package org.spaceroots.mantissa.geometry;
import java.io.Serializable;
/** This class implements vectors in a three-dimensional space.
* Instance of this class are guaranteed to be immutable.
* @version $Id: Vector3D.java 1716 2006-12-13 22:56:35Z luc $
* @author L. Maisonobe
*/
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);
/** 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(double x, double y, 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(double alpha, double delta) {
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(double a, 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(double a1, Vector3D u1, double a2, 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(double a1, Vector3D u1, double a2, Vector3D u2,
double a3, 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(double a1, Vector3D u1, double a2, Vector3D u2,
double a3, Vector3D u3, double a4, 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(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(double factor, 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(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(double factor, Vector3D v) {
return new Vector3D(x - factor * v.x, y - factor * v.y, z - factor * v.z);
}
/** Normalize the instance.
* @return a new normalized vector
* @exception ArithmeticException if the norm is null
*/
public Vector3D normalize() {
double s = getNorm();
if (s == 0) {
throw new ArithmeticException("null norm");
}
return multiply(1 / s);
}
/** Get a vector orthogonal to the instance.
* 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 :
*
* Vector3D k = u.normalize();
* Vector3D i = k.orthogonal();
* Vector3D j = Vector3D.crossProduct(k, i);
*
* @return a new normalized vector orthogonal to the instance
* @exception ArithmeticException if the norm of the instance is null
*/
public Vector3D orthogonal() {
double threshold = 0.6 * getNorm();
if (threshold == 0) {
throw new ArithmeticException("null norm");
}
if ((x >= -threshold) && (x <= threshold)) {
double inverse = 1 / Math.sqrt(y * y + z * z);
return new Vector3D(0, inverse * z, -inverse * y);
} else if ((y >= -threshold) && (y <= threshold)) {
double inverse = 1 / Math.sqrt(x * x + z * z);
return new Vector3D(-inverse * z, 0, inverse * x);
} else {
double inverse = 1 / Math.sqrt(x * x + y * y);
return new Vector3D(inverse * y, -inverse * x, 0);
}
}
/** Compute the angular separation between two vectors.
* 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.
* @param v1 first vector
* @param v2 second vector
* @exception ArithmeticException if either vector has a null norm
*/
public static double angle(Vector3D v1, Vector3D v2) {
double normProduct = v1.getNorm() * v2.getNorm();
if (normProduct == 0) {
throw new ArithmeticException("null norm");
}
double dot = dotProduct(v1, v2);
double threshold = normProduct * 0.9999;
if ((dot < -threshold) || (dot > threshold)) {
// the vectors are almost aligned, compute using the sine
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 multiply(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(Vector3D v1, 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(Vector3D v1, 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;
private static final long serialVersionUID = 7318440192750283659L;
}
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