Module com.marginallyclever.robotoverlord

Package com.marginallyclever.convenience.helpers

Class MatrixHelper

java.lang.Object

com.marginallyclever.convenience.helpers.MatrixHelper

public class MatrixHelper
extends Object

Convenience methods for matrixes

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	MatrixHelper.EulerSequence

Constructor Summary

Constructors

Constructor	Description
MatrixHelper()

Method Summary

Modifier and Type	Method	Description
static javax.vecmath.Matrix4d	createIdentityMatrix4()
static Mesh	createMesh()
static javax.vecmath.Matrix4d	createScaleMatrix4(double scale)
static void	diagonalize(javax.vecmath.Matrix3d a, javax.vecmath.Matrix3d dOut, javax.vecmath.Matrix3d qOut)	returns Q and D such that Diagonal matrix D = QT * A * Q; and A = Q*D*QT see Jacobi_eigenvalue_algorithm see Diagonalization
static javax.vecmath.Matrix3d	eulerToMatrix(javax.vecmath.Vector3d radians, MatrixHelper.EulerSequence sequenceIndex)	Converts Euler angles to a rotation matrix based on the specified Euler sequence.
static double[]	getCartesianBetweenTwoMatrices(javax.vecmath.Matrix4d mStart, javax.vecmath.Matrix4d mEnd)	Use Quaternions to estimate the distance between two matrixes (both linear and rotational).
static void	getCartesianBetweenTwoMatrices(javax.vecmath.Matrix4d mStart, javax.vecmath.Matrix4d mEnd, double[] listOut)	Use Quaternions to estimate the distance between two matrixes (both linear and rotational).
static javax.vecmath.Matrix3d	getMatrixFromAxisAndRotation(javax.vecmath.Vector3d axis, double degrees)	see Wikipedia
static javax.vecmath.Vector3d	getPosition(javax.vecmath.Matrix4d m)
static javax.vecmath.Vector3d	getXAxis(javax.vecmath.Matrix4d m)
static Plane	getXYPlane(javax.vecmath.Matrix4d pivot)
static javax.vecmath.Vector3d	getYAxis(javax.vecmath.Matrix4d m)
static javax.vecmath.Vector3d	getZAxis(javax.vecmath.Matrix4d m)
static boolean	interpolate(javax.vecmath.Matrix4d start, javax.vecmath.Matrix4d end, double alpha, javax.vecmath.Matrix4d result)	Interpolate between two 4d matrixes, (end-start)*i + start where i=[0...1]
static javax.vecmath.Matrix3d	lookAt(javax.vecmath.Vector3d from, javax.vecmath.Vector3d to)	Build a "look at" matrix.
static javax.vecmath.Matrix4d	lookAt(javax.vecmath.Vector3d from, javax.vecmath.Vector3d to, javax.vecmath.Vector3d up)	Build a "look at" matrix.
static javax.vecmath.Vector3d	matrixToEuler(javax.vecmath.Matrix3d mat, MatrixHelper.EulerSequence sequenceIndex)	Assumes the rotational component is a valid rotation matrix.
static javax.vecmath.Vector3d	matrixToEuler(javax.vecmath.Matrix4d mat, MatrixHelper.EulerSequence sequenceIndex)	Convenience method to call matrixToEuler() with only the rotational component.
static void	normalize3(javax.vecmath.Matrix4d mTarget)	normalize the 3x3 component of the mTarget matrix.
static javax.vecmath.Matrix4d	orthographicMatrix4d(double left, double right, double bottom, double top, double near, double far)	Generate an orthographic matrix.
static javax.vecmath.Matrix4d	perspectiveMatrix4d(double fovY, double aspect, double near, double far)	Generate a perspective matrix.
static javax.vecmath.Matrix4d	setOrthographicFiniteFar(double left, double right, double bottom, double top, double near, double far)	Generate an orthographic matrix where near is -1 and far is 1.
static javax.vecmath.Matrix4d	setOrthographicInfiniteFar(double left, double right, double bottom, double top, double near)	Generate a reverse-distance orthographic matrix where near items are 1 and far items are 0.
static javax.vecmath.Matrix4d	setPerspectiveFiniteFar(double fovY, double aspect, double near, double far)	Generate a perspective matrix where near items are -1 and far items are +1.
static javax.vecmath.Matrix4d	setPerspectiveFiniteFarAdvanced(double fovY, double aspect, double near, double far)	Generate a perspective matrix where near items are -1 and far items are +1.
static javax.vecmath.Matrix4d	setPerspectiveFiniteFarSimplified(double fovY, double aspect, double near, double far)	Generate a perspective matrix where near items are -1 and far items are +1.
static javax.vecmath.Matrix4d	setPerspectiveInfiniteFar(double fovY, double aspect, double near)	Generate the reverse perspective matrix, where near items are 1 and far items are 0.
static void	setPosition(javax.vecmath.Matrix4d m, javax.vecmath.Vector3d v)
static void	setXAxis(javax.vecmath.Matrix4d m, javax.vecmath.Vector3d v)
static void	setYAxis(javax.vecmath.Matrix4d m, javax.vecmath.Vector3d v)
static void	setZAxis(javax.vecmath.Matrix4d m, javax.vecmath.Vector3d v)

