jsky.coords
Class Cotr

java.lang.Object
  jsky.coords.Cotr

public class Cotr
extends java.lang.Object

Based on C routintes by Francois Ochsenbein [ESO-IPG].

The static methods provided in this class all deal with coordinate transformations. All spherical coordinates are assumed to be expressed in DEGREES. No function is traced. The parameter mnemonics are:

o

array [alpha, delta] of spherical coordinates, expressed in degrees.

R

3 x 3 Rotation (orthogonal) matrix from old to new coordinate frame

u

vector[x,y,z] of Unit (cosine) direction (x^2+y^2+z^2=1)

Constructor Summary

Cotr()

Method Summary

static void	tr_Euler(double[] euler_angles, double[][] R) Compute the rotation matrix from Euler angles (z, theta, zeta).
static void	tr_oo(double[] o, double[] o2, double[][] R) Rotate polar coordinates using an R rotation matrix (old to new frame) and unit vectors.
static void	tr_oo1(double[] o, double[] o2, double[][] R) Rotate polar coordinates, using the inversed R matrix (new to old frame).
static void	tr_oR(double[] o, double[][] R) Creates the rotation matrix R[3][3].
static void	tr_ou(double[] o, double[] u) Transformation from polar coordinates to Unit vector.
static void	tr_RR(double[][] A, double[][] B, double[][] R) Product of orthogonal matrices B = R * A.
static void	tr_RR1(double[][] A, double[][] B, double[][] R) Product of orthogonal matrices B = R^{-1} * A.
static void	tr_uo(double[] u, double[] o) Computes angles from direction cosines.
static void	tr_uR(double[] u, double[][] R) Creates the rotation matrix.
static void	tr_uu(double[] u1, double[] u2, double[][] R) Rotates the unit vector u1 to u2, as u_2 = R * u_1 (old to new frame)
static void	tr_uu1(double[] u1, double[] u2, double[][] R) Rotates the unit vector u1 to u2, as u_2 = R^{-1} * u_1 (new to old frame).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Cotr

public Cotr()

Method Detail

tr_Euler

public static void tr_Euler(double[] euler_angles,
                            double[][] R)

Compute the rotation matrix from Euler angles (z, theta, zeta). This rotation matrix is actually defined by R = R_z(-z) * R_y(theta) * R_z(-zeta) (from old to new frame).

Parameters:

euler_angles - IN: Euler angles (z, theta, zeta)

R - OUT: rotation matrix

tr_oo

public static void tr_oo(double[] o,
                         double[] o2,
                         double[][] R)

Rotate polar coordinates using an R rotation matrix (old to new frame) and unit vectors.

Parameters:

o - IN: Original angles

o2 - OUT: rotated angles

R - IN: Rotation matrix

tr_oo1

public static void tr_oo1(double[] o,
                          double[] o2,
                          double[][] R)

Rotate polar coordinates, using the inversed R matrix (new to old frame). Use unit vectors

Parameters:

o - IN: Original angles

o2 - OUT: rotated angles

R - IN: Rotation matrix

tr_oR

public static void tr_oR(double[] o,
                         double[][] R)

Creates the rotation matrix R[3][3]. R[3][3] is defined as:

R[0]

(first row) = unit vector towards Zenith

R[1]

(second row) = unit vector towards East

R[2]

(third row) = unit vector towards North

The resulting R matrix can then be used to get the components of a vector v in the local frame.

Parameters:

o - IN: original angles

R - OUT: rotation matrix

tr_ou

public static void tr_ou(double[] o,
                         double[] u)

Transformation from polar coordinates to Unit vector.

Parameters:

o - IN: angles ra + dec in degrees

u - OUT: dir cosines

tr_uo

public static void tr_uo(double[] u,
                         double[] o)

Computes angles from direction cosines.

Parameters:

u - IN: Dir cosines

o - OUT: Angles ra + dec in degrees

tr_uR

public static void tr_uR(double[] u,
                         double[][] R)

Creates the rotation matrix. Creates the rotation matrix R[3][3] with

R[0]

(first row) = unit vector towards Zenith

R[1]

(second row) = unit vector towards East

R[2]

(third row) = unit vector towards North

For the poles,(|z|=1), the rotation axis is assumed be the y axis, i.e. the right ascension is assumed to be 0.

Parameters:

u - IN: Original direction

R - OUT: Rotation matrix

tr_uu

public static void tr_uu(double[] u1,
                         double[] u2,
                         double[][] R)

Rotates the unit vector u1 to u2, as u_2 = R * u_1 (old to new frame)

Parameters:

u1 - IN: Unit vector

u2 - OUT: Resulting unit vector after rotation

R - IN: rotation matrix (e.g. created by tr_oR)

tr_uu1

public static void tr_uu1(double[] u1,
                          double[] u2,
                          double[][] R)

Rotates the unit vector u1 to u2, as u_2 = R^{-1} * u_1 (new to old frame).

Parameters:

u1 - IN: Unit vector

u2 - OUT: Resulting unit vector after rotation

R - IN: rotation matrix (e.g. created by tr_oR)

tr_RR

public static void tr_RR(double[][] A,
                         double[][] B,
                         double[][] R)

Product of orthogonal matrices B = R * A.

Parameters:

A - IN: First Matrix

B - OUT: Result Matrix

R - IN: Rotation Matrix

tr_RR1

public static void tr_RR1(double[][] A,
                          double[][] B,
                          double[][] R)

Product of orthogonal matrices B = R^{-1} * A.

Parameters:

A - IN: First Matrix

B - OUT: Result Matrix

R - IN: Rotation Matrix