Package gaiasky.util.math

Class Matrix4d

java.lang.Object
gaiasky.util.math.Matrix4d
All Implemented Interfaces:
Serializable
public class Matrix4d extends Object implements Serializable
Encapsulates a column major 4 by 4 matrix. Like the Vector3d class it allows the chaining of methods by returning a reference to itself. For example: 
 Matrix4d mat = new Matrix4d().trn(position).mul(camera.combined);
See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final int
    M00
    XX: Typically the unrotated X component for scaling, also the cosine of the angle when rotated on the Y and/or Z axis.
    static final int
    M01
    XY: Typically the negative sine of the angle when rotated on the Z axis.
    static final int
    M02
    XZ: Typically the sine of the angle when rotated on the Y axis.
    static final int
    M03
    XW: Typically the translation of the X component.
    static final int
    M10
    YX: Typically the sine of the angle when rotated on the Z axis.
    static final int
    M11
    YY: Typically the unrotated Y component for scaling, also the cosine of the angle when rotated on the X and/or Z axis.
    static final int
    M12
    YZ: Typically the negative sine of the angle when rotated on the X axis.
    static final int
    M13
    YW: Typically the translation of the Y component.
    static final int
    M20
    ZX: Typically the negative sine of the angle when rotated on the Y axis.
    static final int
    M21
    ZY: Typical the sine of the angle when rotated on the X axis.
    static final int
    M22
    ZZ: Typically the unrotated Z component for scaling, also the cosine of the angle when rotated on the X and/or Y axis.
    static final int
    M23
    ZW: Typically the translation of the Z component.
    static final int
    M30
    WX: Typically the value zero.
    static final int
    M31
    WY: Typically the value zero.
    static final int
    M32
    WZ: Typically the value zero.
    static final int
    M33
    WW: Typically the value one.
    static final double[]
    stmp
     
    final double[]
    tmp
     
    final double[]
    val
     

  • Constructor Summary

    Constructors
    Constructor
    Description
    Matrix4d()
    Constructs an identity matrix
    Matrix4d(double[] values)
    Constructs a matrix from the given double array.
    Matrix4d(float[] values)
     
    Matrix4d(Matrix4d matrix)
    Constructs a matrix from the given matrix.
    Matrix4d(Quaterniond quaternion)
    Constructs a rotation matrix from the given Quaterniond.
    Matrix4d(Vector3d position, Quaterniond rotation, Vector3d scale)
    Construct a matrix from the given translation, rotation and scale.

  • Method Summary

    Modifier and Type
    Method
    Description
    Vector3d
    addTranslationTo(Vector3d position)
     
    static Matrix4d
    changeOfBasis(double[] x, double[] y, double[] z)
    Constructs a change of basis from the canonical basis to the base defined by the given x, y and z vectors.
    static Matrix4d
    changeOfBasis(Vector3d x, Vector3d y, Vector3d z)
    Constructs a change of basis from the canonical basis to the base defined by the given x, y and z vectors.
    Matrix4d
    cpy()
     
    double
    det()
     
    double
    det3x3()
     
    void
    extract4x3Matrix(double[] dst)
    Copies the 4x3 upper-left sub-matrix into double array.
    Quaterniond
    getRotation(Quaterniond rotation)
    Gets the rotation of this matrix.
    Quaterniond
    getRotation(Quaterniond rotation, boolean normalizeAxes)
    Gets the rotation of this matrix.
    Vector3d
    getScale(Vector3d scale)
     
    double
    getScaleX()
     
    double
    getScaleXSquared()
     
    double
    getScaleY()
     
    double
    getScaleYSquared()
     
    double
    getScaleZ()
     
    double
    getScaleZSquared()
     
    double[]
    getTranslation()
     
    Vector3d
    getTranslation(Vector3d position)
     
    float[]
    getTranslationf()
     
    void
    getTranslationf(float[] vec)
     
    com.badlogic.gdx.math.Vector3
    getTranslationf(com.badlogic.gdx.math.Vector3 position)
     
    double[]
    getValues()
     
    float[]
    getValuesFloat()
     
    Matrix4d
    idt()
    Sets the matrix to an identity matrix.
    Matrix4d
    inv()
     