Methods inherited from class java.lang.Object

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

Constructor Details

MatrixHelper

public MatrixHelper()

Method Details

createScaleMatrix4

public static javax.vecmath.Matrix4d createScaleMatrix4(double scale)

createMesh

public static Mesh createMesh()

matrixToEuler

public static javax.vecmath.Vector3d matrixToEuler(javax.vecmath.Matrix4d mat,
 MatrixHelper.EulerSequence sequenceIndex)

Convenience method to call matrixToEuler() with only the rotational component. Assumes the rotational component is a valid rotation matrix. Eulers are using the YXZ convention.

Parameters:

mat - the Matrix4d to convert.

Returns:

a valid Euler solution to the matrix.

matrixToEuler

public static javax.vecmath.Vector3d matrixToEuler(javax.vecmath.Matrix3d mat,
 MatrixHelper.EulerSequence sequenceIndex)

Assumes the rotational component is a valid rotation matrix. Eulers are using the YXZ convention.

Parameters:

mat - the Matrix3d to convert.

sequenceIndex - a MatrixHelper.EulerSequence value.

Returns:

a valid Euler solution to the matrix.

eulerToMatrix

public static javax.vecmath.Matrix3d eulerToMatrix(javax.vecmath.Vector3d radians,
 MatrixHelper.EulerSequence sequenceIndex)

Converts Euler angles to a rotation matrix based on the specified Euler sequence. See also ...

Parameters:

radians - radian rotation values

sequenceIndex - a MatrixHelper.EulerSequence value

Returns:

resulting matrix

interpolate

public static boolean interpolate(javax.vecmath.Matrix4d start,
 javax.vecmath.Matrix4d end,
 double alpha,
 javax.vecmath.Matrix4d result)

Interpolate between two 4d matrixes, (end-start)*i + start where i=[0...1]

Parameters:

start - start matrix

end - end matrix

alpha - double value in the range [0...1]

result - where to store the resulting matrix

Returns:

True if the operation succeeds. False if the inputs are bad or the operation fails.

lookAt

public static javax.vecmath.Matrix3d lookAt(javax.vecmath.Vector3d from,
 javax.vecmath.Vector3d to)

Build a "look at" matrix. The forward axis is pointing (to-from) normalized. The up starts as (0,0,1). left axis is cross product of up and forward. forward is then recalculated as the cross product of left and up.

This will fail if forward is parallel to up.

Parameters:

from - where i'm at

to - what I'm looking at

Returns:

a matrix that will transform a point to the "look at" orientation

lookAt

public static javax.vecmath.Matrix4d lookAt(javax.vecmath.Vector3d from,
 javax.vecmath.Vector3d to,
 javax.vecmath.Vector3d up)

Build a "look at" matrix. The X+ axis is pointing (to-from) normalized. The Z+ starts as pointing up. Y+ is cross product of X and Z. Z is then recalculated based on the correct X and Y. This will fail if to-from is parallel to up.

Parameters:

from - where i'm at

to - what I'm looking at

Returns:

a matrix that will transform a point to the "look at" orientation

getXAxis

public static javax.vecmath.Vector3d getXAxis(javax.vecmath.Matrix4d m)

getYAxis

public static javax.vecmath.Vector3d getYAxis(javax.vecmath.Matrix4d m)

getZAxis

public static javax.vecmath.Vector3d getZAxis(javax.vecmath.Matrix4d m)

getPosition

public static javax.vecmath.Vector3d getPosition(javax.vecmath.Matrix4d m)

setXAxis

public static void setXAxis(javax.vecmath.Matrix4d m,
 javax.vecmath.Vector3d v)

setYAxis

public static void setYAxis(javax.vecmath.Matrix4d m,
 javax.vecmath.Vector3d v)

setZAxis

public static void setZAxis(javax.vecmath.Matrix4d m,
 javax.vecmath.Vector3d v)

setPosition

public static void setPosition(javax.vecmath.Matrix4d m,
 javax.vecmath.Vector3d v)

normalize3

public static void normalize3(javax.vecmath.Matrix4d mTarget)

normalize the 3x3 component of the mTarget matrix. Do not affect position.

