esraMath
Class Geometry

java.lang.Object
  esraMath.Geometry

public class Geometry

extends java.lang.Object

Author:

vincent

Constructor Summary

Geometry()

Method Summary

static double	angle(double[] aa, double[] bb, double[] cc)
static double[]	centerOfGeometry(double[][] positions, double[] weights) Compute the center of geometry of a set of 3D-coordinates and massses.
static double	dihedral(double[] ii, double[] jj, double[] kk, double[] ll) The dihedral angle following IUPAC-IUB convention.
static double	distance(double[] aa, double[] bb)
static double	fitAndRmsd(double[][] posA, double[][] posB, double[] weights) fit two structures and compute the rmsd.
static double[][]	inertiaTensor(double[][] coords, double[] weights) Compute the inertia tensor for a set of 3D-coordinates with masses.
static double	iupac2math(double iupacDihedral) Transform a IUPAC dihedral angle into a dihedral angle following the mathematical standard conventions: a counterclockwise rotation is positive; default ranges go from [0, 2pi]
static double[][]	lineRotationMatrix(double[] p, double[] d, double angle) Build rotation matrix for (counterclockwise) rotation around an arbitary line, using a point and a direction from that point on the line.
static double	rgyr(double[][] positions, double[] masses)
static double	rmsd(double[][] posA, double[][] posB)
static double	rmsd(double[][] posA, double[][] posB, double[] weights)
static double[][]	rotate(double[][] rotMatrix, double[][] coords) Rotate point using a supplied rotationmatrix.
static double[][]	rotateAndShift(double[][] rotMatrix, double[][] coords) Rotate point using a supplied rotationmatrix.

Methods inherited from class java.lang.Object

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

Constructor Detail

Geometry

public Geometry()

Method Detail

distance

public static double distance(double[] aa,
                              double[] bb)

Parameters:

aa -

bb -

Returns:

the distance between two position vectors aa and bb

angle

public static double angle(double[] aa,
                           double[] bb,
                           double[] cc)

Parameters:

aa - first position

bb - second (center) position

cc - third position

Returns:

the (minimum) angle (radians) formed by three positions aa, bb and cc, with bb being the central point.

dihedral

public static double dihedral(double[] ii,
                              double[] jj,
                              double[] kk,
                              double[] ll)

The dihedral angle following IUPAC-IUB convention.

Biochemistry, 9, (1970) 3471.
http://www.iupac.org/goldbook/T06406.pdf

• a clockwise rotation is positive;
• default ranges go from [-pi, pi]

Parameters:

ii -

jj -

kk -

ll -

Returns:

the dihedral angle formed by four positions ii, jj, kk, ll, in that order.

iupac2math

public static double iupac2math(double iupacDihedral)

Transform a IUPAC dihedral angle into a dihedral angle following the mathematical standard conventions:

• a counterclockwise rotation is positive;
• default ranges go from [0, 2pi]

Parameters:

iupacDihedral -

Returns:

the new dihedral in the range [0, 2 pi]

centerOfGeometry

public static double[] centerOfGeometry(double[][] positions,
                                        double[] weights)

Compute the center of geometry of a set of 3D-coordinates and massses.

Parameters:

positions - the coordinates

weights - the weights associated with the coordinates

Returns:

the center of mass (3-vector)

rgyr

public static double rgyr(double[][] positions,
                          double[] masses)

Parameters:

positions -

masses -

Returns:

the radius of gyration of the system

rmsd

public static double rmsd(double[][] posA,
                          double[][] posB)

Parameters:

posA - first positions

posB - second positions

Returns:

rmsd

rmsd

public static double rmsd(double[][] posA,
                          double[][] posB,
                          double[] weights)

Parameters:

posA - first positions

posB - second positions

weights - weightings (e.g. masses)

Returns:

rmsd

fitAndRmsd

public static double fitAndRmsd(double[][] posA,
                                double[][] posB,
                                double[] weights)

fit two structures and compute the rmsd. perform a minimal root-mean-square-distance rototranslational fit and return the corresponding RMSD. equivalent to, but should be faster than, first performing a fit and then calculating the rmsd.

Parameters:

posA - first positions

posB - second positions

weights - weightings (e.g. masses)

Returns:

rmsd

inertiaTensor

public static double[][] inertiaTensor(double[][] coords,
                                       double[] weights)

Compute the inertia tensor for a set of 3D-coordinates with masses.

Parameters:

coords - the coordinates used

weights - the weights associated with the coordinates

Returns:

the inertia tensor (3 x 3 matrix)

lineRotationMatrix

public static double[][] lineRotationMatrix(double[] p,
                                            double[] d,
                                            double angle)

Build rotation matrix for (counterclockwise) rotation around an arbitary line, using a point and a direction from that point on the line.

Parameters:

p - point on line (e.g. origin: 0,0,0)

d - line direction (e.g. z-axis: 0 0 1)

angle - rotation angle in radians (e.g. Math.PI = 180 degrees)

Returns:

rotation/translation matrix

rotate

public static double[][] rotate(double[][] rotMatrix,
                                double[][] coords)

Rotate point using a supplied rotationmatrix.

Parameters:

rotMatrix - rotation matrix

coords - the coordinates to rotate

Returns:

rotated coordinates

rotateAndShift

public static double[][] rotateAndShift(double[][] rotMatrix,
                                        double[][] coords)

Rotate point using a supplied rotationmatrix.

Parameters:

rotMatrix - rotation matrix

coords - the coordinates to rotate

Returns:

rotated coordinates