Package icyllis.arc3d.core

Class Matrix4

java.lang.Object
icyllis.arc3d.core.Matrix4
All Implemented Interfaces:
Matrix4c, Cloneable
public non-sealed class Matrix4 extends Object implements Matrix4c, Cloneable
This class represents a 4x4 matrix and a 3D transformation, using the right-hand rule.

The memory layout (order of components) is the same as GLSL's column-major and HLSL's row-major, this is just a difference in naming and writing. A matrix looks like this:

[m11 m12 m13 m14]
[m21 m22 m23 m24]
[m31 m32 m33 m34]
[m41 m42 m43 m44]

Where [m41 m42 m43] represents the translation, and they are the last four elements in memory.

See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    float
    m11
     
    float
    m12
     
    float
    m13
     
    float
    m14
     
    float
    m21
     
    float
    m22
     
    float
    m23
     
    float
    m24
     
    float
    m31
     
    float
    m32
     
    float
    m33
     
    float
    m34
     
    float
    m41
     
    float
    m42
     
    float
    m43
     
    float
    m44
     

  • Constructor Summary

    Constructors
    Constructor
    Description
    Matrix4()
    Create a new identity matrix.
    Matrix4(float... a)
    Create a matrix from an array of elements in row-major.
    Matrix4(Matrix4c m)
    Create a matrix copied from an existing matrix.

  • Method Summary

    Modifier and Type
    Method
    Description
    void
    add(Matrix4 m)
    Add each element of the given matrix to the corresponding element of this matrix.
    Matrix4
    clone()
     
    static Matrix4
    copy(Matrix4c m)
    Create a copy of mat if not null, otherwise a new identity matrix.
    float
    determinant()
    Return the determinant of this matrix.
    boolean
    equals(Object o)
    Returns whether this matrix is exactly equal to another matrix.
    int
    hashCode()
     
    boolean
    hasPerspective()
     
    boolean
    hasTranslation()
     
    static Matrix4c
    identity()
    Returns a read-only identity matrix.
    boolean
    invert()
    Compute the inverse of this matrix.
    boolean
    invert(Matrix4 dest)
    Compute the inverse of this matrix.
    boolean
    isAffine()
    Returns whether this matrix is seen as an affine transformation.
    boolean
    isApproxEqual(Matrix4 m)
    Returns whether this matrix is approximately equal to given matrix.
    boolean
    isAxisAligned()
    Returns whether this matrix transforms rect to another rect.
    boolean
    isIdentity()
    Returns whether this matrix is approximately equivalent to an identity matrix.
    boolean
    isScaleTranslate()
    Returns whether this matrix at most scales and translates.
    float
    localAARadius(float left, float top, float right, float bottom)
    Return the minimum distance needed to move in local (pre-transform) space to ensure that the transformed coordinates are at least 1px away from the original mapped point.
    float
    localAARadius(Rect2fc bounds)
    Return the minimum distance needed to move in local (pre-transform) space to ensure that the transformed coordinates are at least 1px away from the original mapped point.
    float
    m11()
     
    float
    m12()
     
    float
    m13()
     
    float
    m14()
     
    float
    m21()
     
    float
    m22()
     
    float
    m23()
     
    float
    m24()
     
    float
    m31()
     
    float
    m32()
     
    float
    m33()
     
    float
    m34()
     
    float
    m41()
     
    float
    m42()
     
    float
    m43()
     
    float
    m44()
     
    static Matrix4
    makeOrthographic(float width, float height, float near, float far, boolean flipY)
    Create an orthographic projection matrix.
    static Matrix4
    makeOrthographic(float left, float right, float bottom, float top, float near, float far)
    Create an orthographic projection matrix.
    static Matrix4
    makePerspective(float fov, float aspect, float near, float far)
    Create a perspective projection matrix.
    static Matrix4
    makePerspective(float left, float right, float bottom, float top, float near, float far)
    Create a perspective projection matrix.
    static Matrix4
    makeScale(float x, float y, float z)
    Create a new scaling transformation matrix.
    static Matrix4
    makeTranslate(float x, float y, float z)
    Create a new translation transformation matrix.
    void
    mapPoint(float[] p)
    Map a point in the X-Y plane.
    float
    mapPointX(float x, float y)
     
    float
    mapPointY(float x, float y)
     
    void
    mapRect(float left, float top, float right, float bottom, Rect2f dest)
    Map the four corners of 'r' and return the bounding box of those points.
    void
    mapRect(float left, float top, float right, float bottom, Rect2i dest)
    Map the four corners of 'r' and return the bounding box of those points.
    void
    mapRect(Rect2f r)
    Map the four corners of 'r' and return the bounding box of those points.
    void
    mapRect(Rect2fc r, Rect2f dest)
    Map the four corners of 'r' and return the bounding box of those points.
    void
    mapRect(Rect2fc r, Rect2i dest)
    Map the four corners of 'r' and return the bounding box of those points.
    void
    mapRect(Rect2ic r, Rect2i dest)
    Map the four corners of 'r' and return the bounding box of those points.
    void
    mapRectIn(float left, float top, float right, float bottom, Rect2i dest)
     
    void
    mapRectIn(Rect2fc r, Rect2i dest)
    Map the four corners of 'r' and return the bounding box of those points.
    void
    mapRectOut(float left, float top, float right, float bottom, Rect2i dest)
    Map the four corners of 'r' and return the bounding box of those points.
    void
    mapRectOut(Rect2fc r, Rect2i dest)
    Map the four corners of 'r' and return the bounding box of those points.
    void
    mapRectOut(Rect2ic r, Rect2i dest)
    Map the four corners of 'r' and return the bounding box of those points.
    void
    mapVec3(float[] vec)
     