    static boolean
    inv(double[] values)
    Computes the inverse of the given matrix.
    Matrix4d
    lerp(Matrix4d matrix, double alpha)
    Linearly interpolates between this matrix and the given matrix mixing by alpha
    static void
    mul(double[] mata, double[] matb)
    Multiplies the matrix mata with matrix matb, storing the result in mata.
    Matrix4d
    mul(Matrix4d matrix)
    Postmultiplies this matrix with the given matrix, storing the result in this matrix.
    Matrix4d
    mulLeft(Matrix4d matrix)
    Premultiplies this matrix with the given matrix, storing the result in this matrix.
    static void
    prj(double[] mat, double[] vec)
    Multiplies the vector with the given matrix, performing a division by w.
    static void
    prj(double[] mat, double[] vecs, int offset, int numVecs, int stride)
    Multiplies the vectors with the given matrix, , performing a division by w.
    com.badlogic.gdx.math.Matrix4
    putIn(com.badlogic.gdx.math.Matrix4 aux)
    Sets the given matrix to this matrix
    Matrix4d
    rotate(double axisX, double axisY, double axisZ, double degrees)
    Postmultiplies this matrix with a (counter-clockwise) rotation matrix.
    Matrix4d
    rotate(Quaterniond rotation)
    Postmultiplies this matrix with a (counter-clockwise) rotation matrix.
    Matrix4d
    rotate(Vector3d axis, double degrees)
    Postmultiplies this matrix with a (counter-clockwise) rotation matrix.
    Matrix4d
    rotate(Vector3d v1, Vector3d v2)
    Postmultiplies this matrix by the rotation between two vectors.
    Matrix4d
    rotateRad(double axisX, double axisY, double axisZ, double radians)
    Postmultiplies this matrix with a (counter-clockwise) rotation matrix.
    Matrix4d
    rotateRad(Vector3d axis, double radians)
    Postmultiplies this matrix with a (counter-clockwise) rotation matrix.
    Matrix4d
    scale(double scaleX, double scaleY, double scaleZ)
    Postmultiplies this matrix with a scale matrix.
    Matrix4d
    scl(double scale)
     
    Matrix4d
    scl(double x, double y, double z)
     
    Matrix4d
    scl(Vector3d scale)
     
    Matrix4d
    set(double[] values)
    Sets the matrix to the given matrix as a double array.
    Matrix4d
    set(double quaternionX, double quaternionY, double quaternionZ, double quaternionW)
    Sets the matrix to a rotation matrix representing the quaternion.
    Matrix4d
    set(double translationX, double translationY, double translationZ, double quaternionX, double quaternionY, double quaternionZ, double quaternionW)
    Sets the matrix to a rotation matrix representing the translation and quaternion.
    Matrix4d
    set(double translationX, double translationY, double translationZ, double quaternionX, double quaternionY, double quaternionZ, double quaternionW, double scaleX, double scaleY, double scaleZ)
    Sets the matrix to a rotation matrix representing the translation and quaternion.
    Matrix4d
    set(float[] values)
     
    Matrix4d
    set(com.badlogic.gdx.math.Matrix3 mat)
    Sets this matrix to the given 3x3 matrix.
    Matrix4d
    set(com.badlogic.gdx.math.Matrix4 matrix)
     
    Matrix4d
    set(Matrix4d matrix)
    Sets the matrix to the given matrix.
    Matrix4d
    set(Quaterniond quaternion)
    Sets the matrix to a rotation matrix representing the quaternion.
    Matrix4d
    set(Vector3d position, Quaterniond orientation)
    Set this matrix to the specified translation and rotation.
    Matrix4d
    set(Vector3d position, Quaterniond orientation, Vector3d scale)
    Set this matrix to the specified translation, rotation and scale.
    Matrix4d
    set(Vector3d xAxis, Vector3d yAxis, Vector3d zAxis, Vector3d pos)
    Sets the four columns of the matrix which correspond to the x-, y- and z-axis of the vector space this matrix creates as well as the 4th column representing the translation of any point that is multiplied by this matrix.
    Matrix4d
    setFromEulerAngles(double yaw, double pitch, double roll)
    Sets this matrix to a rotation matrix from the given euler angles.
    Matrix4d
    setToLookAt(Vector3b direction, Vector3b up)
     
    Matrix4d
    setToLookAt(Vector3b position, Vector3b target, Vector3b up)
     
    Matrix4d
    setToLookAt(Vector3d direction, Vector3d up)
    Sets the matrix to a look at matrix with a direction and an up vector.
    Matrix4d
    setToLookAt(Vector3d position, Vector3d target, Vector3d up)
    Sets this matrix to a look at matrix with the given position, target and up vector.
    Matrix4d
    setToOrtho(double left, double right, double bottom, double top, double near, double far)
    Sets the matrix to an orthographic projection like glOrtho (http://www.opengl.org/sdk/docs/man/xhtml/glOrtho.xml) following the OpenGL equivalent
    Matrix4d
    setToOrtho2D(double x, double y, double width, double height)
    Sets this matrix to an orthographic projection matrix with the origin at (x,y) extending by width and height.
    Matrix4d
    setToOrtho2D(double x, double y, double width, double height, double near, double far)
    Sets this matrix to an orthographic projection matrix with the origin at (x,y) extending by width and height, having a near and far plane.
    Matrix4d
    setToProjection(double near, double far, double fov, double aspectRatio)
    Sets the matrix to a projection matrix with a near- and far plane, a field of view in degrees and an aspect ratio.
    Matrix4d
    setToRotation(double axisX, double axisY, double axisZ, double degrees)
    Sets the matrix to a rotation matrix around the given axis.
    Matrix4d
    setToRotation(double x1, double y1, double z1, double x2, double y2, double z2)
    Set the matrix to a rotation matrix between two vectors.
    Matrix4d
    setToRotation(Vector3d axis, double degrees)
    Sets the matrix to a rotation matrix around the given axis.
    Matrix4d
    setToRotation(Vector3d v1, Vector3d v2)
    Set the matrix to a rotation matrix between two vectors.
    Matrix4d
    setToRotationRad(double axisX, double axisY, double axisZ, double radians)
    Sets the matrix to a rotation matrix around the given axis.
    Matrix4d
    setToRotationRad(Vector3d axis, double radians)
    Sets the matrix to a rotation matrix around the given axis.
    Matrix4d
    setToScaling(double x, double y, double z)
    Sets this matrix to a scaling matrix
    Matrix4d
    setToScaling(Vector3d vector)
    Sets this matrix to a scaling matrix
    Matrix4d
    setToTranslation(double x, double y, double z)
    Sets this matrix to a translation matrix, overwriting it first by an identity matrix and then setting the 4th column to the translation vector.
    Matrix4d
    setToTranslation(com.badlogic.gdx.math.Vector3 vector)
     
    Matrix4d
    setToTranslation(Vector3d vector)
    Sets this matrix to a translation matrix, overwriting it first by an identity matrix and then setting the 4th column to the translation vector.
    Matrix4d
    setToTranslationAndScaling(double translationX, double translationY, double translationZ, double scalingX, double scalingY, double scalingZ)
    Sets this matrix to a translation and scaling matrix by first overwriting it with an identity and then setting the translation vector in the 4th column and the scaling vector in the diagonal.
    Matrix4d
    setToTranslationAndScaling(Vector3d translation, Vector3d scaling)
    Sets this matrix to a translation and scaling matrix by first overwriting it with an identity and then setting the translation vector in the 4th column and the scaling vector in the diagonal.
    Matrix4d
    setToWorld(Vector3d position, Vector3d forward, Vector3d up)
     
    Matrix4d
    setTranslation(double x, double y, double z)
    Sets the 4th column to the translation vector.
    Matrix4d
    setTranslation(Vector3d vector)
    Sets the 4th column to the translation vector.
    Matrix4d
    toNormalMatrix()
    removes the translational part and transposes the matrix.
    String
    toString()
     
    Matrix4d
    tra()
    Transposes the matrix.
    Matrix4d
    translate(double[] translation)
    Postmultiplies this matrix by a translation matrix.
    Matrix4d
    translate(double x, double y, double z)
    Postmultiplies this matrix by a translation matrix.
    Matrix4d
    translate(Vector3d translation)
    Postmultiplies this matrix by a translation matrix.
    Matrix4d
    trn(double x, double y, double z)
    Adds a translational component to the matrix in the 4th column.
    Matrix4d
    trn(Vector3d vector)
    Adds a translational component to the matrix in the 4th column.

    Methods inherited from class java.lang.Object

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

  • Field Details

    • M00

      public static final int M00
      XX: Typically the unrotated X component for scaling, also the cosine of the angle when rotated on the Y and/or Z axis. On Vector3d multiplication this value is multiplied with the source X component and added to the target X component.
      See Also:

    • M01

      public static final int M01
      XY: Typically the negative sine of the angle when rotated on the Z axis. On Vector3d multiplication this value is multiplied with the source Y component and added to the target X component.
      See Also:

    • M02

      public static final int M02
      XZ: Typically the sine of the angle when rotated on the Y axis. On Vector3d multiplication this value is multiplied with the source Z component and added to the target X component.
      See Also:

    • M03

      public static final int M03
      XW: Typically the translation of the X component. On Vector3d multiplication this value is added to the target X component.
      See Also:

    • M10

      public static final int M10
      YX: Typically the sine of the angle when rotated on the Z axis. On Vector3d multiplication this value is multiplied with the source X component and added to the target Y component.
      See Also:

    • M11

      public static final int M11
      YY: Typically the unrotated Y component for scaling, also the cosine of the angle when rotated on the X and/or Z axis. On Vector3d multiplication this value is multiplied with the source Y component and added to the target Y component.
      See Also:

    • M12

      public static final int M12
      YZ: Typically the negative sine of the angle when rotated on the X axis. On Vector3d multiplication this value is multiplied with the source Z component and added to the target Y component.
      See Also:

    • M13

      public static final int M13
      YW: Typically the translation of the Y component. On Vector3d multiplication this value is added to the target Y component.
      See Also:

    • M20

      public static final int M20
      ZX: Typically the negative sine of the angle when rotated on the Y axis. On Vector3d multiplication this value is multiplied with the source X component and added to the target Z component.
      See Also:

    • M21

      public static final int M21
      ZY: Typical the sine of the angle when rotated on the X axis. On Vector3d multiplication this value is multiplied with the source Y component and added to the target Z component.
      See Also:

    • M22

      public static final int M22
      ZZ: Typically the unrotated Z component for scaling, also the cosine of the angle when rotated on the X and/or Y axis. On Vector3d multiplication this value is multiplied with the source Z component and added to the target Z component.
      See Also:

    • M23

      public static final int M23
      ZW: Typically the translation of the Z component. On Vector3d multiplication this value is added to the target Z component.
      See Also:

