2D Mathematics More...

Collaboration diagram for Math 2d:

Data Structures
struct	GF_Point2D
	2D point More...

struct	GF_Rect
	rectangle 2D More...

struct	GF_IRect
	pixel-aligned rectangle More...

struct	GF_Matrix2D
	2D matrix More...

Macros
#define	gf_mx2d_init(_obj)
	matrix initialization More...

#define	gf_mx2d_copy(_obj, from)
	matrix copy More...

#define	gf_mx2d_is_identity(_obj)
	matrix identity testing More...

Functions
Fixed	gf_v2d_len (GF_Point2D *vec)
	get 2D vector length More...

Fixed	gf_v2d_distance (GF_Point2D a, GF_Point2D b)
	get distance between 2 points More...

GF_Point2D	gf_v2d_from_polar (Fixed length, Fixed angle)
	2D vector from polar coordinates More...

void	gf_rect_union (GF_Rect rc1, GF_Rect rc2)
	rectangle union More...

GF_Rect	gf_rect_center (Fixed w, Fixed h)
	centers a rectangle More...

Bool	gf_rect_overlaps (GF_Rect rc1, GF_Rect rc2)
	rectangle overlap test More...

Bool	gf_rect_equal (GF_Rect rc1, GF_Rect rc2)
	rectangle identity test More...

void	gf_rect_intersect (GF_Rect rc1, GF_Rect rc2)
	rectangle intersection More...

GF_IRect	gf_rect_pixelize (GF_Rect *r)
	gets the pixelized version of a rectangle More...

void	gf_irect_union (GF_IRect rc1, GF_IRect rc2)

void	gf_mx2d_add_matrix (GF_Matrix2D _this, GF_Matrix2D from)
	2D matrix multiplication More...

void	gf_mx2d_pre_multiply (GF_Matrix2D _this, GF_Matrix2D from)
	2D matrix pre-multiplication More...

void	gf_mx2d_add_translation (GF_Matrix2D *_this, Fixed cx, Fixed cy)
	matrix translating More...

void	gf_mx2d_add_rotation (GF_Matrix2D *_this, Fixed cx, Fixed cy, Fixed angle)
	matrix rotating More...

void	gf_mx2d_add_scale (GF_Matrix2D *_this, Fixed scale_x, Fixed scale_y)
	matrix scaling More...

void	gf_mx2d_add_scale_at (GF_Matrix2D *_this, Fixed scale_x, Fixed scale_y, Fixed cx, Fixed cy, Fixed angle)
	matrix uncentered scaling More...

void	gf_mx2d_add_skew (GF_Matrix2D *_this, Fixed skew_x, Fixed skew_y)
	matrix skewing More...

void	gf_mx2d_add_skew_x (GF_Matrix2D *_this, Fixed angle)
	matrix horizontal skewing More...

void	gf_mx2d_add_skew_y (GF_Matrix2D *_this, Fixed angle)
	matrix vertical skewing More...

void	gf_mx2d_inverse (GF_Matrix2D *_this)
	matrix inversing More...

void	gf_mx2d_apply_coords (GF_Matrix2D _this, Fixed x, Fixed *y)
	matrix coordinate transformation More...

void	gf_mx2d_apply_point (GF_Matrix2D _this, GF_Point2D pt)
	matrix point transformation More...

void	gf_mx2d_apply_rect (GF_Matrix2D _this, GF_Rect rc)
	matrix rectangle transformation More...

Bool	gf_mx2d_decompose (GF_Matrix2D _this, GF_Point2D scale, Fixed rotate, GF_Point2D translate)
	matrix decomposition More...

Detailed Description

This section documents mathematic tools for 2D geometry and color matrices operations

Data Structure Documentation

◆ GF_Point2D

struct GF_Point2D

The 2D point object is used in all the GPAC framework for both point and vector representation.

Data Fields
Fixed	x
Fixed	y

◆ GF_Rect

struct GF_Rect

The 2D rectangle used in the GPAC project.

Data Fields
Fixed	x	the left coordinate of the rectangle
Fixed	y	the top coordinate of the rectangle, regardless of the canvas orientation. In other words, y is always the greatest coordinate value, even if the rectangle is presented bottom-up. This insures proper rectangles testing
Fixed	width	the width of the rectangle. Width must be greater than or equal to 0
Fixed	height	the height of the rectangle. Height must be greater than or equal to 0

◆ GF_IRect

struct GF_IRect

Pixel-aligned rectangle used in the GPAC framework. This is usually needed for 2D drawing algorithms.

