com.io7m.jtensors

Class MatrixM3x3F

java.lang.Object

com.io7m.jtensors.MatrixM3x3F

All Implemented Interfaces:

MatrixReadable3x3FType, MatrixReadableFType

public class MatrixM3x3F
extends Object
implements MatrixReadable3x3FType

A 3x3 mutable matrix type with single precision elements.

Values of type MatrixM3x3F are backed by direct memory, with the rows and columns of the matrices being stored in column-major format. This allows the matrices to be passed to OpenGL directly, without requiring transposition.

Values of this type cannot be accessed safely from multiple threads without explicit synchronization.

See "Mathematics for 3D Game Programming and Computer Graphics" 2nd Ed for the derivations of most of the code in this class (ISBN: 1-58450-277-0).

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	MatrixM3x3F.Context The Context type contains the minimum storage required for all of the functions of the MatrixM3x3F class.

Constructor Summary

Constructors

Constructor and Description
MatrixM3x3F() Construct a new identity matrix.
MatrixM3x3F(MatrixReadable3x3FType source) Construct a new copy of the given matrix.

Method Summary

Methods

Modifier and Type	Method and Description
static MatrixM3x3F	add(MatrixReadable3x3FType m0, MatrixReadable3x3FType m1, MatrixM3x3F out) Elementwise add of matrices m0 and m1.
static MatrixM3x3F	addInPlace(MatrixM3x3F m0, MatrixM3x3F m1) Elementwise add of matrices m0 and m1, returning the result in m0.
static MatrixM3x3F	addRowScaled(MatrixReadable3x3FType m, int row_a, int row_b, int row_c, double r, MatrixM3x3F out) Add the values in row row_b to the values in row row_a scaled by r, saving the resulting row in row row_c of the matrix out.
static MatrixM3x3F	addRowScaledInPlace(MatrixM3x3F m, int row_a, int row_b, int row_c, double r) Add the values in row row_b to the values in row row_a scaled by r, saving the resulting row in row row_c of the matrix m.
static MatrixM3x3F	copy(MatrixReadable3x3FType input, MatrixM3x3F output) Copy the contents of the matrix input to the matrix output, completely replacing all elements.
static double	determinant(MatrixReadable3x3FType m) Calculate the determinant of the matrix m.
boolean	equals(Object obj)
static MatrixM3x3F	exchangeRows(MatrixReadable3x3FType m, int row_a, int row_b, MatrixM3x3F out) Exchange the row row_a and row row_b of the matrix m, saving the exchanged rows to out .
static MatrixM3x3F	exchangeRowsInPlace(MatrixM3x3F m, int row_a, int row_b) Exchange the row row_a and row row_b of the matrix m, saving the exchanged rows to m .
static FloatBuffer	floatBuffer(MatrixM3x3F m)
float	get(int row, int column)
static float	get(MatrixReadable3x3FType m, int row, int column)
FloatBuffer	getFloatBuffer()
void	getRow3F(int row, VectorM3F out) Retrieve row row, saving the result to out.
float	getRowColumnF(int row, int column)
int	hashCode()
static com.io7m.jfunctional.OptionType<MatrixM3x3F>	invert(MatrixReadable3x3FType m, MatrixM3x3F out) Calculate the inverse of the matrix m, saving the resulting matrix to out.
static com.io7m.jfunctional.OptionType<MatrixM3x3F>	invertInPlace(MatrixM3x3F m) Calculate the inverse of the matrix m, saving the resulting matrix to m.
static void	lookAtWithContext(MatrixM3x3F.Context context, VectorReadable3FType origin, VectorReadable3FType target, VectorReadable3FType up, MatrixM3x3F out_matrix, VectorM3F out_translation) Calculate a rotation and translation representing a "camera" looking from the point origin to the point target.
static MatrixM3x3F	makeRotation(double angle, VectorReadable3FType axis) Generate and return a matrix that represents a rotation of angle radians around the axis axis.
static MatrixM3x3F	makeRotation(double angle, VectorReadable3FType axis, MatrixM3x3F out) Generate a matrix that represents a rotation of angle radians around the axis axis and save to out.