    • M30

      public static final int M30
      WX: Typically the value zero. On Vector3d multiplication this value is ignored.
      See Also:

    • M31

      public static final int M31
      WY: Typically the value zero. On Vector3d multiplication this value is ignored.
      See Also:

    • M32

      public static final int M32
      WZ: Typically the value zero. On Vector3d multiplication this value is ignored.
      See Also:

    • M33

      public static final int M33
      WW: Typically the value one. On Vector3d multiplication this value is ignored.
      See Also:

    • stmp

      public static final double[] stmp

    • tmp

      public final double[] tmp

    • val

      public final double[] val

  • Constructor Details

    • Matrix4d

      public Matrix4d()
      Constructs an identity matrix

    • Matrix4d

      public Matrix4d(Matrix4d matrix)
      Constructs a matrix from the given matrix.
      Parameters:
      matrix - The matrix to copy. (This matrix is not modified)

    • Matrix4d

      public Matrix4d(double[] values)
      Constructs a matrix from the given double array. The array must have at least 16 elements; the first 16 will be copied.
      Parameters:
      values - The double array to copy. Remember that this matrix is in column major order. (The double array is not modified.)

    • Matrix4d

      public Matrix4d(float[] values)

    • Matrix4d

      public Matrix4d(Quaterniond quaternion)
      Constructs a rotation matrix from the given Quaterniond.
      Parameters:
      quaternion - The quaternion to be copied. (The quaternion is not modified)

    • Matrix4d

      public Matrix4d(Vector3d position, Quaterniond rotation, Vector3d scale)
      Construct a matrix from the given translation, rotation and scale.
      Parameters:
      position - The translation
      rotation - The rotation, must be normalized
      scale - The scale

  • Method Details

    • set

      public Matrix4d set(Matrix4d matrix)
      Sets the matrix to the given matrix.
      Parameters:
      matrix - The matrix that is to be copied. (The given matrix is not modified)
      Returns:
      This matrix for the purpose of chaining methods together.

    • set

      public Matrix4d set(com.badlogic.gdx.math.Matrix4 matrix)

    • set

      public Matrix4d set(double[] values)
      Sets the matrix to the given matrix as a double array. The double array must have at least 16 elements; the first 16 will be copied.
      Parameters:
      values - The matrix, in double form, that is to be copied. Remember that this matrix is in column major order.
      Returns:
      This matrix for the purpose of chaining methods together.

    • set

      public Matrix4d set(float[] values)

    • set

      public Matrix4d set(Quaterniond quaternion)
      Sets the matrix to a rotation matrix representing the quaternion.
      Parameters:
      quaternion - The quaternion that is to be used to set this matrix.
      Returns:
      This matrix for the purpose of chaining methods together.

    • set

      public Matrix4d set(double quaternionX, double quaternionY, double quaternionZ, double quaternionW)
      Sets the matrix to a rotation matrix representing the quaternion.
      Parameters:
      quaternionX - The X component of the quaternion that is to be used to set this matrix.
      quaternionY - The Y component of the quaternion that is to be used to set this matrix.
      quaternionZ - The Z component of the quaternion that is to be used to set this matrix.
      quaternionW - The W component of the quaternion that is to be used to set this matrix.
      Returns:
      This matrix for the purpose of chaining methods together.

    • set

      public Matrix4d set(Vector3d position, Quaterniond orientation)
      Set this matrix to the specified translation and rotation.
      Parameters:
      position - The translation
      orientation - The rotation, must be normalized
      Returns:
      This matrix for chaining

    • set

      public Matrix4d set(double translationX, double translationY, double translationZ, double quaternionX, double quaternionY, double quaternionZ, double quaternionW)
      Sets the matrix to a rotation matrix representing the translation and quaternion.
      Parameters:
      translationX - The X component of the translation that is to be used to set this matrix.
      translationY - The Y component of the translation that is to be used to set this matrix.
      translationZ - The Z component of the translation that is to be used to set this matrix.
      quaternionX - The X component of the quaternion that is to be used to set this matrix.
      quaternionY - The Y component of the quaternion that is to be used to set this matrix.
      quaternionZ - The Z component of the quaternion that is to be used to set this matrix.
      quaternionW - The W component of the quaternion that is to be used to set this matrix.
      Returns:
      This matrix for the purpose of chaining methods together.

    • set

      public Matrix4d set(Vector3d position, Quaterniond orientation, Vector3d scale)
      Set this matrix to the specified translation, rotation and scale.
      Parameters:
      position - The translation
      orientation - The rotation, must be normalized
      scale - The scale
      Returns:
      This matrix for chaining

    • set

      public Matrix4d set(double translationX, double translationY, double translationZ, double quaternionX, double quaternionY, double quaternionZ, double quaternionW, double scaleX, double scaleY, double scaleZ)
      Sets the matrix to a rotation matrix representing the translation and quaternion.
      Parameters:
      translationX - The X component of the translation that is to be used to set this matrix.
      translationY - The Y component of the translation that is to be used to set this matrix.
      translationZ - The Z component of the translation that is to be used to set this matrix.
      quaternionX - The X component of the quaternion that is to be used to set this matrix.
      quaternionY - The Y component of the quaternion that is to be used to set this matrix.
      quaternionZ - The Z component of the quaternion that is to be used to set this matrix.
      quaternionW - The W component of the quaternion that is to be used to set this matrix.
      scaleX - The X component of the scaling that is to be used to set this matrix.
      scaleY - The Y component of the scaling that is to be used to set this matrix.
      scaleZ - The Z component of the scaling that is to be used to set this matrix.
      Returns:
      This matrix for the purpose of chaining methods together.