    void
    normalizePerspective()
    If the last column of the matrix is [0, 0, 0, not_one]^T, we will treat the matrix as if it is in perspective, even though it stills behaves like its affine.
    void
    postConcat(float r11, float r12, float r13, float r14, float r21, float r22, float r23, float r24, float r31, float r32, float r33, float r34, float r41, float r42, float r43, float r44)
    Post-multiply this matrix by the given rhs matrix.
    void
    postConcat(Matrix3 rhs)
    Post-multiply this matrix by the given rhs matrix.
    void
    postConcat(Matrix4c rhs)
    Post-multiply this matrix by the given rhs matrix.
    void
    postConcat2D(Matrixc rhs)
    Post-multiply this matrix by the given rhs matrix.
    void
    postRotate(double angleX, double angleY, double angleZ)
    Post-rotates this matrix from the given Euler rotation angles in radians.
    void
    postRotate(double x, double y, double z, double angle)
    Post-rotates this matrix about an arbitrary axis with the given angle in radians.
    void
    postRotateX(double angle)
    Post-rotates this matrix about the X-axis with the given angle in radians.
    void
    postRotateY(double angle)
    Post-rotates this matrix about the Y-axis with the given angle in radians.
    void
    postRotateZ(double angle)
    Post-rotates this matrix about the Z-axis with the given angle in radians.
    void
    postScale(float sx, float sy)
    Post-multiply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.
    void
    postScale(float sx, float sy, float sz)
    Post-multiply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.
    void
    postScale(Vector3 s)
    Post-scales this matrix by given vector.
    void
    postScaleX(float s)
    Post-scales this matrix by given vector.
    void
    postScaleY(float s)
    Post-scales this matrix by given vector.
    void
    postScaleZ(float s)
    Post-scales this matrix by given vector.
    void
    postShear(float sxy, float sxz, float syx, float syz, float szx, float szy)
    Post-multiply shearing to this matrix by the given shearing coefficients.
    void
    postShear2D(float sx, float sy)
    Post-multiply 2D shearing to this matrix by the given shearing coefficients.
    void
    postTransform(Vector3 vec)
    Transform a three-dimensional column vector by post-multiplication (this * vec3, w-component is considered as 1).
    void
    postTransform(Vector4 vec)
    Transform a four-dimensional column vector by post-multiplication (matrix * vector).
    void
    postTranslate(float dx, float dy)
    Post-multiply a translation to this matrix by translating by the given number of units in x, y and z.
    void
    postTranslate(float dx, float dy, float dz)
    Post-multiply a translation to this matrix by translating by the given number of units in x, y and z.
    void
    postTranslate(Vector3 t)
    Post-translates this matrix by given changes.
    void
    postTranslateX(float dx)
    Post-translates this matrix by given vector.
    void
    postTranslateY(float dy)
    Post-translates this matrix by given vector.
    void
    postTranslateZ(float dz)
    Post-translates this matrix by given vector.
    void
    preConcat(float l11, float l12, float l13, float l14, float l21, float l22, float l23, float l24, float l31, float l32, float l33, float l34, float l41, float l42, float l43, float l44)
    Pre-multiply this matrix by the given lhs matrix.
    void
    preConcat(Matrix3 lhs)
    Pre-multiply this matrix by the given lhs matrix.
    void
    preConcat(Matrix4c lhs)
    Pre-multiply this matrix by the given lhs matrix.
    void
    preConcat2D(Matrixc lhs)
    Pre-multiply this matrix by the given lhs matrix.
    void
    preRotate(double angleX, double angleY, double angleZ)
    Rotates this matrix from the given Euler rotation angles in radians.
    void
    preRotate(double x, double y, double z, double angle)
    Rotates this matrix about an arbitrary axis with the given angle in radians.
    void
    preRotate(Quaternion q)
    Rotate this matrix by the given quaternion's rotation matrix.
    void
    preRotate(Vector3 axis, float angle)
    Rotates this matrix about an arbitrary axis.
    void
    preRotateX(double angle)
    Rotates this matrix about the X-axis with the given angle in radians.
    void
    preRotateY(double angle)
    Rotates this matrix about the Y-axis with the given angle in radians.
    void
    preRotateZ(double angle)
    Rotates this matrix about the Z-axis with the given angle in radians.
    void
    preScale(float sx, float sy)
    Apply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.
    void
    preScale(float sx, float sy, float sz)
    Apply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.
    void
    preScale(Vector3 s)
    Scales this matrix by given vector.
    void
    preScaleX(float s)
    Scales this matrix by given vector.
    void
    preScaleY(float s)
    Scales this matrix by given vector.
    void
    preScaleZ(float s)
    Scales this matrix by given vector.
    void
    preShear(float sxy, float sxz, float syx, float syz, float szx, float szy)
    Pre-multiply shearing to this matrix by the given shearing coefficients.
    void
    preShear2D(float sx, float sy)
    Pre-multiply 2D shearing to this matrix by the given shearing coefficients.
    void
    preTransform(Vector3 vec)
    Transform a three-dimensional row vector by pre-multiplication (vec3 * this, w-component is considered as 1).
    void
    preTransform(Vector4 vec)
    Transform a four-dimensional row vector by pre-multiplication (vector * matrix).
    void
    preTranslate(float dx, float dy)
    Apply a translation to this matrix by translating by the given number of units in x, y and z.
    void
    preTranslate(float dx, float dy, float dz)
    Apply a translation to this matrix by translating by the given number of units in x, y and z.
    void
    preTranslate(Vector3 t)
    Translates this matrix by given changes.
    void
    preTranslateX(float dx)
    Translates this matrix by given vector.
    void
    preTranslateY(float dy)
    Translates this matrix by given vector.
    void
    preTranslateZ(float dz)
    Translates this matrix by given vector.
    void
    set(float[] a)
    Set the values in the matrix using a float array that contains the matrix elements in row-major order.
    void
    set(float[] a, int offset)
    Set the values in the matrix using a float array that contains the matrix elements in row-major order.
    void
    set(float m11, float m12, float m13, float m14, float m21, float m22, float m23, float m24, float m31, float m32, float m33, float m34, float m41, float m42, float m43, float m44)
    Set the values within this matrix to the given float values.
    void
    set(long p)
    Set the values in the matrix using an address that contains the matrix elements in row-major order (UNSAFE).
    void
    set(Matrix4c m)
    Store the values of the given matrix into this matrix.
    void
    set(ByteBuffer a)
    Set the values in the matrix using a float array that contains the matrix elements in row-major order.
    void
    set(FloatBuffer a)
    Set the values in the matrix using a float array that contains the matrix elements in row-major order.
    void
    setIdentity()
    Reset this matrix to the identity.
    Matrix4
    setOrthographic(float width, float height, float near, float far, boolean flipY)
    Set this matrix to an orthographic projection matrix.
    Matrix4
    setOrthographic(float left, float right, float bottom, float top, float near, float far)
    Set this matrix to an orthographic projection matrix.
    void
    setOrthographic(float left, float right, float bottom, float top, float near, float far, boolean negativeOneToOne)
    Set this matrix to be an orthographic projection transformation for a right-handed coordinate system using the given NDC z range.
    void
    setOrthographicLH(float left, float right, float bottom, float top, float near, float far, boolean negativeOneToOne)
    Set this matrix to be an orthographic projection transformation for a left-handed coordinate system using the given NDC z range.
    void
    setPerspective(double fov, double aspect, float near, float far, boolean negativeOneToOne)
    Set this matrix to be a symmetric perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range.
    Matrix4
    setPerspective(float fov, float aspect, float near, float far)
    Set this matrix to a perspective projection matrix.
    Matrix4
    setPerspective(float left, float right, float bottom, float top, float near, float far)
    Set this matrix to a perspective projection matrix.
    void
    setPerspectiveLH(double fov, double aspect, float near, float far, boolean negativeOneToOne)
    Set this matrix to be a symmetric perspective projection frustum transformation for a left-handed coordinate system using the given NDC z range.
    void
    setRotation(Quaternion q)
    Set this matrix to a rotation matrix by the quaternion's rotation.
    void
    setScale(float x, float y, float z)
    Set this matrix to be a simple scale matrix.
    void
    setScale(Vector3 s)
    Sets this matrix to a scaling matrix by given components.
    void
    setShear(float sxy, float sxz, float syx, float syz, float szx, float szy)
    Resets this matrix to a shearing matrix.
    void
    setTranslate(float x, float y, float z)
    Set this matrix to be a simple translation matrix.
    void
    setTranslate(Vector3 t)
    Sets this matrix to a translation matrix by given components.
    void
    setZero()
    Set all elements of this matrix to 0.
    void
    store(float[] a)
    Store this matrix into the give float array in row-major order.
    void
    store(float[] a, int offset)
    Store this matrix into the give float array in row-major order.
    void
    store(long p)
    Store this matrix into the given address in GLSL column-major or HLSL row-major order.
    void
    store(Matrix4 m)
    Store this matrix elements to the given matrix.
    void
    store(ByteBuffer a)
    Store this matrix into the give float array in row-major order.
    void
    store(FloatBuffer a)
    Store this matrix into the give float array in row-major order.
    void
    storeAs2D(long p)
    Store this matrix as 2D matrix into the given address in GLSL column-major or HLSL row-major order, NOT vec4 aligned.
    void
    storeAs2DAligned(long p)
    Store this matrix as 2D matrix into the given address in GLSL column-major or HLSL row-major order, NOT vec4 aligned.
    void
    subtract(Matrix4 m)
    Subtract each element of the given matrix from the corresponding element of this matrix.
    Matrix
    toMatrix()
    Converts this 4x4 matrix to 3x3 matrix, the third row and column are discarded.
    void
    toMatrix(Matrix dest)
    Converts this 4x4 matrix to 3x3 matrix, the third row and column are discarded.
    Matrix3
    toMatrix3()
    Converts this 4x4 matrix to 3x3 matrix, the fourth row and column are discarded.
    void
    toMatrix3(Matrix3 dest)
    Converts this 4x4 matrix to 3x3 matrix, the fourth row and column are discarded.
    String
    toString()
     
    float
    trace()
    Compute the trace of this matrix.
    void
    transpose()
    Transpose this matrix.