static MatrixM3x3F	makeTranslation2F(VectorReadable2FType v, MatrixM3x3F out) Create a translation matrix that represents a translation by the vector v, writing the resulting matrix to out.
static MatrixM3x3F	makeTranslation2I(VectorReadable2IType v, MatrixM3x3F out) Create a translation matrix that represents a translation by the vector v, writing the resulting matrix to out.
static MatrixM3x3F	multiply(MatrixReadable3x3FType m0, MatrixReadable3x3FType m1, MatrixM3x3F out) Multiply the matrix m0 with the matrix m1, writing the result to out.
static MatrixM3x3F	multiplyInPlace(MatrixM3x3F m0, MatrixReadable3x3FType m1) Multiply the matrix m0 with the matrix m1, writing the result to m0.
static VectorM3F	multiplyVector3F(MatrixReadable3x3FType m, VectorReadable3FType v, VectorM3F out) Multiply the matrix m with the vector v, writing the resulting vector to out.
static MatrixM3x3F	rotate(double angle, MatrixReadable3x3FType m, VectorReadable3FType axis, MatrixM3x3F out) Rotate the matrix m by angle radians around the axis axis, saving the result into out.
static MatrixM3x3F	rotateInPlace(double angle, MatrixM3x3F m, VectorReadable3FType axis) Rotate the matrix m by angle radians around the axis axis, saving the result into m.
static MatrixM3x3F	rotateInPlaceWithContext(MatrixM3x3F.Context context, double angle, MatrixM3x3F m, VectorReadable3FType axis) Rotate the matrix m by angle radians around the axis axis, saving the result into m.
static MatrixM3x3F	rotateWithContext(MatrixM3x3F.Context context, double angle, MatrixReadable3x3FType m, VectorReadable3FType axis, MatrixM3x3F out) Rotate the matrix m by angle radians around the axis axis, saving the result into out.
static VectorM3F	row(MatrixReadable3x3FType m, int row, VectorM3F out)
static MatrixM3x3F	scale(MatrixReadable3x3FType m, double r, MatrixM3x3F out) Scale all elements of the matrix m by the scaling value r, saving the result in out.
static MatrixM3x3F	scaleInPlace(MatrixM3x3F m, double r) Scale all elements of the matrix m by the scaling value r, saving the result in m.
static MatrixM3x3F	scaleRow(MatrixReadable3x3FType m, int row, double r, MatrixM3x3F out) Scale row r of the matrix m by r, saving the result to row r of out.
static MatrixM3x3F	scaleRowInPlace(MatrixM3x3F m, int row, double r) Scale row r of the matrix m by r, saving the result to row r of m.
MatrixM3x3F	set(int row, int column, float value) Set the value at the given row and column.
static MatrixM3x3F	set(MatrixM3x3F m, int row, int column, float value) Set the value in the matrix m at row row, column column to value.
static MatrixM3x3F	setIdentity(MatrixM3x3F m) Set the given matrix m to the identity matrix.
static MatrixM3x3F	setZero(MatrixM3x3F m) Set the given matrix m to the zero matrix.
String	toString()
static double	trace(MatrixReadable3x3FType m) Return the trace of the matrix m.
static MatrixM3x3F	translateByVector2F(MatrixReadable3x3FType m, VectorReadable2FType v, MatrixM3x3F out) Translate the matrix m by the vector v, storing the resulting matrix in out.
static MatrixM3x3F	translateByVector2FInPlace(MatrixM3x3F m, VectorReadable2FType v) Translate the matrix m by the vector v, storing the resulting matrix in m.
static MatrixM3x3F	translateByVector2I(MatrixReadable3x3FType m, VectorReadable2IType v, MatrixM3x3F out) Translate the matrix m by the vector v, storing the resulting matrix in out.
static MatrixM3x3F	translateByVector2IInPlace(MatrixM3x3F m, VectorReadable2IType v) Translate the matrix m by the vector v, storing the resulting matrix in m.
static MatrixM3x3F	transpose(MatrixReadable3x3FType m, MatrixM3x3F out) Transpose the given matrix m, writing the resulting matrix to out.
static MatrixM3x3F	transposeInPlace(MatrixM3x3F m) Transpose the given matrix m, writing the resulting matrix to m.