    • set

      public Matrix4d set(Vector3d xAxis, Vector3d yAxis, Vector3d zAxis, Vector3d pos)
      Sets the four columns of the matrix which correspond to the x-, y- and z-axis of the vector space this matrix creates as well as the 4th column representing the translation of any point that is multiplied by this matrix.
      Parameters:
      xAxis - The x-axis.
      yAxis - The y-axis.
      zAxis - The z-axis.
      pos - The translation vector.

    • cpy

      public Matrix4d cpy()
      Returns:
      a copy of this matrix

    • trn

      public Matrix4d trn(Vector3d vector)
      Adds a translational component to the matrix in the 4th column. The other columns are untouched.
      Parameters:
      vector - The translation vector to add to the current matrix. (This vector is not modified)
      Returns:
      This matrix for the purpose of chaining methods together.

    • trn

      public Matrix4d trn(double x, double y, double z)
      Adds a translational component to the matrix in the 4th column. The other columns are untouched.
      Parameters:
      x - The x-component of the translation vector.
      y - The y-component of the translation vector.
      z - The z-component of the translation vector.
      Returns:
      This matrix for the purpose of chaining methods together.

    • getValues

      public double[] getValues()
      Returns:
      the backing double array

    • getValuesFloat

      public float[] getValuesFloat()

    • mul

      public Matrix4d mul(Matrix4d matrix)
      Postmultiplies this matrix with the given matrix, storing the result in this matrix. For example: 
       A.mul(B) results in A := AB.
      Parameters:
      matrix - The other matrix to multiply by.
      Returns:
      This matrix for the purpose of chaining operations together.

    • mulLeft

      public Matrix4d mulLeft(Matrix4d matrix)
      Premultiplies this matrix with the given matrix, storing the result in this matrix. For example: 
       A.mulLeft(B) results in A := BA.
      Parameters:
      matrix - The other matrix to multiply by.
      Returns:
      This matrix for the purpose of chaining operations together.

    • tra

      public Matrix4d tra()
      Transposes the matrix.
      Returns:
      This matrix for the purpose of chaining methods together.

    • idt

      public Matrix4d idt()
      Sets the matrix to an identity matrix.
      Returns:
      This matrix for the purpose of chaining methods together.

    • inv

      public Matrix4d inv()

    • inv

      public static boolean inv(double[] values)
      Computes the inverse of the given matrix. The matrix array is assumed to hold a 4x4 column major matrix as you can get from Matrix4.val.
      Parameters:
      values - the matrix values.
      Returns:
      false in case the inverse could not be calculated, true otherwise.

    • det

      public double det()
      Returns:
      The determinant of this matrix

    • det3x3

      public double det3x3()
      Returns:
      The determinant of the 3x3 upper left matrix

    • setToProjection

      public Matrix4d setToProjection(double near, double far, double fov, double aspectRatio)
      Sets the matrix to a projection matrix with a near- and far plane, a field of view in degrees and an aspect ratio.
      Parameters:
      near - The near plane
      far - The far plane
      fov - The field of view in degrees
      aspectRatio - The "width over height" aspect ratio
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToOrtho2D

      public Matrix4d setToOrtho2D(double x, double y, double width, double height)
      Sets this matrix to an orthographic projection matrix with the origin at (x,y) extending by width and height. The near plane is set to 0, the far plane is set to 1.
      Parameters:
      x - The x-coordinate of the origin
      y - The y-coordinate of the origin
      width - The width
      height - The height
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToOrtho2D

      public Matrix4d setToOrtho2D(double x, double y, double width, double height, double near, double far)
      Sets this matrix to an orthographic projection matrix with the origin at (x,y) extending by width and height, having a near and far plane.
      Parameters:
      x - The x-coordinate of the origin
      y - The y-coordinate of the origin
      width - The width
      height - The height
      near - The near plane
      far - The far plane
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToOrtho

      public Matrix4d setToOrtho(double left, double right, double bottom, double top, double near, double far)
      Sets the matrix to an orthographic projection like glOrtho (http://www.opengl.org/sdk/docs/man/xhtml/glOrtho.xml) following the OpenGL equivalent
      Parameters:
      left - The left clipping plane
      right - The right clipping plane
      bottom - The bottom clipping plane
      top - The top clipping plane
      near - The near clipping plane
      far - The far clipping plane
      Returns:
      This matrix for the purpose of chaining methods together.

