unscaled) vector
*/
public Vector3D(final double a1, final Vector3D u1, final double a2, final Vector3D u2) {
this.x = a1 * u1.x + a2 * u2.x;
this.y = a1 * u1.y + a2 * u2.y;
this.z = a1 * u1.z + a2 * u2.z;
}
/**
* Linear constructor Build a vector from three other ones and corresponding
* scale factors. The vector built will be a1 * u1 + a2 * u2 + a3 * u3
*
* @param a1
* first scale factor
* @param u1
* first base (unscaled) vector
* @param a2
* second scale factor
* @param u2
* second base (unscaled) vector
* @param a3
* third scale factor
* @param u3
* third base (unscaled) vector
*/
public Vector3D(final double a1, final Vector3D u1, final double a2,
final Vector3D u2, final double a3, final Vector3D u3) {
this.x = a1 * u1.x + a2 * u2.x + a3 * u3.x;
this.y = a1 * u1.y + a2 * u2.y + a3 * u3.y;
this.z = a1 * u1.z + a2 * u2.z + a3 * u3.z;
}
/**
* Linear constructor Build a vector from four other ones and corresponding
* scale factors. The vector built will be a1 * u1 + a2 * u2 + a3 * u3 + a4
* * u4
*
* @param a1
* first scale factor
* @param u1
* first base (unscaled) vector
* @param a2
* second scale factor
* @param u2
* second base (unscaled) vector
* @param a3
* third scale factor
* @param u3
* third base (unscaled) vector
* @param a4
* fourth scale factor
* @param u4
* fourth base (unscaled) vector
*/
public Vector3D(final double a1, final Vector3D u1, final double a2,
final Vector3D u2, final double a3, final Vector3D u3, final double a4,
final Vector3D u4) {
this.x = a1 * u1.x + a2 * u2.x + a3 * u3.x + a4 * u4.x;
this.y = a1 * u1.y + a2 * u2.y + a3 * u3.y + a4 * u4.y;
this.z = a1 * u1.z + a2 * u2.z + a3 * u3.z + a4 * u4.z;
}
/**
* Get the abscissa of the vector.
*
* @return abscissa of the vector
* @see #Vector3D(double, double, double)
*/
public double getX() {
return x;
}
/**
* Get the ordinate of the vector.
*
* @return ordinate of the vector
* @see #Vector3D(double, double, double)
*/
public double getY() {
return y;
}
/**
* Get the height of the vector.
*
* @return height of the vector
* @see #Vector3D(double, double, double)
*/
public double getZ() {
return z;
}
/**
* Get the norm for the vector.
*
* @return euclidian norm for the vector
*/
public double getNorm() {
return Math.sqrt(x * x + y * y + z * z);
}
/**
* Get the azimuth of the vector.
*
* @return azimuth (α) of the vector, between -π and +π
* @see #Vector3D(double, double)
*/
public double getAlpha() {
return Math.atan2(y, x);
}
/**
* Get the elevation of the vector.
*
* @return elevation (δ) of the vector, between -π/2 and +π/2
* @see #Vector3D(double, double)
*/
public double getDelta() {
return Math.asin(z / getNorm());
}
/**
* Add a vector to the instance.
*
* @param v
* vector to add
* @return a new vector
*/
public Vector3D add(final Vector3D v) {
return new Vector3D(x + v.x, y + v.y, z + v.z);
}
/**
* Add a scaled vector to the instance.
*
* @param factor
* scale factor to apply to v before adding it
* @param v
* vector to add
* @return a new vector
*/
public Vector3D add(final double factor, final Vector3D v) {
return new Vector3D(x + factor * v.x, y + factor * v.y, z + factor * v.z);
}
/**
* Subtract a vector from the instance.
*
* @param v
* vector to subtract
* @return a new vector
*/
public Vector3D subtract(final Vector3D v) {
return new Vector3D(x - v.x, y - v.y, z - v.z);
}
/**
* Subtract a scaled vector from the instance.
*
* @param factor
* scale factor to apply to v before subtracting it
* @param v
* vector to subtract
* @return a new vector
*/
public Vector3D subtract(final double factor, final Vector3D v) {
return new Vector3D(x - factor * v.x, y - factor * v.y, z - factor * v.z);
}
/**
* Get a normalized vector aligned with the instance.
