com.io7m.jtensors.core.parameterized.matrices

Class PMatrices4x4D

java.lang.Object

com.io7m.jtensors.core.parameterized.matrices.PMatrices4x4D

public final class PMatrices4x4D
extends Object

Functions over PMatrix4x4D values.

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).

Since:

8.0.0

Method Summary

Modifier and Type	Method and Description
static <A,B,C,D,E,F> PMatrix4x4D<E,F>	add(PMatrix4x4D<A,B> m0, PMatrix4x4D<C,D> m1) Add the matrices m0 and m1.
static <A,B> Vector4D	column0(PMatrix4x4D<A,B> m)
static <A,B> Vector4D	column1(PMatrix4x4D<A,B> m)
static <A,B> Vector4D	column2(PMatrix4x4D<A,B> m)
static <A,B> Vector4D	column3(PMatrix4x4D<A,B> m)
static <A,B> double	determinant(PMatrix4x4D<A,B> m) Calculate the determinant of the matrix m.
static <A,B> PMatrix4x4D<A,B>	identity() The identity matrix.
static <A,B> Optional<PMatrix4x4D<B,A>>	invert(PMatrix4x4D<A,B> m) Calculate the inverse of the matrix m.
static <A,B,C> PMatrix4x4D<A,C>	multiply(PMatrix4x4D<B,C> m0, PMatrix4x4D<A,B> m1) Multiply the matrices m0 and m1.
static <A,B> PVector4D<B>	multiplyVectorPost(PMatrix4x4D<A,B> m, PVector4D<A> v) Multiply the vector v by the matrix m.
static Vector4D	multiplyVectorPost(PMatrix4x4D m, Vector4D v) Multiply the vector v by the matrix m.
static <A,B> PMatrix4x4D<A,B>	ofAxisAngle(double axis_x, double axis_y, double axis_z, double angle) Construct a matrix that will rotate by angle radians around the axis (x, y, z).
static <A,B> PMatrix4x4D<A,B>	ofColumns(Vector4D c0, Vector4D c1, Vector4D c2, Vector4D c3) Construct a matrix from the column vectors (c0, c1, c2, c3).
static <A,B> PMatrix4x4D<A,B>	ofRows(Vector4D r0, Vector4D r1, Vector4D r2, Vector4D r3) Construct a matrix from the row vectors (r0, r1, r2, r3).
static <A,B> PMatrix4x4D<A,B>	ofScale(double x, double y, double z) Construct a matrix that will scale by (x, y, z).
static <A,B> PMatrix4x4D<A,B>	ofTranslation(double x, double y, double z) Construct a matrix that will translate by (x, y, z).
static <A,B> Vector4D	row0(PMatrix4x4D<A,B> m)
static <A,B> Vector4D	row1(PMatrix4x4D<A,B> m)
static <A,B> Vector4D	row2(PMatrix4x4D<A,B> m)
static <A,B> Vector4D	row3(PMatrix4x4D<A,B> m)
static <A,B,C,D> PMatrix4x4D<C,D>	scale(PMatrix4x4D<A,B> m, double r) Scale the matrix m by r.
static <A,B,C,D,E,F> PMatrix4x4D<E,F>	subtract(PMatrix4x4D<A,B> m0, PMatrix4x4D<C,D> m1) Subtract the matrices m0 and m1.
static <A,B> PMatrix4x4D<A,B>	toParameterized(Matrix4x4D m)
static <A,B> Matrix4x4D	toUnparameterized(PMatrix4x4D<A,B> m)
static <A,B> double	trace(PMatrix4x4D<A,B> m) Return the trace of the matrix m.
static <A,B> PMatrix4x4D<A,B>	transpose(PMatrix4x4D<A,B> m) Calculate the transpose of the matrix m.
static <A,B> PMatrix4x4D<A,B>	withColumn(PMatrix4x4D<A,B> m, int column, double r0, double r1, double r2, double r3) Set the column column of m to (r0, r1, r2, r3).
static <A,B> PMatrix4x4D<A,B>	withRow(PMatrix4x4D<A,B> m, int row, double c0, double c1, double c2, double c3) Set the row row of m to (c0, c1, c2, c3).
static <A,B> PMatrix4x4D<A,B>	zero() The zero matrix.

Methods inherited from class java.lang.Object

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

Method Detail

add

public static <A,B,C,D,E,F> PMatrix4x4D<E,F> add(PMatrix4x4D<A,B> m0,
                                                 PMatrix4x4D<C,D> m1)

Add the matrices m0 and m1.

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

C - A phantom type parameter (possibly representing a source coordinate system)

D - A phantom type parameter (possibly representing a target coordinate system)

E - A phantom type parameter (possibly representing a source coordinate system)

F - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m0 - The left matrix

m1 - The right matrix

Returns:

m0 + m1

determinant

public static <A,B> double determinant(PMatrix4x4D<A,B> m)

Calculate the determinant of the matrix m.

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m - The matrix

Returns:

The determinant of m

invert

public static <A,B> Optional<PMatrix4x4D<B,A>> invert(PMatrix4x4D<A,B> m)

Calculate the inverse of the matrix m.

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m - The matrix

Returns:

The inverse of m, or nothing if no inverse exists

multiply

public static <A,B,C> PMatrix4x4D<A,C> multiply(PMatrix4x4D<B,C> m0,
                                                PMatrix4x4D<A,B> m1)

Multiply the matrices m0 and m1.

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

C - A phantom type parameter (possibly representing a source coordinate system)

Parameters:

m0 - The left matrix

m1 - The right matrix

Returns:

m0 * m1

multiplyVectorPost

public static <A,B> PVector4D<B> multiplyVectorPost(PMatrix4x4D<A,B> m,
                                                    PVector4D<A> v)

Multiply the vector v by the matrix m.

This is post multiplication.

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m - The matrix

v - The vector

Returns:

m * v

multiplyVectorPost

public static Vector4D multiplyVectorPost(PMatrix4x4D m,
                                          Vector4D v)

Multiply the vector v by the matrix m.

This is post multiplication.

Parameters:

m - The matrix

v - The vector

Returns:

m * v

ofColumns

public static <A,B> PMatrix4x4D<A,B> ofColumns(Vector4D c0,
                                               Vector4D c1,
                                               Vector4D c2,
                                               Vector4D c3)

Construct a matrix from the column vectors (c0, c1, c2, c3).

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

c0 - The column 0

c1 - The column 1

c2 - The column 2

c3 - The column 3

Returns:

A constructed matrix

ofRows

public static <A,B> PMatrix4x4D<A,B> ofRows(Vector4D r0,
                                            Vector4D r1,
                                            Vector4D r2,
                                            Vector4D r3)

Construct a matrix from the row vectors (r0, r1, r2, r3).

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

r0 - The row 0

r1 - The row 1

r2 - The row 2

r3 - The row 3

Returns:

A constructed matrix

ofScale

public static <A,B> PMatrix4x4D<A,B> ofScale(double x,
                                             double y,
                                             double z)

Construct a matrix that will scale by (x, y, z).

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

x - The X scaling value

y - The Y scaling value

z - The Z scaling value

Returns:

A constructed matrix

ofTranslation

public static <A,B> PMatrix4x4D<A,B> ofTranslation(double x,
                                                   double y,
                                                   double z)

Construct a matrix that will translate by (x, y, z).

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

x - The X scaling value

y - The Y scaling value

z - The Z scaling value

Returns:

A constructed matrix

ofAxisAngle

public static <A,B> PMatrix4x4D<A,B> ofAxisAngle(double axis_x,
                                                 double axis_y,
                                                 double axis_z,
                                                 double angle)

Construct a matrix that will rotate by angle radians around the axis (x, y, z).

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

angle - The angle in radians

axis_x - The X axis value

axis_y - The Y axis value

axis_z - The Z axis value

Returns:

A constructed matrix

row0

public static <A,B> Vector4D row0(PMatrix4x4D<A,B> m)

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a source coordinate system)

Parameters:

m - The matrix

Returns:

Row 0 of the matrix

row1

public static <A,B> Vector4D row1(PMatrix4x4D<A,B> m)

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a source coordinate system)

Parameters:

m - The matrix

Returns:

Row 1 of the matrix

row2

public static <A,B> Vector4D row2(PMatrix4x4D<A,B> m)

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a source coordinate system)

Parameters:

m - The matrix

Returns:

Row 2 of the matrix

row3

public static <A,B> Vector4D row3(PMatrix4x4D<A,B> m)

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a source coordinate system)

Parameters:

m - The matrix

Returns:

Row 3 of the matrix

column0

public static <A,B> Vector4D column0(PMatrix4x4D<A,B> m)

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a source coordinate system)

Parameters:

m - The matrix

Returns:

Column 0 of the matrix

column1

public static <A,B> Vector4D column1(PMatrix4x4D<A,B> m)

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a source coordinate system)

Parameters:

m - The matrix

Returns:

Column 1 of the matrix

column2

public static <A,B> Vector4D column2(PMatrix4x4D<A,B> m)

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a source coordinate system)

Parameters:

m - The matrix

Returns:

Column 2 of the matrix

column3

public static <A,B> Vector4D column3(PMatrix4x4D<A,B> m)

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a source coordinate system)

Parameters:

m - The matrix

Returns:

Column 3 of the matrix

scale

public static <A,B,C,D> PMatrix4x4D<C,D> scale(PMatrix4x4D<A,B> m,
                                               double r)

Scale the matrix m by r.

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

C - A phantom type parameter (possibly representing a source coordinate system)

D - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m - The matrix

r - The scale factor

Returns:

m * r

subtract

public static <A,B,C,D,E,F> PMatrix4x4D<E,F> subtract(PMatrix4x4D<A,B> m0,
                                                      PMatrix4x4D<C,D> m1)

Subtract the matrices m0 and m1.

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

C - A phantom type parameter (possibly representing a source coordinate system)

D - A phantom type parameter (possibly representing a target coordinate system)

E - A phantom type parameter (possibly representing a source coordinate system)

F - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m0 - The left matrix

m1 - The right matrix

Returns:

m0 - m1

trace

public static <A,B> double trace(PMatrix4x4D<A,B> m)

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

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m - The matrix

Returns:

The trace of the matrix

transpose

public static <A,B> PMatrix4x4D<A,B> transpose(PMatrix4x4D<A,B> m)

Calculate the transpose of the matrix m.

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m - The matrix

Returns:

The transpose of m

withColumn

public static <A,B> PMatrix4x4D<A,B> withColumn(PMatrix4x4D<A,B> m,
                                                int column,
                                                double r0,
                                                double r1,
                                                double r2,
                                                double r3)

Set the column column of m to (r0, r1, r2, r3).

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system) * @param r0 The value of row 0 in the column

Parameters:

m - The matrix

column - The column index in the range [0, 3]

r1 - The value of row 1 in the column

r2 - The value of row 2 in the column

r3 - The value of row 3 in the column

Returns:

A matrix with the given row

withRow

public static <A,B> PMatrix4x4D<A,B> withRow(PMatrix4x4D<A,B> m,
                                             int row,
                                             double c0,
                                             double c1,
                                             double c2,
                                             double c3)

Set the row row of m to (c0, c1, c2, c3).

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m - The matrix

row - The row index in the range [0, 3]

c0 - The value of column 0 in the row

c1 - The value of column 1 in the row

c2 - The value of column 2 in the row

c3 - The value of column 3 in the row

Returns:

A matrix with the given row

zero

public static <A,B> PMatrix4x4D<A,B> zero()

The zero matrix.

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Returns:

A matrix with all zero components

identity

public static <A,B> PMatrix4x4D<A,B> identity()

The identity matrix.

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Returns:

A matrix with all diagonal components set to 1 and all other components set to 0.

toUnparameterized

public static <A,B> Matrix4x4D toUnparameterized(PMatrix4x4D<A,B> m)

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m - The input matrix

Returns:

A matrix equal to m but without type parameters

toParameterized

public static <A,B> PMatrix4x4D<A,B> toParameterized(Matrix4x4D m)

Type Parameters:

A - A phantom type parameter (possibly representing a source coordinate system)

B - A phantom type parameter (possibly representing a target coordinate system)

Parameters:

m - The input matrix

Returns:

A matrix equal to m with type parameters