    • setTranslation

      public Matrix4d setTranslation(Vector3d vector)
      Sets the 4th column to the translation vector.
      Parameters:
      vector - The translation vector
      Returns:
      This matrix for the purpose of chaining methods together.

    • setTranslation

      public Matrix4d setTranslation(double x, double y, double z)
      Sets the 4th column to the translation vector.
      Parameters:
      x - The X coordinate of the translation vector
      y - The Y coordinate of the translation vector
      z - The Z coordinate of the translation vector
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToTranslation

      public Matrix4d setToTranslation(Vector3d vector)
      Sets this matrix to a translation matrix, overwriting it first by an identity matrix and then setting the 4th column to the translation vector.
      Parameters:
      vector - The translation vector
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToTranslation

      public Matrix4d setToTranslation(com.badlogic.gdx.math.Vector3 vector)

    • setToTranslation

      public Matrix4d setToTranslation(double x, double y, double z)
      Sets this matrix to a translation matrix, overwriting it first by an identity matrix and then setting the 4th column to the translation vector.
      Parameters:
      x - The x-component of the translation vector.
      y - The y-component of the translation vector.
      z - The z-component of the translation vector.
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToTranslationAndScaling

      public Matrix4d setToTranslationAndScaling(Vector3d translation, Vector3d scaling)
      Sets this matrix to a translation and scaling matrix by first overwriting it with an identity and then setting the translation vector in the 4th column and the scaling vector in the diagonal.
      Parameters:
      translation - The translation vector
      scaling - The scaling vector
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToTranslationAndScaling

      public Matrix4d setToTranslationAndScaling(double translationX, double translationY, double translationZ, double scalingX, double scalingY, double scalingZ)
      Sets this matrix to a translation and scaling matrix by first overwriting it with an identity and then setting the translation vector in the 4th column and the scaling vector in the diagonal.
      Parameters:
      translationX - The x-component of the translation vector
      translationY - The y-component of the translation vector
      translationZ - The z-component of the translation vector
      scalingX - The x-component of the scaling vector
      scalingY - The x-component of the scaling vector
      scalingZ - The x-component of the scaling vector
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToRotation

      public Matrix4d setToRotation(Vector3d axis, double degrees)
      Sets the matrix to a rotation matrix around the given axis.
      Parameters:
      axis - The axis
      degrees - The angle in degrees
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToRotationRad

      public Matrix4d setToRotationRad(Vector3d axis, double radians)
      Sets the matrix to a rotation matrix around the given axis.
      Parameters:
      axis - The axis
      radians - The angle in radians
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToRotation

      public Matrix4d setToRotation(double axisX, double axisY, double axisZ, double degrees)
      Sets the matrix to a rotation matrix around the given axis.
      Parameters:
      axisX - The x-component of the axis
      axisY - The y-component of the axis
      axisZ - The z-component of the axis
      degrees - The angle in degrees
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToRotationRad

      public Matrix4d setToRotationRad(double axisX, double axisY, double axisZ, double radians)
      Sets the matrix to a rotation matrix around the given axis.
      Parameters:
      axisX - The x-component of the axis
      axisY - The y-component of the axis
      axisZ - The z-component of the axis
      radians - The angle in radians
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToRotation

      public Matrix4d setToRotation(Vector3d v1, Vector3d v2)
      Set the matrix to a rotation matrix between two vectors.
      Parameters:
      v1 - The base vector
      v2 - The target vector
      Returns:
      This matrix for the purpose of chaining methods together

    • setToRotation

      public Matrix4d setToRotation(double x1, double y1, double z1, double x2, double y2, double z2)
      Set the matrix to a rotation matrix between two vectors.
      Parameters:
      x1 - The base vectors x value
      y1 - The base vectors y value
      z1 - The base vectors z value
      x2 - The target vector x value
      y2 - The target vector y value
      z2 - The target vector z value
      Returns:
      This matrix for the purpose of chaining methods together

    • setFromEulerAngles

      public Matrix4d setFromEulerAngles(double yaw, double pitch, double roll)
      Sets this matrix to a rotation matrix from the given euler angles.
      Parameters:
      yaw - the yaw in degrees
      pitch - the pitch in degrees
      roll - the roll in degrees
      Returns:
      This matrix

    • setToScaling

      public Matrix4d setToScaling(Vector3d vector)
      Sets this matrix to a scaling matrix
      Parameters:
      vector - The scaling vector
      Returns:
      This matrix for chaining.

    • setToScaling

      public Matrix4d setToScaling(double x, double y, double z)
      Sets this matrix to a scaling matrix
      Parameters:
      x - The x-component of the scaling vector
      y - The y-component of the scaling vector
      z - The z-component of the scaling vector
      Returns:
      This matrix for chaining.

    • setToLookAt

      public Matrix4d setToLookAt(Vector3d direction, Vector3d up)
      Sets the matrix to a look at matrix with a direction and an up vector. Multiply with a translation matrix to get a camera model view matrix.
      Parameters:
      direction - The direction vector
      up - The up vector
      Returns:
      This matrix for the purpose of chaining methods together.