    Methods inherited from class java.lang.Object

    finalize, getClass, notify, notifyAll, wait, wait, wait

  • Field Details

    • m11

      public float m11

    • m12

      public float m12

    • m13

      public float m13

    • m14

      public float m14

    • m21

      public float m21

    • m22

      public float m22

    • m23

      public float m23

    • m24

      public float m24

    • m31

      public float m31

    • m32

      public float m32

    • m33

      public float m33

    • m34

      public float m34

    • m41

      public float m41

    • m42

      public float m42

    • m43

      public float m43

    • m44

      public float m44

  • Constructor Details

    • Matrix4

      public Matrix4()
      Create a new identity matrix.

    • Matrix4

      public Matrix4(@Nonnull Matrix4c m)
      Create a matrix copied from an existing matrix.
      Parameters:
      m - the matrix to create from

    • Matrix4

      public Matrix4(@Nonnull float... a)
      Create a matrix from an array of elements in row-major.
      Parameters:
      a - the array to create from
      See Also:

  • Method Details

    • copy

      @Nonnull public static Matrix4 copy(@Nullable Matrix4c m)
      Create a copy of mat if not null, otherwise a new identity matrix. Note: we assume null is identity.
      Parameters:
      m - the matrix to copy from
      Returns:
      a copy of the matrix

    • identity

      @Nonnull public static Matrix4c identity()
      Returns a read-only identity matrix.
      Returns:
      an identity matrix

    • makeTranslate

      @Nonnull public static Matrix4 makeTranslate(float x, float y, float z)
      Create a new translation transformation matrix.
      Parameters:
      x - the x-component of the translation
      y - the y-component of the translation
      z - the z-component of the translation
      Returns:
      the resulting matrix

    • makeScale

      @Nonnull public static Matrix4 makeScale(float x, float y, float z)
      Create a new scaling transformation matrix.
      Parameters:
      x - the x-component of the scaling
      y - the y-component of the scaling
      z - the z-component of the scaling
      Returns:
      the resulting matrix

    • makeOrthographic

      @Nonnull public static Matrix4 makeOrthographic(float left, float right, float bottom, float top, float near, float far)
      Create an orthographic projection matrix.
      Parameters:
      left - the left frustum plane
      right - the right frustum plane
      bottom - the bottom frustum plane
      top - the top frustum plane
      near - the near frustum plane, must be positive
      far - the far frustum plane, must be positive
      Returns:
      the resulting matrix

    • makeOrthographic

      @Nonnull public static Matrix4 makeOrthographic(float width, float height, float near, float far, boolean flipY)
      Create an orthographic projection matrix. The left plane and top plane are considered to be 0.
      Parameters:
      width - the distance from right frustum plane to left frustum plane
      height - the distance from bottom frustum plane to top frustum plane
      near - the near frustum plane, must be positive
      far - the far frustum plane, must be positive
      flipY - whether to flip the projection vertically
      Returns:
      the resulting matrix

    • makePerspective

      @Nonnull public static Matrix4 makePerspective(float left, float right, float bottom, float top, float near, float far)
      Create a perspective projection matrix.
      Parameters:
      left - the left frustum plane
      right - the right frustum plane
      bottom - the bottom frustum plane
      top - the top frustum plane
      near - the near frustum plane, must be positive
      far - the far frustum plane, must be positive
      Returns:
      the resulting matrix

    • makePerspective

      @Nonnull public static Matrix4 makePerspective(float fov, float aspect, float near, float far)
      Create a perspective projection matrix.
      Parameters:
      fov - the angle of field of view in radians (0,PI)
      aspect - aspect ratio of the view (width / height)
      near - the near frustum plane, must be positive
      far - the far frustum plane, must be positive
      Returns:
      the resulting matrix

    • m11

      public float m11()
      Specified by:
      m11 in interface Matrix4c

    • m12

      public float m12()
      Specified by:
      m12 in interface Matrix4c

    • m13

      public float m13()
      Specified by:
      m13 in interface Matrix4c

    • m14

      public float m14()
      Specified by:
      m14 in interface Matrix4c

    • m21

      public float m21()
      Specified by:
      m21 in interface Matrix4c

    • m22

      public float m22()
      Specified by:
      m22 in interface Matrix4c

    • m23

      public float m23()
      Specified by:
      m23 in interface Matrix4c

    • m24

      public float m24()
      Specified by:
      m24 in interface Matrix4c

    • m31

      public float m31()
      Specified by:
      m31 in interface Matrix4c

    • m32

      public float m32()
      Specified by:
      m32 in interface Matrix4c

    • m33

      public float m33()
      Specified by:
      m33 in interface Matrix4c

    • m34

      public float m34()
      Specified by:
      m34 in interface Matrix4c

    • m41

      public float m41()
      Specified by:
      m41 in interface Matrix4c

    • m42

      public float m42()
      Specified by:
      m42 in interface Matrix4c

    • m43

      public float m43()
      Specified by:
      m43 in interface Matrix4c

    • m44

      public float m44()
      Specified by:
      m44 in interface Matrix4c

    • add

      public void add(@Nonnull Matrix4 m)
      Add each element of the given matrix to the corresponding element of this matrix.
      Parameters:
      m - the addend

    • subtract

      public void subtract(@Nonnull Matrix4 m)
      Subtract each element of the given matrix from the corresponding element of this matrix.
      Parameters:
      m - the subtrahend

    • preConcat

      public void preConcat(@Nonnull Matrix4c lhs)
      Pre-multiply this matrix by the given lhs matrix.

      If M is this matrix and L the lhs matrix, then the new matrix will be L * M (row-major). So when transforming a vector v with the new matrix by using v * L * M, the transformation of the left-hand side matrix will be applied first.

      Parameters:
      lhs - the left-hand side matrix to multiply

    • preConcat

      public void preConcat(float l11, float l12, float l13, float l14, float l21, float l22, float l23, float l24, float l31, float l32, float l33, float l34, float l41, float l42, float l43, float l44)
      Pre-multiply this matrix by the given lhs matrix.

      If M is this matrix and L the lhs matrix, then the new matrix will be L * M (row-major). So when transforming a vector v with the new matrix by using v * L * M, the transformation of the left-hand side matrix will be applied first.