Parameters:

mTarget - the matrix that will be normalized.

createIdentityMatrix4

public static javax.vecmath.Matrix4d createIdentityMatrix4()

getMatrixFromAxisAndRotation

public static javax.vecmath.Matrix3d getMatrixFromAxisAndRotation(javax.vecmath.Vector3d axis,
 double degrees)

see Wikipedia

Parameters:

axis - a normalized vector

degrees - angle in degrees

Returns:

a rotation matrix

diagonalize

public static void diagonalize(javax.vecmath.Matrix3d a,
 javax.vecmath.Matrix3d dOut,
 javax.vecmath.Matrix3d qOut)

returns Q and D such that Diagonal matrix D = QT * A * Q; and A = Q*D*QT see Jacobi_eigenvalue_algorithm see Diagonalization

Parameters:

a - a symmetric matrix.

dOut - where to store the results

qOut - where to store the results

getCartesianBetweenTwoMatrices

public static double[] getCartesianBetweenTwoMatrices(javax.vecmath.Matrix4d mStart,
 javax.vecmath.Matrix4d mEnd)

Use Quaternions to estimate the distance between two matrixes (both linear and rotational).

Parameters:

mStart - matrix of start pose

mEnd - matrix of end pose

Returns:

6 doubles that will be filled with the XYZ translation and RPY rotation.

getCartesianBetweenTwoMatrices

public static void getCartesianBetweenTwoMatrices(javax.vecmath.Matrix4d mStart,
 javax.vecmath.Matrix4d mEnd,
 double[] listOut)

Use Quaternions to estimate the distance between two matrixes (both linear and rotational).

Parameters:

mStart - matrix of start pose

mEnd - matrix of end pose

listOut - a double[6] to store the result. Must not be null.

getXYPlane

public static Plane getXYPlane(javax.vecmath.Matrix4d pivot)

Parameters:

pivot - the matrix to use as the origin.

Returns:

a Plane that is parallel to the XY plane and passes through the origin.

orthographicMatrix4d

public static javax.vecmath.Matrix4d orthographicMatrix4d(double left,
 double right,
 double bottom,
 double top,
 double near,
 double far)

Generate an orthographic matrix.

Parameters:

left - pixels

right - pixels

bottom - pixels

top - pixels

near - distance

far - distance

Returns:

a matrix

setOrthographicFiniteFar

public static javax.vecmath.Matrix4d setOrthographicFiniteFar(double left,
 double right,
 double bottom,
 double top,
 double near,
 double far)

Generate an orthographic matrix where near is -1 and far is 1.

Parameters:

left - pixels

right - pixels

bottom - pixels

top - pixels

near - distance

far - distance

Returns:

a matrix

setOrthographicInfiniteFar

public static javax.vecmath.Matrix4d setOrthographicInfiniteFar(double left,
 double right,
 double bottom,
 double top,
 double near)

Generate a reverse-distance orthographic matrix where near items are 1 and far items are 0.

Parameters:

left - pixels

right - pixels

bottom - pixels

top - pixels

near - distance

Returns:

a matrix

perspectiveMatrix4d

public static javax.vecmath.Matrix4d perspectiveMatrix4d(double fovY,
 double aspect,
 double near,
 double far)

Generate a perspective matrix.

Parameters:

fovY - degrees

aspect - ratio

near - distance

far - distance

Returns:

a matrix

setPerspectiveFiniteFar

public static javax.vecmath.Matrix4d setPerspectiveFiniteFar(double fovY,
 double aspect,
 double near,
 double far)

Generate a perspective matrix where near items are -1 and far items are +1.

Parameters:

fovY - degrees

aspect - ratio

near - distance

far - distance

Returns:

a matrix

setPerspectiveFiniteFarSimplified

public static javax.vecmath.Matrix4d setPerspectiveFiniteFarSimplified(double fovY,
 double aspect,
 double near,
 double far)

Generate a perspective matrix where near items are -1 and far items are +1.

Parameters:

fovY - degrees

aspect - ratio

near - distance

far - distance

Returns:

a matrix

setPerspectiveFiniteFarAdvanced

public static javax.vecmath.Matrix4d setPerspectiveFiniteFarAdvanced(double fovY,
 double aspect,
 double near,
 double far)

Generate a perspective matrix where near items are -1 and far items are +1. This version could more easily be tweaked to adjust left/right for stereoscopic rendering.

Parameters:

fovY - degrees

aspect - ratio

near - distance

far - distance

Returns:

a matrix

setPerspectiveInfiniteFar

public static javax.vecmath.Matrix4d setPerspectiveInfiniteFar(double fovY,
 double aspect,
 double near)

Generate the reverse perspective matrix, where near items are 1 and far items are 0.

Parameters:

fovY - degrees

aspect - ratio

near - distance

Returns:

a matrix