public class Matrix4f extends Object implements Serializable, Cloneable
Modifier and Type | Field and Description |
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float |
m00
The first element of the first row.
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float |
m01
The second element of the first row.
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float |
m02
The third element of the first row.
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float |
m03
The fourth element of the first row.
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float |
m10
The first element of the second row.
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float |
m11
The second element of the second row.
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float |
m12
The third element of the second row.
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float |
m13
The fourth element of the second row.
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float |
m20
The first element of the third row.
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float |
m21
The second element of the third row.
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float |
m22
The third element of the third row.
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float |
m23
The fourth element of the third row.
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float |
m30
The first element of the fourth row.
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float |
m31
The second element of the fourth row.
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float |
m32
The third element of the fourth row.
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float |
m33
The fourth element of the fourth row.
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Constructor and Description |
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Matrix4f()
Constructs and initializes a Matrix4f to all zeros.
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Matrix4f(float[] v)
Constructs and initializes a Matrix4f from the specified 16 element
array.
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Matrix4f(float m00,
float m01,
float m02,
float m03,
float m10,
float m11,
float m12,
float m13,
float m20,
float m21,
float m22,
float m23,
float m30,
float m31,
float m32,
float m33)
Constructs and initializes a Matrix4f from the specified 16 values.
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Matrix4f(Matrix3f m1,
Vector3f t1,
float s)
Constructs and initializes a Matrix4f from the rotation matrix,
translation, and scale values; the scale is applied only to the
rotational components of the matrix (upper 3x3) and not to the
translational components of the matrix.
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Matrix4f(Matrix4d m1)
Constructs a new matrix with the same values as the Matrix4d parameter.
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Matrix4f(Matrix4f m1)
Constructs a new matrix with the same values as the Matrix4f parameter.
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Matrix4f(Quat4f q1,
Vector3f t1,
float s)
Constructs and initializes a Matrix4f from the quaternion, translation,
and scale values; the scale is applied only to the rotational components
of the matrix (upper 3x3) and not to the translational components.
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Modifier and Type | Method and Description |
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void |
add(float scalar)
Adds a scalar to each component of this matrix.
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void |
add(float scalar,
Matrix4f m1)
Adds a scalar to each component of the matrix m1 and places the result
into this.
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void |
add(Matrix4f m1)
Sets the value of this matrix to the sum of itself and matrix m1.
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void |
add(Matrix4f m1,
Matrix4f m2)
Sets the value of this matrix to the matrix sum of matrices m1 and m2.
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Object |
clone()
Creates a new object of the same class as this object.
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float |
determinant()
Computes the determinate of this matrix.
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boolean |
epsilonEquals(Matrix4f m1,
float epsilon)
Returns true if the L-infinite distance between this matrix and matrix m1
is less than or equal to the epsilon parameter, otherwise returns false.
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boolean |
equals(Matrix4f m1)
Returns true if all of the data members of Matrix4f m1 are equal to the
corresponding data members in this Matrix4f.
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boolean |
equals(Object t1)
Returns true if the Object t1 is of type Matrix4f and all of the data
members of t1 are equal to the corresponding data members in this
Matrix4f.
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void |
get(Matrix3d m1)
Performs an SVD normalization of this matrix in order to acquire the
normalized rotational component; the values are placed into the Matrix3d
parameter.
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void |
get(Matrix3f m1)
Performs an SVD normalization of this matrix in order to acquire the
normalized rotational component; the values are placed into the Matrix3f
parameter.
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float |
get(Matrix3f m1,
Vector3f t1)
Performs an SVD normalization of this matrix to calculate the rotation as
a 3x3 matrix, the translation, and the scale.
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void |
get(Quat4f q1)
Performs an SVD normalization of this matrix in order to acquire the
normalized rotational component; the values are placed into the Quat4f
parameter.
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void |
get(Vector3f trans)
Retrieves the translational components of this matrix.
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void |
getColumn(int column,
float[] v)
Copies the matrix values in the specified column into the array
parameter.
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void |
getColumn(int column,
Vector4f v)
Copies the matrix values in the specified column into the vector
parameter.
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float |
getElement(int row,
int column)
Retrieves the value at the specified row and column of this matrix.
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float |
getM00()
Get the first matrix element in the first row.
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float |
getM01()
Get the second matrix element in the first row.
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float |
getM02()
Get the third matrix element in the first row.