    • setToLookAt

      public Matrix4d setToLookAt(Vector3b direction, Vector3b up)

    • setToLookAt

      public Matrix4d setToLookAt(Vector3d position, Vector3d target, Vector3d up)
      Sets this matrix to a look at matrix with the given position, target and up vector.
      Parameters:
      position - the position
      target - the target
      up - the up vector
      Returns:
      This matrix

    • setToLookAt

      public Matrix4d setToLookAt(Vector3b position, Vector3b target, Vector3b up)

    • setToWorld

      public Matrix4d setToWorld(Vector3d position, Vector3d forward, Vector3d up)

    • toString

      public String toString()
      Overrides:
      toString in class Object

    • lerp

      public Matrix4d lerp(Matrix4d matrix, double alpha)
      Linearly interpolates between this matrix and the given matrix mixing by alpha
      Parameters:
      matrix - the matrix
      alpha - the alpha value in the range [0,1]
      Returns:
      This matrix for the purpose of chaining methods together.

    • set

      public Matrix4d set(com.badlogic.gdx.math.Matrix3 mat)
      Sets this matrix to the given 3x3 matrix. The third column of this matrix is set to (0,0,1,0).
      Parameters:
      mat - the matrix

    • scl

      public Matrix4d scl(Vector3d scale)

    • scl

      public Matrix4d scl(double x, double y, double z)

    • scl

      public Matrix4d scl(double scale)

    • getTranslation

      public Vector3d getTranslation(Vector3d position)

    • getTranslationf

      public com.badlogic.gdx.math.Vector3 getTranslationf(com.badlogic.gdx.math.Vector3 position)

    • getTranslation

      public double[] getTranslation()

    • getTranslationf

      public float[] getTranslationf()

    • getTranslationf

      public void getTranslationf(float[] vec)

    • addTranslationTo

      public Vector3d addTranslationTo(Vector3d position)

    • getRotation

      public Quaterniond getRotation(Quaterniond rotation, boolean normalizeAxes)
      Gets the rotation of this matrix.
      Parameters:
      rotation - The Quaterniond to receive the rotation
      normalizeAxes - True to normalize the axes, necessary when the matrix might also include scaling.
      Returns:
      The provided Quaterniond for chaining.

    • getRotation

      public Quaterniond getRotation(Quaterniond rotation)
      Gets the rotation of this matrix.
      Parameters:
      rotation - The Quaterniond to receive the rotation
      Returns:
      The provided Quaterniond for chaining.

    • getScaleXSquared

      public double getScaleXSquared()
      Returns:
      the squared scale factor on the X axis

    • getScaleYSquared

      public double getScaleYSquared()
      Returns:
      the squared scale factor on the Y axis

    • getScaleZSquared

      public double getScaleZSquared()
      Returns:
      the squared scale factor on the Z axis

    • getScaleX

      public double getScaleX()
      Returns:
      the scale factor on the X axis (non-negative)

    • getScaleY

      public double getScaleY()
      Returns:
      the scale factor on the Y axis (non-negative)

    • getScaleZ

      public double getScaleZ()
      Returns:
      the scale factor on the X axis (non-negative)

    • getScale

      public Vector3d getScale(Vector3d scale)

    • toNormalMatrix

      public Matrix4d toNormalMatrix()
      removes the translational part and transposes the matrix.

    • prj

      public static void prj(double[] mat, double[] vec)
      Multiplies the vector with the given matrix, performing a division by w. The matrix array is assumed to hold a 4x4 column major matrix as you can get from val. The vector array is assumed to hold a 3-component vector, with x being the first element, y being the second and z being the last component. The result is stored in the vector array. This is the same as Vector3d.prj(Matrix4d).
      Parameters:
      mat - the matrix
      vec - the vector.

    • prj

      public static void prj(double[] mat, double[] vecs, int offset, int numVecs, int stride)
      Multiplies the vectors with the given matrix, , performing a division by w. The matrix array is assumed to hold a 4x4 column major matrix as you can get from Matrix4.val. The vectors array is assumed to hold 3-component vectors. Offset specifies the offset into the array where the x-component of the first vector is located. The numVecs parameter specifies the number of vectors stored in the vectors array. The stride parameter specifies the number of floats between subsequent vectors and must be >= 3. This is the same as Vector3.prj(Matrix4) applied to multiple vectors.
      Parameters:
      mat - the matrix
      vecs - the vectors
      offset - the offset into the vectors array
      numVecs - the number of vectors
      stride - the stride between vectors in floats

    • translate

      public Matrix4d translate(Vector3d translation)
      Postmultiplies this matrix by a translation matrix. Postmultiplication is also used by OpenGL ES' glTranslate/glRotate/glScale
      Parameters:
      translation -
      Returns:
      This matrix for the purpose of chaining methods together.

    • translate

      public Matrix4d translate(double[] translation)
      Postmultiplies this matrix by a translation matrix. Postmultiplication is also used by OpenGL ES' glTranslate/glRotate/glScale
      Parameters:
      translation -
      Returns:
      This matrix for the purpose of chaining methods together.