Methods inherited from class java.lang.Object

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

Constructor Detail

MatrixM3x3F

public MatrixM3x3F()

Construct a new identity matrix.

MatrixM3x3F

public MatrixM3x3F(MatrixReadable3x3FType source)

Construct a new copy of the given matrix.

Parameters:

source - The source matrix.

Method Detail

add

public static final MatrixM3x3F add(MatrixReadable3x3FType m0,
              MatrixReadable3x3FType m1,
              MatrixM3x3F out)

Elementwise add of matrices m0 and m1.

Parameters:

m0 - The left input matrix.

m1 - The right input matrix.

out - The output matrix.

Returns:

out

addInPlace

public static final MatrixM3x3F addInPlace(MatrixM3x3F m0,
                     MatrixM3x3F m1)

Elementwise add of matrices m0 and m1, returning the result in m0.

Parameters:

m0 - The left input matrix.

m1 - The right input matrix.

Returns:

m0

addRowScaled

public static final MatrixM3x3F addRowScaled(MatrixReadable3x3FType m,
                       int row_a,
                       int row_b,
                       int row_c,
                       double r,
                       MatrixM3x3F out)

Add the values in row row_b to the values in row row_a scaled by r, saving the resulting row in row row_c of the matrix out.

This is one of the three "elementary" operations defined on matrices. See Elementary operations .

Parameters:

m - The input matrix.

row_a - The row on the lefthand side of the addition.

row_b - The row on the righthand side of the addition.

row_c - The destination row.

r - The scaling value.

out - The output matrix.

Returns:

out

addRowScaledInPlace

public static final MatrixM3x3F addRowScaledInPlace(MatrixM3x3F m,
                              int row_a,
                              int row_b,
                              int row_c,
                              double r)

Add the values in row row_b to the values in row row_a scaled by r, saving the resulting row in row row_c of the matrix m.

This is one of the three "elementary" operations defined on matrices. See Elementary operations .

Parameters:

m - The input matrix.

row_a - The row on the lefthand side of the addition.

row_b - The row on the righthand side of the addition.

row_c - The destination row.

r - The scaling value.

Returns:

m

copy

public static final MatrixM3x3F copy(MatrixReadable3x3FType input,
               MatrixM3x3F output)

Copy the contents of the matrix input to the matrix output, completely replacing all elements.

Parameters:

input - The input vector.

output - The output vector.

Returns:

output

determinant

public static final double determinant(MatrixReadable3x3FType m)

Calculate the determinant of the matrix m.

Parameters:

m - The input matrix.

Returns:

The determinant.

exchangeRows

public static final MatrixM3x3F exchangeRows(MatrixReadable3x3FType m,
                       int row_a,
                       int row_b,
                       MatrixM3x3F out)

Exchange the row row_a and row row_b of the matrix m, saving the exchanged rows to out .

This is one of the three "elementary" operations defined on matrices. See Elementary operations .

Parameters:

m - The input matrix.

row_a - The first row.

row_b - The second row.

out - The output matrix.

Returns:

out

exchangeRowsInPlace

public static final MatrixM3x3F exchangeRowsInPlace(MatrixM3x3F m,
                              int row_a,
                              int row_b)

Exchange the row row_a and row row_b of the matrix m, saving the exchanged rows to m .

This is one of the three "elementary" operations defined on matrices. See Elementary operations .

Parameters:

m - The input matrix.

row_a - The first row.

row_b - The second row.

Returns:

m

floatBuffer

public static final FloatBuffer floatBuffer(MatrixM3x3F m)

Parameters:

m - The input matrix.