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float |
getM03()
Get the fourth element of the first row.
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float |
getM10()
Get first matrix element in the second row.
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float |
getM11()
Get second matrix element in the second row.
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float |
getM12()
Get the third matrix element in the second row.
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float |
getM13()
Get the fourth element of the second row.
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float |
getM20()
Get the first matrix element in the third row.
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float |
getM21()
Get the second matrix element in the third row.
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float |
getM22()
Get the third matrix element in the third row.
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float |
getM23()
Get the fourth element of the third row.
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float |
getM30()
Get the first element of the fourth row.
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float |
getM31()
Get the second element of the fourth row.
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float |
getM32()
Get the third element of the fourth row.
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float |
getM33()
Get the fourth element of the fourth row.
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void |
getRotationScale(Matrix3f m1)
Gets the upper 3x3 values of this matrix and places them into the matrix
m1.
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void |
getRow(int row,
float[] v)
Copies the matrix values in the specified row into the array parameter.
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void |
getRow(int row,
Vector4f v)
Copies the matrix values in the specified row into the vector parameter.
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float |
getScale()
Performs an SVD normalization of this matrix to calculate and return the
uniform scale factor.
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int |
hashCode()
Returns a hash code value based on the data values in this object.
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void |
invert()
Inverts this matrix in place.
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void |
invert(Matrix4f m1)
Sets the value of this matrix to the matrix inverse of the passed (user
declared) matrix m1.
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void |
mul(float scalar)
Multiplies each element of this matrix by a scalar.
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void |
mul(float scalar,
Matrix4f m1)
Multiplies each element of matrix m1 by a scalar and places the result
into this.
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void |
mul(Matrix4f m1)
Sets the value of this matrix to the result of multiplying itself with
matrix m1.
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void |
mul(Matrix4f m1,
Matrix4f m2)
Sets the value of this matrix to the result of multiplying the two
argument matrices together.
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void |
mulTransposeBoth(Matrix4f m1,
Matrix4f m2)
Multiplies the transpose of matrix m1 times the transpose of matrix m2,
and places the result into this.
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void |
mulTransposeLeft(Matrix4f m1,
Matrix4f m2)
Multiplies the transpose of matrix m1 times matrix m2, and places the
result into this.
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void |
mulTransposeRight(Matrix4f m1,
Matrix4f m2)
Multiplies matrix m1 times the transpose of matrix m2, and places the
result into this.
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void |
negate()
Negates the value of this matrix: this = -this.
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void |
negate(Matrix4f m1)
Sets the value of this matrix equal to the negation of of the Matrix4f
parameter.
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void |
rotX(float angle)
Sets the value of this matrix to a counter clockwise rotation about the x
axis.
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void |
rotY(float angle)
Sets the value of this matrix to a counter clockwise rotation about the y
axis.
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void |
rotZ(float angle)
Sets the value of this matrix to a counter clockwise rotation about the z
axis.
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void |
set(AxisAngle4d a1)
Sets the value of this matrix to the matrix conversion of the double
precision axis and angle argument.
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void |
set(AxisAngle4f a1)
Sets the value of this matrix to the matrix conversion of the (single
precision) axis and angle argument.
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void |
set(float scale)
Sets the value of this matrix to a scale matrix with the the passed scale
amount.
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void |
set(float[] m)
Sets the values in this Matrix4f equal to the row-major array parameter
(ie, the first four elements of the array will be copied into the first
row of this matrix, etc.).
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void |
set(float scale,
Vector3f t1)
Sets the value of this transform to a scale and translation matrix; the
scale is not applied to the translation and all of the matrix values are
modified.
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void |
set(Matrix3d m1)
Sets the rotational component (upper 3x3) of this matrix to the matrix
values in the double precision Matrix3d argument; the other elements of
this matrix are initialized as if this were an identity matrix (i.e.,
affine matrix with no translational component).
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void |
set(Matrix3d m1,
Vector3d t1,
double scale)
Sets the value of this matrix from the rotation expressed by the rotation
matrix m1, the translation t1, and the scale factor.
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void |
set(Matrix3f m1)
Sets the rotational component (upper 3x3) of this matrix to the matrix
values in the single precision Matrix3f argument; the other elements of
this matrix are initialized as if this were an identity matrix (i.e.,
affine matrix with no translational component).