*
* @return a new normalized vector
* @exception ArithmeticException
* if the norm is zero
*/
public Vector3D normalize() {
final double s = getNorm();
if (s == 0) {
throw new ArithmeticException("cannot normalize a zero norm vector");
}
return scalarMultiply(1 / s);
}
/**
* Get a vector orthogonal to the instance.
* <p>
* There are an infinite number of normalized vectors orthogonal to the
* instance. This method picks up one of them almost arbitrarily. It is
* useful when one needs to compute a reference frame with one of the axes
* in a predefined direction. The following example shows how to build a
* frame having the k axis aligned with the known vector u :
*
* <pre>
* <code>
* Vector3D k = u.normalize();
* Vector3D i = k.orthogonal();
* Vector3D j = Vector3D.crossProduct(k, i);
* </code>
* </pre>
*
* </p>
*
* @return a new normalized vector orthogonal to the instance
* @exception ArithmeticException
* if the norm of the instance is null
*/
public Vector3D orthogonal() {
final double threshold = 0.6 * getNorm();
if (threshold == 0) {
throw new ArithmeticException("null norm");
}
if ((x >= -threshold) && (x <= threshold)) {
final double inverse = 1 / Math.sqrt(y * y + z * z);
return new Vector3D(0, inverse * z, -inverse * y);
} else if ((y >= -threshold) && (y <= threshold)) {
final double inverse = 1 / Math.sqrt(x * x + z * z);
return new Vector3D(-inverse * z, 0, inverse * x);
}
final double inverse = 1 / Math.sqrt(x * x + y * y);
return new Vector3D(inverse * y, -inverse * x, 0);
}
/**
* Compute the angular separation between two vectors.
* <p>
* This method computes the angular separation between two vectors using the
* dot product for well separated vectors and the cross product for almost
* aligned vectors. This allow to have a good accuracy in all cases, even
* for vectors very close to each other.
* </p>
*
* @param v1
* first vector
* @param v2
* second vector
* @return angular separation between v1 and v2
* @exception ArithmeticException
* if either vector has a null norm
*/
public static double angle(final Vector3D v1, final Vector3D v2) {
final double normProduct = v1.getNorm() * v2.getNorm();
if (normProduct == 0) {
throw new ArithmeticException("null norm");
}
final double dot = dotProduct(v1, v2);
final double threshold = normProduct * 0.9999;
if ((dot < -threshold) || (dot > threshold)) {
// the vectors are almost aligned, compute using the sine
final Vector3D v3 = crossProduct(v1, v2);
if (dot >= 0) {
return Math.asin(v3.getNorm() / normProduct);
}
return Math.PI - Math.asin(v3.getNorm() / normProduct);
}
// the vectors are sufficiently separated to use the cosine
return Math.acos(dot / normProduct);
}
/**
* Get the opposite of the instance.
*
* @return a new vector which is opposite to the instance
*/
public Vector3D negate() {
return new Vector3D(-x, -y, -z);
}
/**
* Multiply the instance by a scalar
*
* @param a
* scalar
* @return a new vector
*/
public Vector3D scalarMultiply(final double a) {
return new Vector3D(a * x, a * y, a * z);
}
/**
* Compute the dot-product of two vectors.
*
* @param v1
* first vector
* @param v2
* second vector
* @return the dot product v1.v2
*/
public static double dotProduct(final Vector3D v1, final Vector3D v2) {
return v1.x * v2.x + v1.y * v2.y + v1.z * v2.z;
}
/**
* Compute the cross-product of two vectors.
*
* @param v1
* first vector
* @param v2
* second vector
* @return the cross product v1 ^ v2 as a new Vector
*/
public static Vector3D crossProduct(final Vector3D v1, final Vector3D v2) {
return new Vector3D(v1.y * v2.z - v1.z * v2.y, v1.z * v2.x - v1.x * v2.z, v1.x
* v2.y - v1.y * v2.x);
}
/** Abscissa. */
private final double x;
/** Ordinate. */
private final double y;
/** Height. */
private final double z;
/** Serializable version identifier */
private static final long serialVersionUID = -5721105387745193385L;
}