      Parameters:
      l11 - the m11 element of the left-hand side matrix
      l12 - the m12 element of the left-hand side matrix
      l13 - the m13 element of the left-hand side matrix
      l14 - the m14 element of the left-hand side matrix
      l21 - the m21 element of the left-hand side matrix
      l22 - the m22 element of the left-hand side matrix
      l23 - the m23 element of the left-hand side matrix
      l24 - the m24 element of the left-hand side matrix
      l31 - the m31 element of the left-hand side matrix
      l32 - the m32 element of the left-hand side matrix
      l33 - the m33 element of the left-hand side matrix
      l34 - the m34 element of the left-hand side matrix
      l41 - the m41 element of the left-hand side matrix
      l42 - the m42 element of the left-hand side matrix
      l43 - the m43 element of the left-hand side matrix
      l44 - the m44 element of the left-hand side matrix

    • postConcat

      public void postConcat(@Nonnull Matrix4c rhs)
      Post-multiply this matrix by the given rhs matrix.

      If M is this matrix and R the rhs matrix, then the new matrix will be M * R (row-major). So when transforming a vector v with the new matrix by using v * M * R, the transformation of this matrix will be applied first.

      Parameters:
      rhs - the right-hand side matrix to multiply

    • postConcat

      public void postConcat(float r11, float r12, float r13, float r14, float r21, float r22, float r23, float r24, float r31, float r32, float r33, float r34, float r41, float r42, float r43, float r44)
      Post-multiply this matrix by the given rhs matrix.

      If M is this matrix and R the rhs matrix, then the new matrix will be M * R (row-major). So when transforming a vector v with the new matrix by using v * M * R, the transformation of this matrix will be applied first.

      Parameters:
      r11 - the m11 element of the right-hand side matrix
      r12 - the m12 element of the right-hand side matrix
      r13 - the m13 element of the right-hand side matrix
      r14 - the m14 element of the right-hand side matrix
      r21 - the m21 element of the right-hand side matrix
      r22 - the m22 element of the right-hand side matrix
      r23 - the m23 element of the right-hand side matrix
      r24 - the m24 element of the right-hand side matrix
      r31 - the m31 element of the right-hand side matrix
      r32 - the m32 element of the right-hand side matrix
      r33 - the m33 element of the right-hand side matrix
      r34 - the m34 element of the right-hand side matrix
      r41 - the m41 element of the right-hand side matrix
      r42 - the m42 element of the right-hand side matrix
      r43 - the m43 element of the right-hand side matrix
      r44 - the m44 element of the right-hand side matrix

    • preConcat2D

      public void preConcat2D(@Nonnull Matrixc lhs)
      Pre-multiply this matrix by the given lhs matrix. The matrix will be expanded to a 4x4 matrix. 
      
 [ a b c ]      [ a b 0 c ]
 [ d e f ]  ->  [ d e 0 f ]
 [ g h i ]      [ 0 0 1 0 ]
                [ g h 0 i ]
      If M is this matrix and L the lhs matrix, then the new matrix will be L * M (row-major). So when transforming a vector v with the new matrix by using v * L * M, the transformation of the left-hand side matrix will be applied first.
      Parameters:
      lhs - the left-hand side matrix to multiply

    • postConcat2D

      public void postConcat2D(@Nonnull Matrixc rhs)
      Post-multiply this matrix by the given rhs matrix. The matrix will be expanded to a 4x4 matrix. 
      
 [ a b c ]      [ a b 0 c ]
 [ d e f ]  ->  [ d e 0 f ]
 [ g h i ]      [ 0 0 1 0 ]
                [ g h 0 i ]
      If M is this matrix and R the rhs matrix, then the new matrix will be M * R (row-major). So when transforming a vector v with the new matrix by using v * M * R, the transformation of this matrix will be applied first.
      Parameters:
      rhs - the right-hand side matrix to multiply

    • preConcat

      public void preConcat(@Nonnull Matrix3 lhs)
      Pre-multiply this matrix by the given lhs matrix. The matrix will be expanded to a 4x4 matrix. 
      
 [ a b c ]      [ a b c 0 ]
 [ d e f ]  ->  [ d e f 0 ]
 [ g h i ]      [ g h i 0 ]
                [ 0 0 0 1 ]
      If M is this matrix and L the lhs matrix, then the new matrix will be L * M (row-major). So when transforming a vector v with the new matrix by using v * L * M, the transformation of the left-hand side matrix will be applied first.
      Parameters:
      lhs - the left-hand side matrix to multiply

    • postConcat

      public void postConcat(@Nonnull Matrix3 rhs)
      Post-multiply this matrix by the given rhs matrix. The matrix will be expanded to a 4x4 matrix. 
      
 [ a b c ]      [ a b c 0 ]
 [ d e f ]  ->  [ d e f 0 ]
 [ g h i ]      [ g h i 0 ]
                [ 0 0 0 1 ]
      If M is this matrix and R the rhs matrix, then the new matrix will be M * R (row-major). So when transforming a vector v with the new matrix by using v * M * R, the transformation of this matrix will be applied first.
      Parameters:
      rhs - the right-hand side matrix to multiply

    • setZero

      public void setZero()
      Set all elements of this matrix to 0.

    • setIdentity

      public void setIdentity()
      Reset this matrix to the identity.

    • set

      public void set(@Nonnull Matrix4c m)
      Store the values of the given matrix into this matrix.
      Parameters:
      m - the matrix to copy from

    • set

      public void set(float m11, float m12, float m13, float m14, float m21, float m22, float m23, float m24, float m31, float m32, float m33, float m34, float m41, float m42, float m43, float m44)
      Set the values within this matrix to the given float values.
      Parameters:
      m11 - the new value of m11
      m12 - the new value of m12
      m13 - the new value of m13
      m14 - the new value of m14
      m21 - the new value of m21
      m22 - the new value of m22
      m23 - the new value of m23
      m24 - the new value of m24
      m31 - the new value of m31
      m32 - the new value of m32
      m33 - the new value of m33
      m34 - the new value of m34
      m41 - the new value of m41
      m42 - the new value of m42
      m43 - the new value of m43
      m44 - the new value of m44

    • set

      public void set(@Nonnull float[] a)
      Set the values in the matrix using a float array that contains the matrix elements in row-major order.
      Parameters:
      a - the array to copy from

    • set

      public void set(@Nonnull float[] a, int offset)
      Set the values in the matrix using a float array that contains the matrix elements in row-major order.
      Parameters:
      a - the array to copy from
      offset - the element offset

    • set

      public void set(@Nonnull ByteBuffer a)
      Set the values in the matrix using a float array that contains the matrix elements in row-major order.
      Parameters:
      a - the array to copy from

    • set

      public void set(@Nonnull FloatBuffer a)
      Set the values in the matrix using a float array that contains the matrix elements in row-major order.
      Parameters:
      a - the array to copy from

    • set

      public void set(long p)
      Set the values in the matrix using an address that contains the matrix elements in row-major order (UNSAFE).
      Parameters:
      p - the pointer of the array to copy from

    • store

      public void store(@Nonnull Matrix4 m)
      Store this matrix elements to the given matrix.
      Specified by:
      store in interface Matrix4c
      Parameters:
      m - the matrix to store

    • store

      public void store(@Nonnull float[] a)
      Store this matrix into the give float array in row-major order.
      Specified by:
      store in interface Matrix4c
      Parameters:
      a - the array to store into

    • store

      public void store(@Nonnull float[] a, int offset)
      Store this matrix into the give float array in row-major order.
      Specified by:
      store in interface Matrix4c
      Parameters:
      a - the array to store into
      offset - the element offset

    • store

      public void store(@Nonnull ByteBuffer a)
      Store this matrix into the give float array in row-major order.
      Specified by:
      store in interface Matrix4c
      Parameters:
      a - the pointer of the array to store

    • store

      public void store(@Nonnull FloatBuffer a)
      Store this matrix into the give float array in row-major order.
      Specified by:
      store in interface Matrix4c
      Parameters:
      a - the pointer of the array to store

    • store

      public void store(long p)
      Store this matrix into the given address in GLSL column-major or HLSL row-major order.
      Specified by:
      store in interface Matrix4c
      Parameters:
      p - the pointer of the array to store

    • storeAs2D

      public void storeAs2D(long p)
      Store this matrix as 2D matrix into the given address in GLSL column-major or HLSL row-major order, NOT vec4 aligned.