Returns:

A view of the buffer that backs this matrix.

get

public static final float get(MatrixReadable3x3FType m,
        int row,
        int column)

Parameters:

row - The row

column - The column

m - The input matrix

Returns:

The value from the matrix m at row row, column column.

invert

public static final com.io7m.jfunctional.OptionType<MatrixM3x3F> invert(MatrixReadable3x3FType m,
                                                  MatrixM3x3F out)

Calculate the inverse of the matrix m, saving the resulting matrix to out. The function returns Some(out) iff it was possible to invert the matrix, and None otherwise. It is not possible to invert a matrix that has a determinant of 0.

Parameters:

m - The input matrix.

out - The output matrix.

Returns:

out

See Also:

determinant(MatrixReadable3x3FType)

invertInPlace

public static final com.io7m.jfunctional.OptionType<MatrixM3x3F> invertInPlace(MatrixM3x3F m)

Calculate the inverse of the matrix m, saving the resulting matrix to m. The function returns Some(m) iff it was possible to invert the matrix, and None otherwise. It is not possible to invert a matrix that has a determinant of 0.

Parameters:

m - The input matrix.

Returns:

m

See Also:

determinant(MatrixReadable3x3FType)

lookAtWithContext

public static final void lookAtWithContext(MatrixM3x3F.Context context,
                     VectorReadable3FType origin,
                     VectorReadable3FType target,
                     VectorReadable3FType up,
                     MatrixM3x3F out_matrix,
                     VectorM3F out_translation)

Calculate a rotation and translation representing a "camera" looking from the point origin to the point target. target must represent the "up" vector for the camera. Usually, this is simply a unit vector (0, 1, 0) representing the Y axis.

The function uses preallocated storage from context.

The view is expressed as a rotation matrix and a translation vector, written to out_matrix and out_translation, respectively.

Parameters:

context - Preallocated storage

out_matrix - The output matrix

out_translation - The output translation

origin - The position of the viewer

target - The target being viewed

up - The up vector

makeRotation

public static final MatrixM3x3F makeRotation(double angle,
                       VectorReadable3FType axis)

Generate and return a matrix that represents a rotation of angle radians around the axis axis.

The function assumes a right-handed coordinate system and therefore a positive rotation around any axis represents a counter-clockwise rotation around that axis.

Parameters:

angle - The angle in radians.

axis - The axis.

Returns:

out

Since:

5.0.0

makeRotation

public static final MatrixM3x3F makeRotation(double angle,
                       VectorReadable3FType axis,
                       MatrixM3x3F out)

Generate a matrix that represents a rotation of angle radians around the axis axis and save to out.

The function assumes a right-handed coordinate system and therefore a positive rotation around any axis represents a counter-clockwise rotation around that axis.

Parameters:

angle - The angle in radians.

axis - The axis.

out - The output matrix.

Returns:

out

Since:

5.0.0

makeTranslation2F

public static final MatrixM3x3F makeTranslation2F(VectorReadable2FType v,
                            MatrixM3x3F out)

Create a translation matrix that represents a translation by the vector v, writing the resulting matrix to out.

Parameters:

v - The translation vector.

out - The output matrix.

Returns:

out

makeTranslation2I

public static final MatrixM3x3F makeTranslation2I(VectorReadable2IType v,
                            MatrixM3x3F out)

Create a translation matrix that represents a translation by the vector v, writing the resulting matrix to out.

Parameters:

v - The translation vector.

out - The output matrix.

Returns:

out

multiply

public static final MatrixM3x3F multiply(MatrixReadable3x3FType m0,
                   MatrixReadable3x3FType m1,
                   MatrixM3x3F out)

Multiply the matrix m0 with the matrix m1, writing the result to out.

Parameters:

m0 - The left input vector.

m1 - The right input vector.

out - The output vector.

Returns:

out

multiplyInPlace

public static final MatrixM3x3F multiplyInPlace(MatrixM3x3F m0,
                          MatrixReadable3x3FType m1)

Multiply the matrix m0 with the matrix m1, writing the result to m0.

Parameters:

m0 - The left input vector.

m1 - The right input vector.

Returns:

out

multiplyVector3F

public static final VectorM3F multiplyVector3F(MatrixReadable3x3FType m,
                         VectorReadable3FType v,
                         VectorM3F out)

Multiply the matrix m with the vector v, writing the resulting vector to out.

Parameters:

m - The input matrix.

v - The input vector.

out - The output vector.

Returns:

out

rotate

public static final MatrixM3x3F rotate(double angle,
                 MatrixReadable3x3FType m,
                 VectorReadable3FType axis,
                 MatrixM3x3F out)

Rotate the matrix m by angle radians around the axis axis, saving the result into out.

Parameters:

angle - The angle in radians.

m - The input matrix.

axis - A vector representing an axis.

out - The output matrix.

Returns:

out

Since:

5.0.0

rotateInPlace

public static final MatrixM3x3F rotateInPlace(double angle,
                        MatrixM3x3F m,
                        VectorReadable3FType axis)

Rotate the matrix m by angle radians around the axis axis, saving the result into m.

Parameters:

angle - The angle in radians.

m - The input matrix.

axis - A vector representing an axis.

Returns:

m

Since:

5.0.0

rotateInPlaceWithContext

public static final MatrixM3x3F rotateInPlaceWithContext(MatrixM3x3F.Context context,
                                   double angle,
                                   MatrixM3x3F m,
                                   VectorReadable3FType axis)

Rotate the matrix m by angle radians around the axis axis, saving the result into m. The function uses preallocated storage in context to avoid allocating memory. The function assumes a right-handed coordinate system.

Parameters:

context - Preallocated storage.

angle - The angle in radians.

m - The input matrix.

axis - A vector representing an axis.

Returns:

m

Since:

5.0.0

rotateWithContext

public static final MatrixM3x3F rotateWithContext(MatrixM3x3F.Context context,
                            double angle,
                            MatrixReadable3x3FType m,
                            VectorReadable3FType axis,
                            MatrixM3x3F out)

Rotate the matrix m by angle radians around the axis axis, saving the result into out. The function uses preallocated storage in context to avoid allocating memory. The function assumes a right-handed coordinate system.

Parameters:

context - Preallocated storage.

angle - The angle in radians.

m - The input matrix.

axis - A vector representing an axis.

out - The output matrix.

Returns:

out

Since:

5.0.0

row

public static final VectorM3F row(MatrixReadable3x3FType m,
            int row,
            VectorM3F out)

Parameters:

m - The input matrix

row - The row

out - The output vector

Returns:

Row row of the matrix m in the vector out.

scale

public static final MatrixM3x3F scale(MatrixReadable3x3FType m,
                double r,
                MatrixM3x3F out)

Scale all elements of the matrix m by the scaling value r, saving the result in out.

Parameters:

m - The input matrix.

r - The scaling value.

out - The output matrix

Returns:

out

scaleInPlace

public static final MatrixM3x3F scaleInPlace(MatrixM3x3F m,
                       double r)

Scale all elements of the matrix m by the scaling value r, saving the result in m.

Parameters:

m - The input matrix.

r - The scaling value.

Returns:

m

scaleRow

public static final MatrixM3x3F scaleRow(MatrixReadable3x3FType m,
                   int row,
                   double r,
                   MatrixM3x3F out)

Scale row r of the matrix m by r, saving the result to row r of out.

This is one of the three "elementary" operations defined on matrices. See Elementary operations .

Parameters:

m - The input matrix.

row - The index of the row (0 <= row < 4).

r - The scaling value.

out - The output matrix.

Returns:

out

scaleRowInPlace

public static final MatrixM3x3F scaleRowInPlace(MatrixM3x3F m,
                          int row,
                          double r)

Scale row r of the matrix m by r, saving the result to row r of m.

This is one of the three "elementary" operations defined on matrices. See Elementary operations .