Data Fields
s32	x	the left coordinate of the rectangle
s32	y	the top coordinate of the rectangle, regardless of the canvas orientation. In other words, y is always the greatest coordinate value, even if the rectangle is presented bottom-up. This insures proper rectangles operations
s32	width	the width of the rectangle. Width must be greater than or equal to 0
s32	height	the height of the rectangle. Height must be greater than or equal to 0

◆ GF_Matrix2D

struct GF_Matrix2D

The 2D affine matrix object usied in GPAC. The transformation of P(x,y) in P'(X, Y) is:

X = m[0]*x + m[1]*y + m[2];

Y = m[3]*x + m[4]*y + m[5];

Data Fields
Fixed	m[6]

Macro Definition Documentation

◆ gf_mx2d_init

#define gf_mx2d_init ( _obj )

Inits the matrix to the identity matrix

◆ gf_mx2d_copy

#define gf_mx2d_copy	(	_obj,
		from
	)

Copies the matrix _from to the matrix _obj

◆ gf_mx2d_is_identity

#define gf_mx2d_is_identity ( _obj )

This macro evaluates to 1 if the matrix _obj is the identity matrix, 0 otherwise

Function Documentation

◆ gf_v2d_len()

Fixed gf_v2d_len ( GF_Point2D * vec )

Gets the length of a 2D vector

Parameters

vec	the target vector

Returns: length of the vector

◆ gf_v2d_distance()

Fixed gf_v2d_distance	(	GF_Point2D *	a,
		GF_Point2D *	b
	)

Gets the distance between the 2 points

Parameters

a	first point
b	second point

Returns: distance

◆ gf_v2d_from_polar()

GF_Point2D gf_v2d_from_polar	(	Fixed	length,
		Fixed	angle
	)

Constructs a 2D vector from its polar coordinates

Parameters

length	the length of the vector
angle	the angle of the vector in radians

Returns: the 2D vector

◆ gf_rect_union()

void gf_rect_union	(	GF_Rect *	rc1,
		GF_Rect *	rc2
	)

Gets the union of two rectangles.

Parameters

rc1	first rectangle of the union. Upon return, this rectangle will contain the result of the union
rc2	second rectangle of the union

◆ gf_rect_center()

GF_Rect gf_rect_center	(	Fixed	w,
		Fixed	h
	)

Builds a rectangle centered on the origin

Parameters

w	width of the rectangle
h	height of the rectangle

Returns: centered rectangle object

◆ gf_rect_overlaps()

Bool gf_rect_overlaps	(	GF_Rect	rc1,
		GF_Rect	rc2
	)

Tests if two rectangles overlap.

Parameters

rc1	first rectangle to test
rc2	second rectangle to test

Returns: 1 if rectangles overlap, 0 otherwise

◆ gf_rect_equal()

Bool gf_rect_equal	(	GF_Rect *	rc1,
		GF_Rect *	rc2
	)

Tests if two rectangles are identical.

Parameters

rc1	first rectangle to test
rc2	second rectangle to test

Returns: 1 if rectangles are identical, 0 otherwise

◆ gf_rect_intersect()

void gf_rect_intersect	(	GF_Rect *	rc1,
		GF_Rect *	rc2
	)

Intersects two rectangle.

Parameters

rc1	rectangle to use, updated to intersection result
rc2	second rectangle to use

◆ gf_rect_pixelize()

GF_IRect gf_rect_pixelize ( GF_Rect * r )

Gets the smallest pixel-aligned rectangle completely containing a rectangle

Parameters

r	the rectangle to transform

Returns: the pixel-aligned transformed rectangle

◆ gf_irect_union()

void gf_irect_union	(	GF_IRect *	rc1,
		GF_IRect *	rc2
	)

add adds rc2 to rc1 - the new rc1 contains the old rc1 and rc2

Parameters

rc1	target rectangle
rc2	rectangle to add

◆ gf_mx2d_add_matrix()

void gf_mx2d_add_matrix	(	GF_Matrix2D *	_this,
		GF_Matrix2D *	from
	)

Multiplies two 2D matrices from*_this

Parameters

_this	matrix being transformed. Once the function is called, _this contains the result matrix
from	transformation matrix to add

◆ gf_mx2d_pre_multiply()

void gf_mx2d_pre_multiply	(	GF_Matrix2D *	_this,
		GF_Matrix2D *	from
	)

Multiplies two 2D matrices _this*from

Parameters

_this	matrix being transformed. Once the function is called, _this contains the result matrix
from	transformation matrix to add

◆ gf_mx2d_add_translation()

void gf_mx2d_add_translation	(	GF_Matrix2D *	_this,
		Fixed	cx,
		Fixed	cy
	)

Translates a 2D matrix

Parameters

_this	matrix being transformed. Once the function is called, _this contains the result matrix
cx	horizontal translation
cy	vertical translation

◆ gf_mx2d_add_rotation()

void gf_mx2d_add_rotation	(	GF_Matrix2D *	_this,
		Fixed	cx,
		Fixed	cy,
		Fixed	angle
	)

Rotates a 2D matrix

Parameters

_this	matrix being transformed. Once the function is called, _this contains the result matrix
cx	horizontal rotation center coordinate
cy	vertical rotation center coordinate
angle	rotation angle in radians

◆ gf_mx2d_add_scale()

void gf_mx2d_add_scale	(	GF_Matrix2D *	_this,
		Fixed	scale_x,
		Fixed	scale_y
	)