      Equivalent to call toMatrix() and Matrix.store(long).

      Specified by:
      storeAs2D in interface Matrix4c
      Parameters:
      p - the pointer of the array to store

    • storeAs2DAligned

      public void storeAs2DAligned(long p)
      Store this matrix as 2D matrix into the given address in GLSL column-major or HLSL row-major order, NOT vec4 aligned.

      Equivalent to call toMatrix() and Matrix.storeAligned(long).

      Specified by:
      storeAs2DAligned in interface Matrix4c
      Parameters:
      p - the pointer of the array to store

    • determinant

      public float determinant()
      Return the determinant of this matrix.
      Specified by:
      determinant in interface Matrix4c
      Returns:
      the determinant

    • trace

      public float trace()
      Compute the trace of this matrix.
      Returns:
      the trace of this matrix

    • transpose

      public void transpose()
      Transpose this matrix.

    • invert

      @CheckReturnValue public boolean invert()
      Compute the inverse of this matrix. This matrix will be inverted if it is invertible, otherwise it keeps the same as before.
      Returns:
      true if this matrix is invertible.

    • invert

      public boolean invert(@Nullable Matrix4 dest)
      Compute the inverse of this matrix. The matrix will be inverted if this matrix is invertible, otherwise it keeps the same as before.
      Specified by:
      invert in interface Matrix4c
      Parameters:
      dest - the destination matrix
      Returns:
      true if this matrix is invertible.

    • setOrthographic

      @Nonnull public Matrix4 setOrthographic(float left, float right, float bottom, float top, float near, float far)
      Set this matrix to an orthographic projection matrix.
      Parameters:
      left - the left frustum plane
      right - the right frustum plane
      bottom - the bottom frustum plane
      top - the top frustum plane
      near - the near frustum plane, must be positive
      far - the far frustum plane, must be positive
      Returns:
      this

    • setOrthographic

      @Nonnull public Matrix4 setOrthographic(float width, float height, float near, float far, boolean flipY)
      Set this matrix to an orthographic projection matrix.
      Parameters:
      width - the distance from right frustum plane to left frustum plane
      height - the distance from bottom frustum plane to top frustum plane
      near - the near frustum plane, must be positive
      far - the far frustum plane, must be positive
      flipY - whether to flip the projection vertically
      Returns:
      this

    • setOrthographic

      public void setOrthographic(float left, float right, float bottom, float top, float near, float far, boolean negativeOneToOne)
      Set this matrix to be an orthographic projection transformation for a right-handed coordinate system using the given NDC z range.
      Parameters:
      left - the distance from the center to the left frustum edge
      right - the distance from the center to the right frustum edge
      bottom - the distance from the center to the bottom frustum edge
      top - the distance from the center to the top frustum edge
      near - near clipping plane distance
      far - far clipping plane distance
      negativeOneToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when false or whether to use OpenGL's NDC z range of [-1..+1] when true

    • setOrthographicLH

      public void setOrthographicLH(float left, float right, float bottom, float top, float near, float far, boolean negativeOneToOne)
      Set this matrix to be an orthographic projection transformation for a left-handed coordinate system using the given NDC z range.
      Parameters:
      left - the distance from the center to the left frustum edge
      right - the distance from the center to the right frustum edge
      bottom - the distance from the center to the bottom frustum edge
      top - the distance from the center to the top frustum edge
      near - near clipping plane distance
      far - far clipping plane distance
      negativeOneToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when false or whether to use OpenGL's NDC z range of [-1..+1] when true

    • setPerspective

      @Nonnull public Matrix4 setPerspective(float left, float right, float bottom, float top, float near, float far)
      Set this matrix to a perspective projection matrix.
      Parameters:
      left - the left frustum plane
      right - the right frustum plane
      bottom - the bottom frustum plane
      top - the top frustum plane
      near - the near frustum plane, must be positive
      far - the far frustum plane, must be positive
      Returns:
      this

    • setPerspective

      @Nonnull public Matrix4 setPerspective(float fov, float aspect, float near, float far)
      Set this matrix to a perspective projection matrix.
      Parameters:
      fov - the angle of field of view in radians (0,PI)
      aspect - aspect ratio of the view (width / height)
      near - the near frustum plane, must be positive
      far - the far frustum plane, must be positive
      Returns:
      this

    • setPerspective

      public void setPerspective(double fov, double aspect, float near, float far, boolean negativeOneToOne)
      Set this matrix to be a symmetric perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range.
      Parameters:
      fov - the field of view in radians (must be greater than zero and less than PI)
      aspect - the aspect ratio of the view (i.e. width / height)
      near - the near clipping plane, must be positive
      far - the far clipping plane, must be positive
      negativeOneToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when false or whether to use OpenGL's NDC z range of [-1..+1] when true

    • setPerspectiveLH

      public void setPerspectiveLH(double fov, double aspect, float near, float far, boolean negativeOneToOne)
      Set this matrix to be a symmetric perspective projection frustum transformation for a left-handed coordinate system using the given NDC z range.
      Parameters:
      fov - the field of view in radians (must be greater than zero and less than PI)
      aspect - the aspect ratio of the view (i.e. width / height)
      near - the near clipping plane, must be positive
      far - the far clipping plane, must be positive
      negativeOneToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when false or whether to use OpenGL's NDC z range of [-1..+1] when true

    • preTranslateX

      public void preTranslateX(float dx)
      Translates this matrix by given vector. This is equivalent to pre-multiplying by a translation matrix.
      Parameters:
      dx - the x-component of the translation

    • postTranslateX

      public void postTranslateX(float dx)
      Post-translates this matrix by given vector. This is equivalent to post-multiplying by a translation matrix.
      Parameters:
      dx - the x-component of the translation

    • preTranslateY

      public void preTranslateY(float dy)
      Translates this matrix by given vector. This is equivalent to pre-multiplying by a translation matrix.
      Parameters:
      dy - the y-component of the translation

    • postTranslateY

      public void postTranslateY(float dy)
      Post-translates this matrix by given vector. This is equivalent to post-multiplying by a translation matrix.
      Parameters:
      dy - the y-component of the translation

    • preTranslateZ

      public void preTranslateZ(float dz)
      Translates this matrix by given vector. This is equivalent to pre-multiplying by a translation matrix.
      Parameters:
      dz - the z-component of the translation

    • postTranslateZ

      public void postTranslateZ(float dz)
      Post-translates this matrix by given vector. This is equivalent to post-multiplying by a translation matrix.
      Parameters:
      dz - the z-component of the translation

    • preTranslate

      public void preTranslate(@Nonnull Vector3 t)
      Translates this matrix by given changes. This is equivalent to pre-multiplying by a translation matrix. (translation * this)
      Parameters:
      t - the translation vector

    • preTranslate

      public void preTranslate(float dx, float dy, float dz)
      Apply a translation to this matrix by translating by the given number of units in x, y and z.

      If M is this matrix and T the translation matrix, then the new matrix will be T * M (row-major). So when transforming a vector v with the new matrix by using v * T * M, the translation will be applied first.