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void |
set(Matrix3f m1,
Vector3f t1,
float scale)
Sets the value of this matrix from the rotation expressed by the rotation
matrix m1, the translation t1, and the scale factor.
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void |
set(Matrix4d m1)
Sets the value of this matrix to the float value of the passed matrix4d
m1.
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void |
set(Matrix4f m1)
Sets the value of this matrix to a copy of the passed matrix m1.
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void |
set(Quat4d q1)
Sets the value of this matrix to the matrix conversion of the double
precision quaternion argument.
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void |
set(Quat4d q1,
Vector3d t1,
double s)
Sets the value of this matrix from the rotation expressed by the
quaternion q1, the translation t1, and the scale s.
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void |
set(Quat4f q1)
Sets the value of this matrix to the matrix conversion of the single
precision quaternion argument.
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void |
set(Quat4f q1,
Vector3f t1,
float s)
Sets the value of this matrix from the rotation expressed by the
quaternion q1, the translation t1, and the scale s.
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void |
set(Vector3f v1)
Sets the value of this matrix to a translate matrix with the passed
translation value.
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void |
set(Vector3f t1,
float scale)
Sets the value of this transform to a scale and translation matrix; the
translation is scaled by the scale factor and all of the matrix values
are modified.
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void |
setColumn(int column,
float[] v)
Sets the specified column of this matrix4f to the four values provided.
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void |
setColumn(int column,
float x,
float y,
float z,
float w)
Sets the specified column of this matrix4f to the four values provided.
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void |
setColumn(int column,
Vector4f v)
Sets the specified column of this matrix4f to the vector provided.
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void |
setElement(int row,
int column,
float value)
Sets the specified element of this matrix4f to the value provided.
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void |
setIdentity()
Sets this Matrix4f to identity.
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void |
setM00(float m00)
Set the first matrix element in the first row.
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void |
setM01(float m01)
Set the second matrix element in the first row.
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void |
setM02(float m02)
Set the third matrix element in the first row.
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void |
setM03(float m03)
Set the fourth element of the first row.
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void |
setM10(float m10)
Set first matrix element in the second row.
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void |
setM11(float m11)
Set the second matrix element in the second row.
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void |
setM12(float m12)
Set the third matrix element in the second row.
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void |
setM13(float m13)
Set the fourth element of the second row.
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void |
setM20(float m20)
Set the first matrix element in the third row.
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void |
setM21(float m21)
Set the second matrix element in the third row.
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void |
setM22(float m22)
Set the third matrix element in the third row.
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void |
setM23(float m23)
Set the fourth element of the third row.
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void |
setM30(float m30)
Set the first element of the fourth row.
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void |
setM31(float m31)
Set the second element of the fourth row.
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void |
setM32(float m32)
Set the third element of the fourth row.
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void |
setM33(float m33)
Set the fourth element of the fourth row.
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void |
setRotation(AxisAngle4f a1)
Sets the rotational component (upper 3x3) of this matrix to the matrix
equivalent values of the axis-angle argument; the other elements of this
matrix are unchanged; a singular value decomposition is performed on this
object's upper 3x3 matrix to factor out the scale, then this object's
upper 3x3 matrix components are replaced by the matrix equivalent of the
axis-angle, and then the scale is reapplied to the rotational components.
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void |
setRotation(Matrix3d m1)
Sets the rotational component (upper 3x3) of this matrix to the matrix
values in the double precision Matrix3d argument; the other elements of
this matrix are unchanged; a singular value decomposition is performed on
this object's upper 3x3 matrix to factor out the scale, then this
object's upper 3x3 matrix components are replaced by the passed rotation
components, and then the scale is reapplied to the rotational components.
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void |
setRotation(Matrix3f m1)
Sets the rotational component (upper 3x3) of this matrix to the matrix
values in the single precision Matrix3f argument; the other elements of
this matrix are unchanged; a singular value decomposition is performed on
this object's upper 3x3 matrix to factor out the scale, then this
object's upper 3x3 matrix components are replaced by the passed rotation
components, and then the scale is reapplied to the rotational components.
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void |
setRotation(Quat4d q1)
Sets the rotational component (upper 3x3) of this matrix to the matrix
equivalent values of the quaternion argument; the other elements of this
matrix are unchanged; a singular value decomposition is performed on this
object's upper 3x3 matrix to factor out the scale, then this object's
upper 3x3 matrix components are replaced by the matrix equivalent of the
quaternion, and then the scale is reapplied to the rotational components.
