Module com.io7m.jtensors.core

Package com.io7m.jtensors.core.parameterized.matrices

Class PMatrices3x3D

java.lang.Object

com.io7m.jtensors.core.parameterized.matrices.PMatrices3x3D

public final class PMatrices3x3D
extends Object

Functions over PMatrix3x3D 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	Description
static <A,B,C,D,E,F> PMatrix3x3D<E,F>	add(PMatrix3x3D<A,B> m0, PMatrix3x3D<C,D> m1)	Add the matrices m0 and m1.
static <A,B> Vector3D	column0(PMatrix3x3D<A,B> m)
static <A,B> Vector3D	column1(PMatrix3x3D<A,B> m)
static <A,B> Vector3D	column2(PMatrix3x3D<A,B> m)
static <A,B> double	determinant(PMatrix3x3D<A,B> m)	Calculate the determinant of the matrix m.
static <A,B> PMatrix3x3D<A,B>	identity()	The identity matrix.
static <A,B> Optional<PMatrix3x3D<B,A>>	invert(PMatrix3x3D<A,B> m)	Calculate the inverse of the matrix m.
static <A,B,C> PMatrix3x3D<A,C>	multiply(PMatrix3x3D<B,C> m0, PMatrix3x3D<A,B> m1)	Multiply the matrices m0 and m1.
static <A,B> PVector3D<B>	multiplyVectorPost(PMatrix3x3D<A,B> m, PVector3D<A> v)	Multiply the vector v by the matrix m.
static Vector3D	multiplyVectorPost(PMatrix3x3D m, Vector3D v)	Multiply the vector v by the matrix m.
static <A,B> PMatrix3x3D<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> PMatrix3x3D<A,B>	ofColumns(Vector3D c0, Vector3D c1, Vector3D c2)	Construct a matrix from the column vectors (c0, c1, c2).
static <A,B> PMatrix3x3D<A,B>	ofRows(Vector3D r0, Vector3D r1, Vector3D r2)	Construct a matrix from the row vectors (r0, r1, r2).
static <A,B> PMatrix3x3D<A,B>	ofScale(double x, double y, double z)	Construct a matrix that will scale by (x, y, z).
static <A,B> Vector3D	row0(PMatrix3x3D<A,B> m)
static <A,B> Vector3D	row1(PMatrix3x3D<A,B> m)
static <A,B> Vector3D	row2(PMatrix3x3D<A,B> m)
static <A,B,C,D> PMatrix3x3D<C,D>	scale(PMatrix3x3D<A,B> m, double r)	Scale the matrix m by r.
static <A,B,C,D,E,F> PMatrix3x3D<E,F>	subtract(PMatrix3x3D<A,B> m0, PMatrix3x3D<C,D> m1)	Subtract the matrices m0 and m1.
static <A,B> PMatrix3x3D<A,B>	toParameterized(Matrix3x3D m)
static <A,B> Matrix3x3D	toUnparameterized(PMatrix3x3D<A,B> m)
static <A,B> double	trace(PMatrix3x3D<A,B> m)	Return the trace of the matrix m.
static <A,B> PMatrix3x3D<A,B>	transpose(PMatrix3x3D<A,B> m)	Calculate the transpose of the matrix m.
static <A,B> PMatrix3x3D<A,B>	withColumn(PMatrix3x3D<A,B> m, int column, double r0, double r1, double r2)	Set the column column of m to (r0, r1, r2).
static <A,B> PMatrix3x3D<A,B>	withRow(PMatrix3x3D<A,B> m, int row, double c0, double c1, double c2)	Set the row row of m to (c0, c1, c2).
static <A,B> PMatrix3x3D<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> PMatrix3x3D<E,F> add(PMatrix3x3D<A,B> m0,
                                                 PMatrix3x3D<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(PMatrix3x3D<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<PMatrix3x3D<B,A>> invert(PMatrix3x3D<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> PMatrix3x3D<A,C> multiply(PMatrix3x3D<B,C> m0,
                                                PMatrix3x3D<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> PVector3D<B> multiplyVectorPost(PMatrix3x3D<A,B> m,
                                                    PVector3D<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 Vector3D multiplyVectorPost(PMatrix3x3D m,
                                          Vector3D 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> PMatrix3x3D<A,B> ofColumns(Vector3D c0,
                                               Vector3D c1,
                                               Vector3D c2)

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

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

Returns:

A constructed matrix

ofRows

public static <A,B> PMatrix3x3D<A,B> ofRows(Vector3D r0,
                                            Vector3D r1,
                                            Vector3D r2)

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

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

Returns:

A constructed matrix

ofScale

public static <A,B> PMatrix3x3D<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

ofAxisAngle

public static <A,B> PMatrix3x3D<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> Vector3D row0(PMatrix3x3D<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> Vector3D row1(PMatrix3x3D<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> Vector3D row2(PMatrix3x3D<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

column0

public static <A,B> Vector3D column0(PMatrix3x3D<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> Vector3D column1(PMatrix3x3D<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> Vector3D column2(PMatrix3x3D<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

scale

public static <A,B,C,D> PMatrix3x3D<C,D> scale(PMatrix3x3D<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> PMatrix3x3D<E,F> subtract(PMatrix3x3D<A,B> m0,
                                                      PMatrix3x3D<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(PMatrix3x3D<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> PMatrix3x3D<A,B> transpose(PMatrix3x3D<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> PMatrix3x3D<A,B> withColumn(PMatrix3x3D<A,B> m,
                                                int column,
                                                double r0,
                                                double r1,
                                                double r2)

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

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, 2]

r1 - The value of row 1 in the column

r2 - The value of row 2 in the column

Returns:

A matrix with the given row

withRow

public static <A,B> PMatrix3x3D<A,B> withRow(PMatrix3x3D<A,B> m,
                                             int row,
                                             double c0,
                                             double c1,
                                             double c2)

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

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, 2]

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

Returns:

A matrix with the given row

zero

public static <A,B> PMatrix3x3D<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> PMatrix3x3D<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> Matrix3x3D toUnparameterized(PMatrix3x3D<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> PMatrix3x3D<A,B> toParameterized(Matrix3x3D 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