      Parameters:
      dx - the x-component of the translation
      dy - the y-component of the translation
      dz - the z-component of the translation

    • preTranslate

      public void preTranslate(float dx, float dy)
      Apply a translation to this matrix by translating by the given number of units in x, y and z.

      If M is this matrix and T the translation matrix, then the new matrix will be T * M (row-major). So when transforming a vector v with the new matrix by using v * T * M, the translation will be applied first.

      Parameters:
      dx - the x-component of the translation
      dy - the y-component of the translation

    • postTranslate

      public void postTranslate(@Nonnull Vector3 t)
      Post-translates this matrix by given changes. This is equivalent to post-multiplying by a translation matrix. (this * translation)
      Parameters:
      t - the translation vector

    • postTranslate

      public void postTranslate(float dx, float dy, float dz)
      Post-multiply a translation to this matrix by translating by the given number of units in x, y and z.

      If M is this matrix and T the translation matrix, then the new matrix will be M * T (row-major). So when transforming a vector v with the new matrix by using v * M * T, the translation will be applied last.

      Parameters:
      dx - the x-component of the translation
      dy - the y-component of the translation
      dz - the z-component of the translation

    • postTranslate

      public void postTranslate(float dx, float dy)
      Post-multiply a translation to this matrix by translating by the given number of units in x, y and z.

      If M is this matrix and T the translation matrix, then the new matrix will be M * T (row-major). So when transforming a vector v with the new matrix by using v * M * T, the translation will be applied last.

      Parameters:
      dx - the x-component of the translation
      dy - the y-component of the translation

    • setTranslate

      public void setTranslate(@Nonnull Vector3 t)
      Sets this matrix to a translation matrix by given components.
      Parameters:
      t - the translation vector

    • setTranslate

      public void setTranslate(float x, float y, float z)
      Set this matrix to be a simple translation matrix.
      Parameters:
      x - the x-component of the translation
      y - the y-component of the translation
      z - the z-component of the translation

    • preScaleX

      public void preScaleX(float s)
      Scales this matrix by given vector. This is equivalent to pre-multiplying by a scale matrix.
      Parameters:
      s - the x-component of the scale

    • postScaleX

      public void postScaleX(float s)
      Post-scales this matrix by given vector. This is equivalent to post-multiplying by a scale matrix.
      Parameters:
      s - the x-component of the scale

    • preScaleY

      public void preScaleY(float s)
      Scales this matrix by given vector. This is equivalent to pre-multiplying by a scale matrix.
      Parameters:
      s - the y-component of the scale

    • postScaleY

      public void postScaleY(float s)
      Post-scales this matrix by given vector. This is equivalent to post-multiplying by a scale matrix.
      Parameters:
      s - the y-component of the scale

    • preScaleZ

      public void preScaleZ(float s)
      Scales this matrix by given vector. This is equivalent to pre-multiplying by a scale matrix.
      Parameters:
      s - the x-component of the scale

    • postScaleZ

      public void postScaleZ(float s)
      Post-scales this matrix by given vector. This is equivalent to post-multiplying by a scale matrix.
      Parameters:
      s - the x-component of the scale

    • preScale

      public void preScale(@Nonnull Vector3 s)
      Scales this matrix by given vector. This is equivalent to pre-multiplying by a scale matrix.
      Parameters:
      s - the scale vector

    • preScale

      public void preScale(float sx, float sy, float sz)
      Apply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.

      If M is this matrix and S the scaling matrix, then the new matrix will be S * M (row-major). So when transforming a vector v with the new matrix by using v * S * M, the scaling will be applied first.

      Parameters:
      sx - the x-component of the scale
      sy - the y-component of the scale
      sz - the z-component of the scale

    • preScale

      public void preScale(float sx, float sy)
      Apply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.

      If M is this matrix and S the scaling matrix, then the new matrix will be S * M (row-major). So when transforming a vector v with the new matrix by using v * S * M, the scaling will be applied first.

      Parameters:
      sx - the x-component of the scale
      sy - the y-component of the scale

    • postScale

      public void postScale(@Nonnull Vector3 s)
      Post-scales this matrix by given vector. This is equivalent to post-multiplying by a scale matrix.
      Parameters:
      s - the scale vector

    • postScale

      public void postScale(float sx, float sy, float sz)
      Post-multiply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.

      If M is this matrix and S the scaling matrix, then the new matrix will be M * S (row-major). So when transforming a vector v with the new matrix by using v * M * S, the scaling will be applied last.

      Parameters:
      sx - the x-component of the scale
      sy - the y-component of the scale
      sz - the z-component of the scale

    • postScale

      public void postScale(float sx, float sy)
      Post-multiply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.

      If M is this matrix and S the scaling matrix, then the new matrix will be M * S (row-major). So when transforming a vector v with the new matrix by using v * M * S, the scaling will be applied last.

      Parameters:
      sx - the x-component of the scale
      sy - the y-component of the scale

    • setScale

      public void setScale(@Nonnull Vector3 s)
      Sets this matrix to a scaling matrix by given components.
      Parameters:
      s - the scale vector

    • setScale

      public void setScale(float x, float y, float z)
      Set this matrix to be a simple scale matrix.
      Parameters:
      x - the x-component of the scale
      y - the y-component of the scale
      z - the z-component of the scale

    • preShear

      public void preShear(float sxy, float sxz, float syx, float syz, float szx, float szy)
      Pre-multiply shearing to this matrix by the given shearing coefficients.

      This is equivalent to pre-multiplying by a shearing matrix.

      1 sxy sxz
      syx 1 syz
      szx szy 1
      Parameters:
      sxy - the y-component of the shearing in x direction, x is unchanged
      sxz - the z-component of the shearing in x direction, x is unchanged
      syx - the x-component of the shearing in y direction, y is unchanged
      syz - the z-component of the shearing in y direction, y is unchanged
      szx - the x-component of the shearing in z direction, z is unchanged
      szy - the y-component of the shearing in z direction, z is unchanged

    • postShear

      public void postShear(float sxy, float sxz, float syx, float syz, float szx, float szy)
      Post-multiply shearing to this matrix by the given shearing coefficients.

      This is equivalent to post-multiplying by a shearing matrix.

      1 sxy sxz
      syx 1 syz
      szx szy 1
      Parameters:
      sxy - the y-component of the shearing in x direction, x is unchanged
      sxz - the z-component of the shearing in x direction, x is unchanged
      syx - the x-component of the shearing in y direction, y is unchanged
      syz - the z-component of the shearing in y direction, y is unchanged
      szx - the x-component of the shearing in z direction, z is unchanged
      szy - the y-component of the shearing in z direction, z is unchanged

    • preShear2D

      public void preShear2D(float sx, float sy)
      Pre-multiply 2D shearing to this matrix by the given shearing coefficients.
      Parameters:
      sx - the x-component of the shearing in y direction, y is unchanged (horizontal shearing)
      sy - the y-component of the shearing in x direction, x is unchanged (vertical shearing)

    • postShear2D

      public void postShear2D(float sx, float sy)
      Post-multiply 2D shearing to this matrix by the given shearing coefficients.
      Parameters:
      sx - the x-component of the shearing in y direction, y is unchanged (horizontal shearing)
      sy - the y-component of the shearing in x direction, x is unchanged (vertical shearing)

    • setShear

      public void setShear(float sxy, float sxz, float syx, float syz, float szx, float szy)
      Resets this matrix to a shearing matrix.