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void |
setRotation(Quat4f q1)
Sets the rotational component (upper 3x3) of this matrix to the matrix
equivalent values of the quaternion argument; the other elements of this
matrix are unchanged; a singular value decomposition is performed on this
object's upper 3x3 matrix to factor out the scale, then this object's
upper 3x3 matrix components are replaced by the matrix equivalent of the
quaternion, and then the scale is reapplied to the rotational components.
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void |
setRotationScale(Matrix3f m1)
Replaces the upper 3x3 matrix values of this matrix with the values in
the matrix m1.
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void |
setRow(int row,
float[] v)
Sets the specified row of this matrix4f to the four values provided in
the passed array.
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void |
setRow(int row,
float x,
float y,
float z,
float w)
Sets the specified row of this matrix4f to the four values provided.
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void |
setRow(int row,
Vector4f v)
Sets the specified row of this matrix4f to the Vector provided.
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void |
setScale(float scale)
Sets the scale component of the current matrix by factoring out the
current scale (by doing an SVD) from the rotational component and
multiplying by the new scale.
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void |
setTranslation(Vector3f trans)
Modifies the translational components of this matrix to the values of the
Vector3f argument; the other values of this matrix are not modified.
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void |
setZero()
Sets this matrix to all zeros.
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void |
sub(Matrix4f m1)
Sets this matrix to the matrix difference of itself and matrix m1 (this =
this - m1).
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void |
sub(Matrix4f m1,
Matrix4f m2)
Performs an element-by-element subtraction of matrix m2 from matrix m1
and places the result into matrix this (this = m2 - m1).
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String |
toString()
Returns a string that contains the values of this Matrix4f.
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void |
transform(Point3f point)
Transforms the point parameter with this Matrix4f and places the result
back into point.
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void |
transform(Point3f point,
Point3f pointOut)
Transforms the point parameter with this Matrix4f and places the result
into pointOut.
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void |
transform(Tuple4f vec)
Transform the vector vec using this Transform and place the result back
into vec.
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void |
transform(Tuple4f vec,
Tuple4f vecOut)
Transform the vector vec using this Matrix4f and place the result into
vecOut.
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void |
transform(Vector3f normal)
Transforms the normal parameter by this transform and places the value
back into normal.
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void |
transform(Vector3f normal,
Vector3f normalOut)
Transforms the normal parameter by this Matrix4f and places the value
into normalOut.
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void |
transpose()
Sets the value of this matrix to its transpose in place.
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void |
transpose(Matrix4f m1)
Sets the value of this matrix to the transpose of the argument matrix.
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public float m00
public float m01
public float m02
public float m03
public float m10
public float m11
public float m12
public float m13
public float m20
public float m21
public float m22
public float m23
public float m30
public float m31
public float m32
public float m33
public Matrix4f(float m00, float m01, float m02, float m03, float m10, float m11, float m12, float m13, float m20, float m21, float m22, float m23, float m30, float m31, float m32, float m33)
m00
- the [0][0] elementm01
- the [0][1] elementm02
- the [0][2] elementm03
- the [0][3] elementm10
- the [1][0] elementm11
- the [1][1] elementm12
- the [1][2] elementm13
- the [1][3] elementm20
- the [2][0] elementm21
- the [2][1] elementm22
- the [2][2] elementm23
- the [2][3] elementm30
- the [3][0] elementm31
- the [3][1] elementm32
- the [3][2] elementm33
- the [3][3] elementpublic Matrix4f(float[] v)
v
- the array of length 16 containing in orderpublic Matrix4f(Quat4f q1, Vector3f t1, float s)
q1
- the quaternion value representing the rotational componentt1
- the translational component of the matrixs