    • translate

      public Matrix4d translate(double x, double y, double z)
      Postmultiplies this matrix by a translation matrix. Postmultiplication is also used by OpenGL ES' 1.x glTranslate/glRotate/glScale.
      Parameters:
      x - Translation in the x-axis.
      y - Translation in the y-axis.
      z - Translation in the z-axis.
      Returns:
      This matrix for the purpose of chaining methods together.

    • mul

      public static void mul(double[] mata, double[] matb)
      Multiplies the matrix mata with matrix matb, storing the result in mata. The arrays are assumed to hold 4x4 column major matrices as you can get from val. This is the same as mul(Matrix4d).
      Parameters:
      mata - the first matrix.
      matb - the second matrix.

    • rotate

      public Matrix4d rotate(Vector3d axis, double degrees)
      Postmultiplies this matrix with a (counter-clockwise) rotation matrix. Postmultiplication is also used by OpenGL ES' 1.x glTranslate/glRotate/glScale.
      Parameters:
      axis - The vector axis to rotate around.
      degrees - The angle in degrees.
      Returns:
      This matrix for the purpose of chaining methods together.

    • rotateRad

      public Matrix4d rotateRad(Vector3d axis, double radians)
      Postmultiplies this matrix with a (counter-clockwise) rotation matrix. Postmultiplication is also used by OpenGL ES' 1.x glTranslate/glRotate/glScale.
      Parameters:
      axis - The vector axis to rotate around.
      radians - The angle in radians.
      Returns:
      This matrix for the purpose of chaining methods together.

    • rotate

      public Matrix4d rotate(double axisX, double axisY, double axisZ, double degrees)
      Postmultiplies this matrix with a (counter-clockwise) rotation matrix. Postmultiplication is also used by OpenGL ES' 1.x glTranslate/glRotate/glScale
      Parameters:
      axisX - The x-axis component of the vector to rotate around.
      axisY - The y-axis component of the vector to rotate around.
      axisZ - The z-axis component of the vector to rotate around.
      degrees - The angle in degrees
      Returns:
      This matrix for the purpose of chaining methods together.

    • rotateRad

      public Matrix4d rotateRad(double axisX, double axisY, double axisZ, double radians)
      Postmultiplies this matrix with a (counter-clockwise) rotation matrix. Postmultiplication is also used by OpenGL ES' 1.x glTranslate/glRotate/glScale
      Parameters:
      axisX - The x-axis component of the vector to rotate around.
      axisY - The y-axis component of the vector to rotate around.
      axisZ - The z-axis component of the vector to rotate around.
      radians - The angle in radians
      Returns:
      This matrix for the purpose of chaining methods together.

    • rotate

      public Matrix4d rotate(Quaterniond rotation)
      Postmultiplies this matrix with a (counter-clockwise) rotation matrix. Postmultiplication is also used by OpenGL ES' 1.x glTranslate/glRotate/glScale.
      Parameters:
      rotation -
      Returns:
      This matrix for the purpose of chaining methods together.

    • rotate

      public Matrix4d rotate(Vector3d v1, Vector3d v2)
      Postmultiplies this matrix by the rotation between two vectors.
      Parameters:
      v1 - The base vector
      v2 - The target vector
      Returns:
      This matrix for the purpose of chaining methods together

    • scale

      public Matrix4d scale(double scaleX, double scaleY, double scaleZ)
      Postmultiplies this matrix with a scale matrix. Postmultiplication is also used by OpenGL ES' 1.x glTranslate/glRotate/glScale.
      Parameters:
      scaleX - The scale in the x-axis.
      scaleY - The scale in the y-axis.
      scaleZ - The scale in the z-axis.
      Returns:
      This matrix for the purpose of chaining methods together.

    • extract4x3Matrix

      public void extract4x3Matrix(double[] dst)
      Copies the 4x3 upper-left sub-matrix into double array. The destination array is supposed to be a column major matrix.
      Parameters:
      dst - the destination matrix

    • putIn

      public com.badlogic.gdx.math.Matrix4 putIn(com.badlogic.gdx.math.Matrix4 aux)
      Sets the given matrix to this matrix
      Parameters:
      aux - The out matrix
      Returns:
      The aux matrix

    • changeOfBasis

      public static Matrix4d changeOfBasis(Vector3d x, Vector3d y, Vector3d z)
      Constructs a change of basis from the canonical basis to the base defined by the given x, y and z vectors.
      Parameters:
      x - The x vector of the new basis expressed in the canonical basis.
      y - The y vector of the new basis expressed in the canonical basis.
      z - The z vector of the new basis expressed in the canonical basis.
      Returns:
      The change of basis matrix.

    • changeOfBasis

      public static Matrix4d changeOfBasis(double[] x, double[] y, double[] z)
      Constructs a change of basis from the canonical basis to the base defined by the given x, y and z vectors.
      Parameters:
      x - The x vector of the new basis expressed in the canonical basis.
      y - The y vector of the new basis expressed in the canonical basis.
      z - The z vector of the new basis expressed in the canonical basis.
      Returns:
      The change of basis matrix.