    • preRotateX

      public void preRotateX(double angle)
      Rotates this matrix about the X-axis with the given angle in radians.

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      This is equivalent to pre-multiplying by a rotation matrix.

      1 0 0
      0 cosθ sinθ
      0 -sinθ cosθ
      Parameters:
      angle - the rotation angle in radians.

    • postRotateX

      public void postRotateX(double angle)
      Post-rotates this matrix about the X-axis with the given angle in radians.

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      This is equivalent to post-multiplying by a rotation matrix.

      1 0 0
      0 cosθ sinθ
      0 -sinθ cosθ
      Parameters:
      angle - the rotation angle in radians.

    • preRotateY

      public void preRotateY(double angle)
      Rotates this matrix about the Y-axis with the given angle in radians.

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      This is equivalent to pre-multiplying by a rotation matrix.

      cosθ 0 -sinθ
      0 1 0
      sinθ 0 cosθ
      Parameters:
      angle - the rotation angle in radians.

    • postRotateY

      public void postRotateY(double angle)
      Post-rotates this matrix about the Y-axis with the given angle in radians.

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      This is equivalent to post-multiplying by a rotation matrix.

      cosθ 0 -sinθ
      0 1 0
      sinθ 0 cosθ
      Parameters:
      angle - the rotation angle in radians.

    • preRotateZ

      public void preRotateZ(double angle)
      Rotates this matrix about the Z-axis with the given angle in radians.

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      This is equivalent to pre-multiplying by a rotation matrix.

      cosθ sinθ 0
      -sinθ cosθ 0
      0 0 1
      Parameters:
      angle - the rotation angle in radians.

    • postRotateZ

      public void postRotateZ(double angle)
      Post-rotates this matrix about the Z-axis with the given angle in radians.

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      This is equivalent to post-multiplying by a rotation matrix.

      cosθ sinθ 0
      -sinθ cosθ 0
      0 0 1
      Parameters:
      angle - the rotation angle in radians.

    • preRotate

      public void preRotate(double angleX, double angleY, double angleZ)
      Rotates this matrix from the given Euler rotation angles in radians.

      The rotations are applied in the given order and using chained rotation per axis:

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      This is equivalent to pre-multiplying by three rotation matrices.

      Parameters:
      angleX - the Euler pitch angle in radians. (rotation about the X axis)
      angleY - the Euler yaw angle in radians. (rotation about the Y axis)
      angleZ - the Euler roll angle in radians. (rotation about the Z axis)
      See Also:

    • postRotate

      public void postRotate(double angleX, double angleY, double angleZ)
      Post-rotates this matrix from the given Euler rotation angles in radians.

      The rotations are applied in the given order and using chained rotation per axis:

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      This is equivalent to post-multiplying by three rotation matrices.

      Parameters:
      angleX - the Euler pitch angle in radians. (rotation about the X axis)
      angleY - the Euler yaw angle in radians. (rotation about the Y axis)
      angleZ - the Euler roll angle in radians. (rotation about the Z axis)
      See Also:

    • preRotate

      public void preRotate(@Nonnull Vector3 axis, float angle)
      Rotates this matrix about an arbitrary axis. The axis must be a normalized (unit) vector. If the axis is X, Y or Z, use axis-specified methods to rotate this matrix which are faster.

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      Parameters:
      axis - the rotation axis
      angle - rotation angle in radians
      See Also:

    • preRotate

      public void preRotate(double x, double y, double z, double angle)
      Rotates this matrix about an arbitrary axis with the given angle in radians. The axis described by the three components must be normalized. If it is known that the rotation axis is X, Y or Z, use axis-specified methods instead.

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      This is equivalent to pre-multiplying by a quaternion.

      Parameters:
      x - x-coordinate of rotation axis
      y - y-coordinate of rotation axis
      z - z-coordinate of rotation axis
      angle - rotation angle in radians
      See Also:

    • preRotate

      public void preRotate(@Nonnull Quaternion q)
      Rotate this matrix by the given quaternion's rotation matrix. (quat * this)
      Parameters:
      q - the quaternion to rotate by.

    • postRotate

      public void postRotate(double x, double y, double z, double angle)
      Post-rotates this matrix about an arbitrary axis with the given angle in radians. The axis described by the three components must be normalized. If it is known that the rotation axis is X, Y or Z, use axis-specified methods instead.

      When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

      This is equivalent to post-multiplying by a quaternion.

      Parameters:
      x - x-coordinate of rotation axis
      y - y-coordinate of rotation axis
      z - z-coordinate of rotation axis
      angle - rotation angle in radians
      See Also:

    • setRotation

      public void setRotation(@Nonnull Quaternion q)
      Set this matrix to a rotation matrix by the quaternion's rotation.
      Parameters:
      q - the quaternion to set by.

    • preTransform

      public void preTransform(@Nonnull Vector4 vec)
      Transform a four-dimensional row vector by pre-multiplication (vector * matrix). This is equivalent to (matrix * vector) in GLSL.
      Parameters:
      vec - the vector to transform

    • postTransform

      public void postTransform(@Nonnull Vector4 vec)
      Transform a four-dimensional column vector by post-multiplication (matrix * vector). This is equivalent to (vector * matrix) in GLSL.
      Parameters:
      vec - the vector to transform

    • preTransform

      public void preTransform(@Nonnull Vector3 vec)
      Transform a three-dimensional row vector by pre-multiplication (vec3 * this, w-component is considered as 1). This should be used with position vectors.
      Parameters:
      vec - the vector to transform

    • postTransform

      public void postTransform(@Nonnull Vector3 vec)
      Transform a three-dimensional column vector by post-multiplication (this * vec3, w-component is considered as 1). This should be used with normal vectors.
      Parameters:
      vec - the vector to transform

    • mapRect

      public void mapRect(@Nonnull Rect2f r)
      Map the four corners of 'r' and return the bounding box of those points. The four corners of 'r' are assumed to have z = 0 and w = 1. If the matrix has perspective, the returned rectangle will be the bounding box of the projected points after being clipped to w > 0.
      Specified by:
      mapRect in interface Matrix4c

    • mapRect

      public void mapRect(@Nonnull Rect2fc r, @Nonnull Rect2f dest)
      Map the four corners of 'r' and return the bounding box of those points. The four corners of 'r' are assumed to have z = 0 and w = 1. If the matrix has perspective, the returned rectangle will be the bounding box of the projected points after being clipped to w > 0.
      Specified by:
      mapRect in interface Matrix4c

    • mapRect

      public void mapRect(float left, float top, float right, float bottom, @Nonnull Rect2f dest)
      Map the four corners of 'r' and return the bounding box of those points. The four corners of 'r' are assumed to have z = 0 and w = 1. If the matrix has perspective, the returned rectangle will be the bounding box of the projected points after being clipped to w > 0.

    • mapRect

      public void mapRect(@Nonnull Rect2fc r, @Nonnull Rect2i dest)
      Map the four corners of 'r' and return the bounding box of those points. The four corners of 'r' are assumed to have z = 0 and w = 1. If the matrix has perspective, the returned rectangle will be the bounding box of the projected points after being clipped to w > 0.
      Specified by:
      mapRect in interface Matrix4c

    • mapRect

      public void mapRect(@Nonnull Rect2ic r, @Nonnull Rect2i dest)
      Map the four corners of 'r' and return the bounding box of those points. The four corners of 'r' are assumed to have z = 0 and w = 1. If the matrix has perspective, the returned rectangle will be the bounding box of the projected points after being clipped to w > 0.
      Specified by:
      mapRect in interface Matrix4c

    • mapRect

      public void mapRect(float left, float top, float right, float bottom, @Nonnull Rect2i dest)
      Map the four corners of 'r' and return the bounding box of those points. The four corners of 'r' are assumed to have z = 0 and w = 1. If the matrix has perspective, the returned rectangle will be the bounding box of the projected points after being clipped to w > 0.