- the scale value applied to the rotational componentspublic Matrix4f(Matrix4d m1)
m1
- the source matrixpublic Matrix4f(Matrix4f m1)
m1
- the source matrixpublic Matrix4f(Matrix3f m1, Vector3f t1, float s)
m1
- the rotation matrix representing the rotational componentst1
- the translational components of the matrixs
- the scale value applied to the rotational componentspublic Matrix4f()
public String toString()
public final void setIdentity()
public final void setElement(int row, int column, float value)
row
- the row number to be modified (zero indexed)column
- the column number to be modified (zero indexed)value
- the new valuepublic final float getElement(int row, int column)
row
- the row number to be retrieved (zero indexed)column
- the column number to be retrieved (zero indexed)public final void getRow(int row, Vector4f v)
row
- the matrix rowv
- the vector into which the matrix row values will be copiedpublic final void getRow(int row, float[] v)
row
- the matrix rowv
- the array into which the matrix row values will be copiedpublic final void getColumn(int column, Vector4f v)
column
- the matrix columnv
- the vector into which the matrix row values will be copiedpublic final void getColumn(int column, float[] v)
column
- the matrix columnv
- the array into which the matrix row values will be copiedpublic final void setScale(float scale)
scale
- the new scale amountpublic final void get(Matrix3d m1)
m1
- matrix into which the rotational component is placedpublic final void get(Matrix3f m1)
m1
- matrix into which the rotational component is placedpublic final float get(Matrix3f m1, Vector3f t1)
m1
- the normalized matrix representing the rotationt1
- the translation componentpublic final void get(Quat4f q1)
q1
- quaternion into which the rotation component is placedpublic final void get(Vector3f trans)
trans
- the vector that will receive the translational componentpublic final void getRotationScale(Matrix3f m1)
m1
- the matrix that will hold the valuespublic final float getScale()
public final void setRotationScale(Matrix3f m1)
m1
- the matrix that will be the new upper 3x3public final void setRow(int row, float x, float y, float z, float w)
row
- the row number to be modified (zero indexed)x
- the first column elementy
- the second column elementz
- the third column elementw
- the fourth column elementpublic final void setRow(int row, Vector4f v)
row
- the row number to be modified (zero indexed)v
- the replacement rowpublic final void setRow(int row, float[] v)
row
- the row number to be modified (zero indexed)v
- the replacement rowpublic final void setColumn(int column, float x, float y, float z, float w)
column
- the column number to be modified (zero indexed)x
- the first row elementy
- the second row elementz
- the third row elementw
- the fourth row elementpublic final void setColumn(int column, Vector4f v)
column
- the column number to be modified (zero indexed)v
- the replacement columnpublic final void setColumn(int column, float[] v)
column
- the column number to be modified (zero indexed)v
- the replacement columnpublic final void add(float scalar)
scalar
- the scalar adderpublic final void add(float scalar, Matrix4f m1)
scalar
- the scalar adderm1
- the original matrix valuespublic final void add(Matrix4f m1, Matrix4f m2)
m1
- the first matrixm2
- the second matrixpublic final void add(Matrix4f m1)
m1
- the other matrixpublic final void sub(Matrix4f m1, Matrix4f m2)
m1
- the first matrixm2
- the second matrixpublic final void sub(Matrix4f m1)
m1
- the other matrixpublic final void transpose()
public final void transpose(Matrix4f m1)
m1
- the matrix to be transposedpublic final void set(Quat4f q1)
q1
- the quaternion to be convertedpublic final void set(AxisAngle4f a1)
a1
- the axis and angle to be convertedpublic final void set(Quat4d q1)
q1
- the quaternion to be convertedpublic final void set(AxisAngle4d a1)
a1
- the axis and angle to be convertedpublic final void set(Quat4d q1, Vector3d t1, double s)
q1
- the rotation expressed as a quaterniont1
- the translations
- the scale valuepublic final void set(Quat4f q1, Vector3f t1, float s)
q1
- the rotation expressed as a quaterniont1
- the translations
- the scale valuepublic final void set(Matrix4d m1)
m1
- the matrix4d to be converted to floatpublic final void set(Matrix4f m1)
m1
- the matrix to be copiedpublic final void invert(Matrix4f m1)
m1
- the matrix to be invertedpublic final void invert()
public final float determinant()
public final void set(Matrix3f m1)
m1
- the single-precision 3x3 matrixpublic final void set(Matrix3d m1)
m1
- the double-precision 3x3 matrixpublic final void set(float scale)
scale
- the scale factor for the matrixpublic final void set(float[] m)
m
- the single precision array of length 16public final void set(Vector3f v1)
