Math 2d

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
#define	gf_mx2d_copy(_obj, from)
	matrix copy
#define	gf_mx2d_is_identity(_obj)
	matrix identity testing

Functions
Fixed	gf_v2d_len (GF_Point2D *vec)
	get 2D vector length
Fixed	gf_v2d_distance (GF_Point2D *a, GF_Point2D *b)
	get distance between 2 points
GF_Point2D	gf_v2d_from_polar (Fixed length, Fixed angle)
	2D vector from polar coordinates
void	gf_rect_union (GF_Rect *rc1, GF_Rect *rc2)
	rectangle union
GF_Rect	gf_rect_center (Fixed w, Fixed h)
	centers a rectangle
Bool	gf_rect_overlaps (GF_Rect rc1, GF_Rect rc2)
	rectangle overlap test
Bool	gf_rect_equal (GF_Rect *rc1, GF_Rect *rc2)
	rectangle identity test
void	gf_rect_intersect (GF_Rect *rc1, GF_Rect *rc2)
	rectangle intersection
GF_IRect	gf_rect_pixelize (GF_Rect *r)
	gets the pixelized version of a rectangle
void	gf_irect_union (GF_IRect *rc1, GF_IRect *rc2)
void	gf_mx2d_add_matrix (GF_Matrix2D *_this, GF_Matrix2D *from)
	2D matrix multiplication
void	gf_mx2d_pre_multiply (GF_Matrix2D *_this, GF_Matrix2D *from)
	2D matrix pre-multiplication
void	gf_mx2d_add_translation (GF_Matrix2D *_this, Fixed cx, Fixed cy)
	matrix translating
void	gf_mx2d_add_rotation (GF_Matrix2D *_this, Fixed cx, Fixed cy, Fixed angle)
	matrix rotating
void	gf_mx2d_add_scale (GF_Matrix2D *_this, Fixed scale_x, Fixed scale_y)
	matrix scaling
void	gf_mx2d_add_scale_at (GF_Matrix2D *_this, Fixed scale_x, Fixed scale_y, Fixed cx, Fixed cy, Fixed angle)
	matrix uncentered scaling
void	gf_mx2d_add_skew (GF_Matrix2D *_this, Fixed skew_x, Fixed skew_y)
	matrix skewing
void	gf_mx2d_add_skew_x (GF_Matrix2D *_this, Fixed angle)
	matrix horizontal skewing
void	gf_mx2d_add_skew_y (GF_Matrix2D *_this, Fixed angle)
	matrix vertical skewing
void	gf_mx2d_inverse (GF_Matrix2D *_this)
	matrix inversing
void	gf_mx2d_apply_coords (GF_Matrix2D *_this, Fixed *x, Fixed *y)
	matrix coordinate transformation
void	gf_mx2d_apply_point (GF_Matrix2D *_this, GF_Point2D *pt)
	matrix point transformation
void	gf_mx2d_apply_rect (GF_Matrix2D *_this, GF_Rect *rc)
	matrix rectangle transformation
Bool	gf_mx2d_decompose (GF_Matrix2D *_this, GF_Point2D *scale, Fixed *rotate, GF_Point2D *translate)
	matrix decomposition

Detailed Description

2D Mathematics

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

---

Data Structure Documentation

GF_Point2D

struct GF_Point2D

2D point

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

rectangle 2D

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

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

2D matrix

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

)

matrix initialization

Inits the matrix to the identity matrix

gf_mx2d_copy

#define gf_mx2d_copy	(		_obj,
			from
	)

matrix copy

Copies the matrix _from to the matrix _obj

gf_mx2d_is_identity

#define gf_mx2d_is_identity

(

_obj

)

matrix identity testing

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

)

get 2D vector length

Gets the length of a 2D vector

Parameters

vec	the target vector

Returns

length of the vector

Here is the caller graph for this function:

gf_v2d_distance()

Fixed gf_v2d_distance	(	GF_Point2D *	a,
		GF_Point2D *	b
	)

get distance between 2 points

Gets the distance between the 2 points

Parameters

a	first point
b	second point

Returns

distance

Here is the call graph for this function:

Here is the caller graph for this function:

gf_v2d_from_polar()

GF_Point2D gf_v2d_from_polar	(	Fixed	length,
		Fixed	angle
	)

