core.math
Class Mat2

java.lang.Object
  core.math.Mat2

public class Mat2

extends java.lang.Object

Mat2 is a 2x2 matrix = < [[a, b], [c, d]] > This class stores and operates on a 2x2 matrix. Methods that begin with a capital letter modify "this", while methods that begin with a lowercase letter create a new Mat2 to store the result.

Field Summary

double	a a,b,c,d are the components of the matrix
double	b a,b,c,d are the components of the matrix
double	c a,b,c,d are the components of the matrix
double	d a,b,c,d are the components of the matrix
static Mat2	Ident Do not modify Ident = the identity matrix
static Mat2	Invalid Do not modify Invalid = an invalid Mat2
static double	tolerance Do not modify tolerance is the per-component zero-value maximium
static Mat2	Zero Do not modify Zero = the zero matrix

Constructor Summary

Mat2()
Constructs a new Mat2 = [[1, 0], [0, 1]]

Mat2(double a, double b, double c, double d)
Constructs a new Mat2 = [[a, b], [c, d]]

Mat2(Mat2 m)
Constructs a new Mat2 = "m"

Method Summary

Mat2	add(Mat2 m) Returns: a new Mat2 that is the sum of "this" and "m"
Mat2	Add(Mat2 m) Adds "m" to "this" Returns: resulting "this"
Mat2	addscaled(Mat2 m, double s) Returns: a new Mat2 that is the sum of "this" and "s*m"
Mat2	AddScaled(Mat2 m, double s) Adds "s*m" to "this" Returns: resulting "this"
double	det() Returns: the determinant of "this"
double	dot(Mat2 m) Returns: the dot product of "this" and "m"
boolean	equals(Mat2 m) Returns: true if "this" equals "m", false otherwise
double	getScale() Returns: the geometric mean of the magnitude of the x- and y-axes of "this" used as a left-multiplying linear transform
Mat2	invert() Returns: a new Mat2 that is the inverse of "this" Requires: "this" is not singular
Mat2	Invert() Inverts "this" Returns: resulting "this" Requires: "this" is not singular
boolean	isOrthogonal()
boolean	isOrthoNormal() Returns: true if the x- and y-axes of "this" as a left-multiplying linear transform are orthonormal, false otherwise
boolean	isOrthoScaled() Returns: true if the x- and y-axes of "this" as a left-multiplying linear transform are orthogonal and of equal magnitude, else false
boolean	isZero() Returns: true if "this" is zero, false otherwise
Vec2	lmul(Vec2 v) Returns: a new Vec2 that is "v*this"
Mat2	mul(Mat2 m) Returns: a new Mat2 that is "m*this"
Mat2	Mul(Mat2 m) Multiplies "this" to the left by "m" Returns: resulting "this"
Vec2	mul(Vec2 v) Returns: a new Vec2 that is "this*v"
Mat2	neg() Returns: a new Mat2 that is the opposite of "this"
Mat2	Neg() Negates "this" Returns: resulting "this"
Mat2	rmul(Mat2 m) Returns: a new Mat2 that is "this*m"
Mat2	RMul(Mat2 m) Multiplies "this" to the right by "m" Returns: resulting "this"
Mat2	scale(double s) Returns: a new Mat2 that is "s*this"
Mat2	Scale(double s) Scales "this" by "s" Returns: resulting "this"
Mat2	Set(double a, double b, double c, double d) Sets "this" to [[a, b], [c, d]].
Mat2	Set(Mat2 m) Sets the value of "this" to that of "m" Returns: resulting "this"
Mat2	SetIdent() Sets "this" to the identity matrix.
Mat2	SetZero() Sets "this" to zero.
Mat2	sub(Mat2 m) Returns: a new Mat2 that is the difference between "this" and "m"
Mat2	Sub(Mat2 m) Subtracts "m" from "this" Returns: resulting "this"
Vec2	xaxis() Returns: a new Vec2 containing the x-axis of "this" when it is used as a linear transform left-multiplying a vector
Vec2	yaxis()