v1
- the translation amountpublic final void set(float scale, Vector3f t1)
scale
- the scale factor for the matrixt1
- the translation amountpublic final void set(Vector3f t1, float scale)
t1
- the translation amountscale
- the scale factor for the matrixpublic final void set(Matrix3f m1, Vector3f t1, float scale)
m1
- the rotation componentt1
- the translation componentscale
- the scale componentpublic final void set(Matrix3d m1, Vector3d t1, double scale)
m1
- the rotation componentt1
- the translation componentscale
- the scale factorpublic final void setTranslation(Vector3f trans)
trans
- the translational componentpublic final void rotX(float angle)
angle
- the angle to rotate about the X axis in radianspublic final void rotY(float angle)
angle
- the angle to rotate about the Y axis in radianspublic final void rotZ(float angle)
angle
- the angle to rotate about the Z axis in radianspublic final void mul(float scalar)
scalar
- the scalar multiplier.public final void mul(float scalar, Matrix4f m1)
scalar
- the scalar multiplier.m1
- the original matrix.public final void mul(Matrix4f m1)
m1
- the other matrixpublic final void mul(Matrix4f m1, Matrix4f m2)
m1
- the first matrixm2
- the second matrixpublic final void mulTransposeBoth(Matrix4f m1, Matrix4f m2)
m1
- the matrix on the left hand side of the multiplicationm2
- the matrix on the right hand side of the multiplicationpublic final void mulTransposeRight(Matrix4f m1, Matrix4f m2)
m1
- the matrix on the left hand side of the multiplicationm2
- the matrix on the right hand side of the multiplicationpublic final void mulTransposeLeft(Matrix4f m1, Matrix4f m2)
m1
- the matrix on the left hand side of the multiplicationm2
- the matrix on the right hand side of the multiplicationpublic boolean equals(Matrix4f m1)
m1
- the matrix with which the comparison is made.public boolean equals(Object t1)
public boolean epsilonEquals(Matrix4f m1, float epsilon)
m1
- the matrix to be compared to this matrixepsilon
- the threshold valuepublic int hashCode()
public final void transform(Tuple4f vec, Tuple4f vecOut)
vec
- the single precision vector to be transformedvecOut
- the vector into which the transformed values are placedpublic final void transform(Tuple4f vec)
vec
- the single precision vector to be transformedpublic final void transform(Point3f point, Point3f pointOut)
point
- the input point to be transformed.pointOut
- the transformed pointpublic final void transform(Point3f point)
point
- the input point to be transformed.public final void transform(Vector3f normal, Vector3f normalOut)
normal
- the input normal to be transformed.normalOut
- the transformed normalpublic final void transform(Vector3f normal)
normal
- the input normal to be transformed.public final void setRotation(Matrix3d m1)
m1
- double precision 3x3 matrixpublic final void setRotation(Matrix3f m1)
m1
- single precision 3x3 matrixpublic final void setRotation(Quat4f q1)
q1
- the quaternion that specifies the rotationpublic final void setRotation(Quat4d q1)
q1
- the quaternion that specifies the rotationpublic final void setRotation(AxisAngle4f a1)
a1
- the axis-angle to be converted (x, y, z, angle)public final void setZero()
public final void negate()
public final void negate(Matrix4f m1)
m1
- the source matrixpublic Object clone()
clone
in class Object
OutOfMemoryError
- if there is not enough memory.Cloneable
public final float getM00()
public final void setM00(float m00)
m00
- The m00 to set.public final float getM01()
public final void setM01(float m01)
m01
- The m01 to set.public final float getM02()
public final void setM02(float m02)
m02
- The m02 to set.public final float getM10()
public final void setM10(float m10)
m10
- The m10 to set.public final float getM11()
public final void setM11(float m11)
m11
- The m11 to set.public final float getM12()
public final void setM12(float m12)
m12
- The m12 to set.public final float getM20()
public final void setM20(float m20)
m20
- The m20 to set.public final float getM21()
public final void setM21(float m21)
m21
- The m21 to set.public final float getM22()
public final void setM22(float m22)
m22
- The m22 to set.public final float getM03()
public final void setM03(float m03)
m03
- The m03 to set.public final float getM13()
public final void setM13(float m13)
m13
- The m13 to set.public final float getM23()
public final void setM23(float m23)
m23
- The m23 to set.public final float getM30()
public final void setM30(float m30)
m30
- The m30 to set.public final float getM31()
public final void setM31(float m31)
m31
- The m31 to set.public final float getM32()
public final void setM32(float m32)
m32
- The m32 to set.public final float getM33()
public final void setM33(float m33)
m33
- The m33 to set.Copyright © 2015–2021 Fiji. All rights reserved.