    • mapRectOut

      public void mapRectOut(@Nonnull Rect2ic r, @Nonnull Rect2i dest)
      Map the four corners of 'r' and return the bounding box of those points. The four corners of 'r' are assumed to have z = 0 and w = 1. If the matrix has perspective, the returned rectangle will be the bounding box of the projected points after being clipped to w > 0.
      Specified by:
      mapRectOut in interface Matrix4c

    • mapRectOut

      public void mapRectOut(@Nonnull Rect2fc r, @Nonnull Rect2i dest)
      Map the four corners of 'r' and return the bounding box of those points. The four corners of 'r' are assumed to have z = 0 and w = 1. If the matrix has perspective, the returned rectangle will be the bounding box of the projected points after being clipped to w > 0.
      Specified by:
      mapRectOut in interface Matrix4c

    • mapRectOut

      public void mapRectOut(float left, float top, float right, float bottom, @Nonnull Rect2i dest)
      Map the four corners of 'r' and return the bounding box of those points. The four corners of 'r' are assumed to have z = 0 and w = 1. If the matrix has perspective, the returned rectangle will be the bounding box of the projected points after being clipped to w > 0.

    • mapRectIn

      public void mapRectIn(@Nonnull Rect2fc r, @Nonnull Rect2i dest)
      Description copied from interface: Matrix4c
      Map the four corners of 'r' and return the bounding box of those points. The four corners of 'r' are assumed to have z = 0 and w = 1. If the matrix has perspective, the returned rectangle will be the bounding box of the projected points after being clipped to w > 0.
      Specified by:
      mapRectIn in interface Matrix4c

    • mapRectIn

      public void mapRectIn(float left, float top, float right, float bottom, @Nonnull Rect2i dest)

    • mapPoint

      public void mapPoint(@Nonnull float[] p)
      Map a point in the X-Y plane.
      Parameters:
      p - the point to transform

    • mapPointX

      public float mapPointX(float x, float y)

    • mapPointY

      public float mapPointY(float x, float y)

    • mapVec3

      public void mapVec3(float[] vec)

    • isAffine

      public boolean isAffine()
      Returns whether this matrix is seen as an affine transformation. Otherwise, there's a perspective projection.
      Returns:
      true if this matrix is affine.

    • isScaleTranslate

      public boolean isScaleTranslate()
      Returns whether this matrix at most scales and translates.
      Specified by:
      isScaleTranslate in interface Matrix4c
      Returns:
      true if this matrix is scale, translate, or both.

    • isAxisAligned

      public boolean isAxisAligned()
      Returns whether this matrix transforms rect to another rect. If true, this matrix is identity, or/and scales, or/and rotates round Z axis a multiple of 90 degrees, or mirrors on axes. In all cases, this matrix is affine and may also have translation.

      For example: 

      
      Matrix4 matrix = Matrix4.identity();
      matrix.translate(3, 5, 7);
      matrix.scale(2, 3, 4);
      matrix.rotateX(MathUtil.PI_DIV_4);
      matrix.rotateZ(MathUtil.PI_DIV_2);
      Specified by:
      isAxisAligned in interface Matrix4c
      Returns:
      true if this matrix transform one rect into another

    • normalizePerspective

      public void normalizePerspective()
      If the last column of the matrix is [0, 0, 0, not_one]^T, we will treat the matrix as if it is in perspective, even though it stills behaves like its affine. If we divide everything by the not_one value, then it will behave the same, but will be treated as affine, and therefore faster (e.g. clients can forward-difference calculations).

    • hasPerspective

      public boolean hasPerspective()
      Specified by:
      hasPerspective in interface Matrix4c

    • hasTranslation

      public boolean hasTranslation()

    • isIdentity

      public boolean isIdentity()
      Returns whether this matrix is approximately equivalent to an identity matrix.
      Returns:
      true if this matrix is identity.

    • localAARadius

      public float localAARadius(Rect2fc bounds)
      Return the minimum distance needed to move in local (pre-transform) space to ensure that the transformed coordinates are at least 1px away from the original mapped point. This minimum distance is specific to the given local 'bounds' since the scale factors change with perspective.

      If the bounds will be clipped by the w=0 plane or otherwise is ill-conditioned, this will return positive infinity.

      Specified by:
      localAARadius in interface Matrix4c

    • localAARadius

      public float localAARadius(float left, float top, float right, float bottom)
      Return the minimum distance needed to move in local (pre-transform) space to ensure that the transformed coordinates are at least 1px away from the original mapped point. This minimum distance is specific to the given local 'bounds' since the scale factors change with perspective.

      If the bounds will be clipped by the w=0 plane or otherwise is ill-conditioned, this will return positive infinity.

      Specified by:
      localAARadius in interface Matrix4c

    • toMatrix

      public void toMatrix(@Nonnull Matrix dest)
      Converts this 4x4 matrix to 3x3 matrix, the third row and column are discarded. 
      
 [ a b x c ]      [ a b c ]
 [ d e x f ]  ->  [ d e f ]
 [ x x x x ]      [ g h i ]
 [ g h x i ]
      Specified by:
      toMatrix in interface Matrix4c

    • toMatrix

      @Nonnull public Matrix toMatrix()
      Converts this 4x4 matrix to 3x3 matrix, the third row and column are discarded. 
      
 [ a b x c ]      [ a b c ]
 [ d e x f ]  ->  [ d e f ]
 [ x x x x ]      [ g h i ]
 [ g h x i ]
      Specified by:
      toMatrix in interface Matrix4c

    • toMatrix3

      public void toMatrix3(@Nonnull Matrix3 dest)
      Converts this 4x4 matrix to 3x3 matrix, the fourth row and column are discarded. 
      
 [ a b c x ]      [ a b c ]
 [ d e f x ]  ->  [ d e f ]
 [ g h i x ]      [ g h i ]
 [ x x x x ]
      Specified by:
      toMatrix3 in interface Matrix4c

    • toMatrix3

      @Nonnull public Matrix3 toMatrix3()
      Converts this 4x4 matrix to 3x3 matrix, the fourth row and column are discarded. 
      
 [ a b c x ]      [ a b c ]
 [ d e f x ]  ->  [ d e f ]
 [ g h i x ]      [ g h i ]
 [ x x x x ]
      Specified by:
      toMatrix3 in interface Matrix4c

    • isApproxEqual

      public boolean isApproxEqual(@Nonnull Matrix4 m)
      Returns whether this matrix is approximately equal to given matrix.
      Specified by:
      isApproxEqual in interface Matrix4c
      Parameters:
      m - the matrix to compare.
      Returns:
      true if this matrix is equivalent to other matrix.

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object

    • equals

      public boolean equals(Object o)
      Returns whether this matrix is exactly equal to another matrix.
      Overrides:
      equals in class Object
      Parameters:
      o - the reference object with which to compare.
      Returns:
      true if this object is the same as the o values.

    • toString

      public String toString()
      Overrides:
      toString in class Object

    • clone

      @Nonnull public Matrix4 clone()
      Specified by:
      clone in interface Matrix4c
      Overrides:
      clone in class Object
      Returns:
      a copy of this matrix