Parameters:

m - The input matrix.

row - The index of the row (0 <= row < 4).

r - The scaling value.

Returns:

m

set

public static final MatrixM3x3F set(MatrixM3x3F m,
              int row,
              int column,
              float value)

Set the value in the matrix m at row row, column column to value.

Parameters:

m - The input matrix

row - The row

column - The column

value - The value

Returns:

m

setIdentity

public static final MatrixM3x3F setIdentity(MatrixM3x3F m)

Set the given matrix m to the identity matrix.

Parameters:

m - The matrix

Returns:

m

setZero

public static final MatrixM3x3F setZero(MatrixM3x3F m)

Set the given matrix m to the zero matrix.

Parameters:

m - The matrix

Returns:

m

trace

public static final double trace(MatrixReadable3x3FType m)

Return the trace of the matrix m. The trace is defined as the sum of the diagonal elements of the matrix.

Parameters:

m - The input matrix

Returns:

The trace of the matrix

Since:

5.0.0

translateByVector2F

public static final MatrixM3x3F translateByVector2F(MatrixReadable3x3FType m,
                              VectorReadable2FType v,
                              MatrixM3x3F out)

Translate the matrix m by the vector v, storing the resulting matrix in out.

Parameters:

m - The input matrix.

v - The translation vector.

out - The output matrix.

Returns:

out

translateByVector2FInPlace

public static final MatrixM3x3F translateByVector2FInPlace(MatrixM3x3F m,
                                     VectorReadable2FType v)

Translate the matrix m by the vector v, storing the resulting matrix in m.

Parameters:

m - The input matrix.

v - The translation vector.

Returns:

m

translateByVector2I

public static final MatrixM3x3F translateByVector2I(MatrixReadable3x3FType m,
                              VectorReadable2IType v,
                              MatrixM3x3F out)

Translate the matrix m by the vector v, storing the resulting matrix in out.

Parameters:

m - The input matrix.

v - The translation vector.

out - The output matrix.

Returns:

out

translateByVector2IInPlace

public static final MatrixM3x3F translateByVector2IInPlace(MatrixM3x3F m,
                                     VectorReadable2IType v)

Translate the matrix m by the vector v, storing the resulting matrix in m.

Parameters:

m - The input matrix.

v - The translation vector.

Returns:

m

transpose

public static final MatrixM3x3F transpose(MatrixReadable3x3FType m,
                    MatrixM3x3F out)

Transpose the given matrix m, writing the resulting matrix to out.

Parameters:

m - The input matrix.

out - The output matrix.

Returns:

out

transposeInPlace

public static final MatrixM3x3F transposeInPlace(MatrixM3x3F m)

Transpose the given matrix m, writing the resulting matrix to m.

Parameters:

m - The input matrix.

Returns:

m

equals

public final boolean equals(@Nullable
             Object obj)

Overrides:

equals in class Object

get

public final float get(int row,
        int column)

Parameters:

row - The row

column - The column

Returns:

The value at the given row and column

getFloatBuffer

public final FloatBuffer getFloatBuffer()

Specified by:

getFloatBuffer in interface MatrixReadableFType

Returns:

A view of the buffer that backs this matrix.

getRow3F

public final void getRow3F(int row,
            VectorM3F out)

Description copied from interface: MatrixReadable3x3FType

Retrieve row row, saving the result to out.

Specified by:

getRow3F in interface MatrixReadable3x3FType

Parameters:

row - The index of the row, starting at 0.

out - The output vector.

getRowColumnF

public final float getRowColumnF(int row,
                  int column)

Specified by:

getRowColumnF in interface MatrixReadableFType

Parameters:

row - The row

column - The column

Returns:

The value from the matrix at row row , column column.

hashCode

public final int hashCode()

Overrides:

hashCode in class Object

set

public final MatrixM3x3F set(int row,
              int column,
              float value)

Set the value at the given row and column.

Parameters:

row - The row

column - The column

value - The value

Returns:

this

toString

public final String toString()

Overrides:

toString in class Object