PIXI.groupD8

namespace groupD8

Implements the dihedral group D8, which is similar to group D4; D8 is the same but with diagonals, and it is used for texture rotations.

The directions the U- and V- axes after rotation of an angle of a: GD8Constant are the vectors (uX(a), uY(a)) and (vX(a), vY(a)). These aren't necessarily unit vectors.

Origin:
This is the small part of gameofbombs.com portal system. It works.

See:

Summary

Properties from groupD8

number	static E = 0
number	static MAIN_DIAGONAL = 10
number	static MIRROR_HORIZONTAL = 12
number	static MIRROR_VERTICAL = 8
number	static N = 6
number	static NE = 7
number	static NW = 5
number	static REVERSE_DIAGONAL = 14
number	static S = 2
number	static SE = 1
number	static SW = 3
number	static W = 4

Methods from groupD8

PIXI.GD8Symmetry	static add(rotationSecond: PIXI.GD8Symmetry, rotationFirst: PIXI.GD8Symmetry) Composes the two D8 operations.
PIXI.GD8Symmetry	static byDirection(dx: number, dy: number)
PIXI.GD8Symmetry	static inv(rotation: PIXI.GD8Symmetry)
boolean	static isVertical(rotation: PIXI.GD8Symmetry)
void	static matrixAppendRotationInv(matrix: PIXI.Matrix, rotation: PIXI.GD8Symmetry, tx: number, ty: number)
number	static rotate180(rotation: number)
PIXI.GD8Symmetry	static sub(rotationSecond: PIXI.GD8Symmetry, rotationFirst: PIXI.GD8Symmetry)
PIXI.GD8Symmetry	static uX(ind: PIXI.GD8Symmetry)
PIXI.GD8Symmetry	static uY(ind: PIXI.GD8Symmetry)
PIXI.GD8Symmetry	static vX(ind: PIXI.GD8Symmetry)
PIXI.GD8Symmetry	static vY(ind: PIXI.GD8Symmetry)

Public Properties

E groupD8.ts:115

static E: number = 0

Rotation	Direction
0°	East

MAIN_DIAGONAL groupD8.ts:194

static MAIN_DIAGONAL: number = 10

Reflection about the main diagonal.

MIRROR_HORIZONTAL groupD8.ts:201

static MIRROR_HORIZONTAL: number = 12

Reflection about X-axis.

MIRROR_VERTICAL groupD8.ts:187

static MIRROR_VERTICAL: number = 8

Reflection about Y-axis.

N groupD8.ts:169

static N: number = 6

Rotation	Direction
-90°/270°↻	North

NE groupD8.ts:178

static NE: number = 7

Rotation	Direction
-45°/315°↻	Northeast

NW groupD8.ts:160

static NW: number = 5

Rotation	Direction
-135°/225°↻	Northwest

REVERSE_DIAGONAL groupD8.ts:208

static REVERSE_DIAGONAL: number = 14

Reflection about reverse diagonal.

S groupD8.ts:133

static S: number = 2

Rotation	Direction
90°↻	South

SE groupD8.ts:124

static SE: number = 1

Rotation	Direction
45°↻	Southeast

SW groupD8.ts:142

static SW: number = 3

Rotation	Direction
135°↻	Southwest

W groupD8.ts:151

static W: number = 4

Rotation	Direction
180°	West

Public Methods

add groupD8.ts:264

static add(rotationSecond: PIXI.GD8Symmetry, rotationFirst: PIXI.GD8Symmetry) → {PIXI.GD8Symmetry}

Composes the two D8 operations.

Taking ^ as reflection:

	E=0	S=2	W=4	N=6	E^=8	S^=10	W^=12	N^=14
E=0	E	S	W	N	E^	S^	W^	N^
S=2	S	W	N	E	S^	W^	N^	E^
W=4	W	N	E	S	W^	N^	E^	S^
N=6	N	E	S	W	N^	E^	S^	W^
E^=8	E^	N^	W^	S^	E	N	W	S
S^=10	S^	E^	N^	W^	S	E	N	W
W^=12	W^	S^	E^	N^	W	S	E	N
N^=14	N^	W^	S^	E^	N	W	S	E

This is a Cayley table

Parameters:
Name	Type	Description
rotationSecond	PIXI.GD8Symmetry	Second operation, which is the row in the above cayley table.
rotationFirst	PIXI.GD8Symmetry	First operation, which is the column in the above cayley table.

Returns:
Type	Description
PIXI.GD8Symmetry	Composed operation

byDirection groupD8.ts:321

static byDirection(dx: number, dy: number) → {PIXI.GD8Symmetry}

Approximates the vector V(dx,dy) into one of the eight directions provided by groupD8.

Parameters:
Name	Type	Description
dx	number	X-component of the vector
dy	number	Y-component of the vector

Returns:
Type	Description
PIXI.GD8Symmetry	Approximation of the vector into one of the eight symmetries.

inv groupD8.ts:247

static inv(rotation: PIXI.GD8Symmetry) → {PIXI.GD8Symmetry}

Parameters:
Name	Type	Description
rotation	PIXI.GD8Symmetry	symmetry whose opposite is needed. Only rotations have opposite symmetries while reflections don't.

Returns:
Type	Description
PIXI.GD8Symmetry	The opposite symmetry of `rotation`

isVertical groupD8.ts:312

static isVertical(rotation: PIXI.GD8Symmetry) → {boolean}

Checks if the rotation angle is vertical, i.e. south or north. It doesn't work for reflections.

Parameters:
Name	Type	Description
rotation	PIXI.GD8Symmetry	The number to check.

Returns:
Type	Description
boolean	Whether or not the direction is vertical

matrixAppendRotationInv groupD8.ts:367

static matrixAppendRotationInv(matrix: PIXI.Matrix, rotation: PIXI.GD8Symmetry, tx: number, ty: number) → {void}

Helps sprite to compensate texture packer rotation.

Parameters:
Name	Type	Default	Description
matrix	PIXI.Matrix		sprite world matrix
rotation	PIXI.GD8Symmetry		The rotation factor to use.
tx	number	0	sprite anchoring
ty	number	0	sprite anchoring

Returns:
Type	Description
void

rotate180 groupD8.ts:303

static rotate180(rotation: number) → {number}

Adds 180 degrees to rotation, which is a commutative operation.

Parameters:
Name	Type	Description
rotation	number	The number to rotate.

Returns:
Type	Description
number	Rotated number

sub groupD8.ts:292

static sub(rotationSecond: PIXI.GD8Symmetry, rotationFirst: PIXI.GD8Symmetry) → {PIXI.GD8Symmetry}

Reverse of add.

Parameters:
Name	Type	Description
rotationSecond	PIXI.GD8Symmetry	Second operation
rotationFirst	PIXI.GD8Symmetry	First operation

Returns:
Type	Description
PIXI.GD8Symmetry	Result

uX groupD8.ts:215

static uX(ind: PIXI.GD8Symmetry) → {PIXI.GD8Symmetry}

Parameters:
Name	Type	Description
ind	PIXI.GD8Symmetry	sprite rotation angle.

Returns:
Type	Description
PIXI.GD8Symmetry	The X-component of the U-axis after rotating the axes.

uY groupD8.ts:223

static uY(ind: PIXI.GD8Symmetry) → {PIXI.GD8Symmetry}

Parameters:
Name	Type	Description
ind	PIXI.GD8Symmetry	sprite rotation angle.

Returns:
Type	Description
PIXI.GD8Symmetry	The Y-component of the U-axis after rotating the axes.

vX groupD8.ts:231

static vX(ind: PIXI.GD8Symmetry) → {PIXI.GD8Symmetry}

Parameters:
Name	Type	Description
ind	PIXI.GD8Symmetry	sprite rotation angle.

Returns:
Type	Description
PIXI.GD8Symmetry	The X-component of the V-axis after rotating the axes.

vY groupD8.ts:239

static vY(ind: PIXI.GD8Symmetry) → {PIXI.GD8Symmetry}

Parameters:
Name	Type	Description
ind	PIXI.GD8Symmetry	sprite rotation angle.

Returns:
Type	Description
PIXI.GD8Symmetry	The Y-component of the V-axis after rotating the axes.