Scales a 2D matrix

Parameters

_this	matrix being transformed. Once the function is called, _this contains the result matrix
scale_x	horizontal scaling factor
scale_y	vertical scaling factor

◆ gf_mx2d_add_scale_at()

void gf_mx2d_add_scale_at	(	GF_Matrix2D *	_this,
		Fixed	scale_x,
		Fixed	scale_y,
		Fixed	cx,
		Fixed	cy,
		Fixed	angle
	)

Scales a 2D matrix with a non-centered scale

Parameters

_this	matrix being transformed. Once the function is called, _this contains the result matrix
scale_x	horizontal scaling factor
scale_y	vertical scaling factor
cx	horizontal scaling center coordinate
cy	vertical scaling center coordinate
angle	scale orienttion angle in radians

◆ gf_mx2d_add_skew()

void gf_mx2d_add_skew	(	GF_Matrix2D *	_this,
		Fixed	skew_x,
		Fixed	skew_y
	)

Skews a 2D matrix

Parameters

_this	matrix being transformed. Once the function is called, _this contains the result matrix
skew_x	horizontal skew factor
skew_y	vertical skew factor

◆ gf_mx2d_add_skew_x()

void gf_mx2d_add_skew_x	(	GF_Matrix2D *	_this,
		Fixed	angle
	)

Skews a 2D matrix horizontally by a given angle

Parameters

_this	matrix being transformed. Once the function is called, _this contains the result matrix
angle	horizontal skew angle in radians

◆ gf_mx2d_add_skew_y()

void gf_mx2d_add_skew_y	(	GF_Matrix2D *	_this,
		Fixed	angle
	)

Skews a 2D matrix vertically by a given angle

Parameters

_this	matrix being transformed. Once the function is called, _this contains the result matrix
angle	vertical skew angle in radians

◆ gf_mx2d_inverse()

void gf_mx2d_inverse ( GF_Matrix2D * _this )

Inverses a 2D matrix

Parameters

_this matrix being transformed. Once the function is called, _this contains the result matrix

◆ gf_mx2d_apply_coords()

void gf_mx2d_apply_coords	(	GF_Matrix2D *	_this,
		Fixed *	x,
		Fixed *	y
	)

Applies a 2D matrix transformation to coordinates

Parameters

_this	transformation matrix
x	pointer to horizontal coordinate. Once the function is called, x contains the transformed horizontal coordinate
y	pointer to vertical coordinate. Once the function is called, y contains the transformed vertical coordinate

◆ gf_mx2d_apply_point()

void gf_mx2d_apply_point	(	GF_Matrix2D *	_this,
		GF_Point2D *	pt
	)

Applies a 2D matrix transformation to a 2D point

Parameters

_this	transformation matrix
pt	pointer to 2D point. Once the function is called, pt contains the transformed point

◆ gf_mx2d_apply_rect()

void gf_mx2d_apply_rect	(	GF_Matrix2D *	_this,
		GF_Rect *	rc
	)

Applies a 2D matrix transformation to a rectangle, giving the enclosing rectangle of the transformed one

Parameters

_this	transformation matrix
rc	pointer to rectangle. Once the function is called, rc contains the transformed rectangle

◆ gf_mx2d_decompose()

Bool gf_mx2d_decompose	(	GF_Matrix2D *	_this,
		GF_Point2D *	scale,
		Fixed *	rotate,
		GF_Point2D *	translate
	)

Decomposes a 2D matrix M as M=Scale x Rotation x Translation if possible

Parameters

_this	transformation matrix
scale	resulting scale part
rotate	resulting rotation part
translate	resulting translation part

Returns: 0 if matrix cannot be decomposed, 1 otherwise

Data Structures

Macros

Functions

Detailed Description

Data Structure Documentation

◆ GF_Point2D

◆ GF_Rect

◆ GF_IRect

◆ GF_Matrix2D

Macro Definition Documentation

◆ gf_mx2d_init

◆ gf_mx2d_copy

◆ gf_mx2d_is_identity

Function Documentation

◆ gf_v2d_len()

◆ gf_v2d_distance()

◆ gf_v2d_from_polar()

◆ gf_rect_union()

◆ gf_rect_center()

◆ gf_rect_overlaps()

◆ gf_rect_equal()

◆ gf_rect_intersect()

◆ gf_rect_pixelize()

◆ gf_irect_union()

◆ gf_mx2d_add_matrix()

◆ gf_mx2d_pre_multiply()

◆ gf_mx2d_add_translation()

◆ gf_mx2d_add_rotation()

◆ gf_mx2d_add_scale()

◆ gf_mx2d_add_scale_at()

◆ gf_mx2d_add_skew()

◆ gf_mx2d_add_skew_x()

◆ gf_mx2d_add_skew_y()

◆ gf_mx2d_inverse()

◆ gf_mx2d_apply_coords()

◆ gf_mx2d_apply_point()

◆ gf_mx2d_apply_rect()

◆ gf_mx2d_decompose()