Methods inherited from class java.lang.Object

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

Field Detail

a

public double a

a,b,c,d are the components of the matrix

b

public double b

a,b,c,d are the components of the matrix

c

public double c

a,b,c,d are the components of the matrix

d

public double d

a,b,c,d are the components of the matrix

Zero

public static Mat2 Zero

Do not modify Zero = the zero matrix

Ident

public static Mat2 Ident

Do not modify Ident = the identity matrix

Invalid

public static Mat2 Invalid

Do not modify Invalid = an invalid Mat2

tolerance

public static double tolerance

Do not modify tolerance is the per-component zero-value maximium

Constructor Detail

Mat2

public Mat2()

Constructs a new Mat2 = [[1, 0], [0, 1]]

Mat2

public Mat2(Mat2 m)

Constructs a new Mat2 = "m"

Mat2

public Mat2(double a,
            double b,
            double c,
            double d)

Constructs a new Mat2 = [[a, b], [c, d]]

Method Detail

Set

public Mat2 Set(Mat2 m)

Sets the value of "this" to that of "m" Returns: resulting "this"

Set

public Mat2 Set(double a,
                double b,
                double c,
                double d)

Sets "this" to [[a, b], [c, d]]. Returns: resulting "this"

SetZero

public Mat2 SetZero()

Sets "this" to zero. Returns: resulting "this"

SetIdent

public Mat2 SetIdent()

Sets "this" to the identity matrix. Returns" resulting "this"

isZero

public boolean isZero()

Returns: true if "this" is zero, false otherwise

equals

public boolean equals(Mat2 m)

Returns: true if "this" equals "m", false otherwise

Add

public Mat2 Add(Mat2 m)

Adds "m" to "this" Returns: resulting "this"

add

public Mat2 add(Mat2 m)

Returns: a new Mat2 that is the sum of "this" and "m"

AddScaled

public Mat2 AddScaled(Mat2 m,
                      double s)

Adds "s*m" to "this" Returns: resulting "this"

addscaled

public Mat2 addscaled(Mat2 m,
                      double s)

Returns: a new Mat2 that is the sum of "this" and "s*m"

Sub

public Mat2 Sub(Mat2 m)

Subtracts "m" from "this" Returns: resulting "this"

sub

public Mat2 sub(Mat2 m)

Returns: a new Mat2 that is the difference between "this" and "m"

Neg

public Mat2 Neg()

Negates "this" Returns: resulting "this"

neg

public Mat2 neg()

Returns: a new Mat2 that is the opposite of "this"

dot

public double dot(Mat2 m)

Returns: the dot product of "this" and "m"

Scale

public Mat2 Scale(double s)

Scales "this" by "s" Returns: resulting "this"

scale

public Mat2 scale(double s)

Returns: a new Mat2 that is "s*this"

Mul

public Mat2 Mul(Mat2 m)

Multiplies "this" to the left by "m" Returns: resulting "this"

mul

public Mat2 mul(Mat2 m)

Returns: a new Mat2 that is "m*this"

RMul

public Mat2 RMul(Mat2 m)

Multiplies "this" to the right by "m" Returns: resulting "this"

rmul

public Mat2 rmul(Mat2 m)

Returns: a new Mat2 that is "this*m"

mul

public Vec2 mul(Vec2 v)

Returns: a new Vec2 that is "this*v"

lmul

public Vec2 lmul(Vec2 v)

Returns: a new Vec2 that is "v*this"

det

public double det()

Returns: the determinant of "this"

Invert

public Mat2 Invert()

Inverts "this" Returns: resulting "this" Requires: "this" is not singular

invert

public Mat2 invert()

Returns: a new Mat2 that is the inverse of "this" Requires: "this" is not singular

xaxis

public Vec2 xaxis()

Returns: a new Vec2 containing the x-axis of "this" when it is used as a linear transform left-multiplying a vector

yaxis

public Vec2 yaxis()

isOrthogonal

public boolean isOrthogonal()

isOrthoNormal

public boolean isOrthoNormal()

Returns: true if the x- and y-axes of "this" as a left-multiplying linear transform are orthonormal, false otherwise

isOrthoScaled

public boolean isOrthoScaled()

Returns: true if the x- and y-axes of "this" as a left-multiplying linear transform are orthogonal and of equal magnitude, else false

getScale

public double getScale()

Returns: the geometric mean of the magnitude of the x- and y-axes of "this" used as a left-multiplying linear transform