2D vector from polar coordinates

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

Here is the caller graph for this function:

gf_rect_union()

void gf_rect_union	(	GF_Rect *	rc1,
		GF_Rect *	rc2
	)

rectangle union

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

Here is the caller graph for this function:

gf_rect_center()

GF_Rect gf_rect_center	(	Fixed	w,
		Fixed	h
	)

centers a rectangle

Builds a rectangle centered on the origin

Parameters

w	width of the rectangle
h	height of the rectangle

Returns

centered rectangle object

Here is the caller graph for this function:

gf_rect_overlaps()

Bool gf_rect_overlaps	(	GF_Rect	rc1,
		GF_Rect	rc2
	)

rectangle overlap test

Tests if two rectangles overlap.

Parameters

rc1	first rectangle to test
rc2	second rectangle to test

Returns

1 if rectangles overlap, 0 otherwise

Here is the caller graph for this function:

gf_rect_equal()

Bool gf_rect_equal	(	GF_Rect *	rc1,
		GF_Rect *	rc2
	)

rectangle identity test

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

Here is the caller graph for this function:

gf_rect_intersect()

void gf_rect_intersect	(	GF_Rect *	rc1,
		GF_Rect *	rc2
	)

rectangle intersection

Intersects two rectangle.

Parameters

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

Here is the call graph for this function:

Here is the caller graph for this function:

gf_rect_pixelize()

GF_IRect gf_rect_pixelize

(

GF_Rect *

r

)

gets the pixelized version of a rectangle

Gets the smallest pixel-aligned rectangle completely containing a rectangle

Parameters

r	the rectangle to transform

Returns

the pixel-aligned transformed rectangle

Here is the caller graph for this function:

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

Here is the caller graph for this function:

gf_mx2d_add_matrix()

void gf_mx2d_add_matrix	(	GF_Matrix2D *	_this,
		GF_Matrix2D *	from
	)

2D matrix multiplication

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

Here is the caller graph for this function:

gf_mx2d_pre_multiply()

void gf_mx2d_pre_multiply	(	GF_Matrix2D *	_this,
		GF_Matrix2D *	from
	)

2D matrix pre-multiplication

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

Here is the caller graph for this function:

gf_mx2d_add_translation()

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

matrix translating

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

Here is the call graph for this function:

Here is the caller graph for this function:

gf_mx2d_add_rotation()

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

matrix rotating

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

Here is the call graph for this function:

Here is the caller graph for this function:

gf_mx2d_add_scale()

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

matrix scaling

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

Here is the call graph for this function:

Here is the caller graph for this function:

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
	)

matrix uncentered scaling

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

Here is the call graph for this function:

Here is the caller graph for this function:

gf_mx2d_add_skew()

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

matrix skewing

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

Here is the call graph for this function:

Here is the caller graph for this function:

gf_mx2d_add_skew_x()

void gf_mx2d_add_skew_x	(	GF_Matrix2D *	_this,
		Fixed	angle
	)

matrix horizontal skewing

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

Here is the call graph for this function:

Here is the caller graph for this function:

gf_mx2d_add_skew_y()

void gf_mx2d_add_skew_y	(	GF_Matrix2D *	_this,
		Fixed	angle
	)

matrix vertical skewing

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

Here is the call graph for this function:

Here is the caller graph for this function:

gf_mx2d_inverse()

void gf_mx2d_inverse

(

GF_Matrix2D *

_this

)

matrix inversing

Inverses a 2D matrix

Parameters

_this

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

Here is the caller graph for this function:

gf_mx2d_apply_coords()

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

matrix coordinate transformation

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

Here is the caller graph for this function:

gf_mx2d_apply_point()

void gf_mx2d_apply_point	(	GF_Matrix2D *	_this,
		GF_Point2D *	pt
	)

matrix point transformation

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

Here is the call graph for this function:

Here is the caller graph for this function:

gf_mx2d_apply_rect()

void gf_mx2d_apply_rect	(	GF_Matrix2D *	_this,
		GF_Rect *	rc
	)

matrix rectangle transformation

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

Here is the call graph for this function:

Here is the caller graph for this function:

gf_mx2d_decompose()

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

matrix decomposition

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

Here is the caller graph for this function: