3D Mathematics More...

Collaboration diagram for Math 3d:

Data Structures
struct	GF_Vec
	3D point or vector More...

struct	GF_Vec4
	4D vector More...

struct	GF_Matrix
	3D matrix More...

struct	GF_BBox
	3D Bounding Box More...

struct	GF_Plane
	Plane object. More...

struct	GF_Ray
	3D Ray More...

Macros
#define	gf_vec_equal(v1, v2)

#define	gf_vec_rev(v)

#define	gf_vec_diff(res, v1, v2)

#define	gf_vec_add(res, v1, v2)

#define	gf_quat_len(v)

#define	gf_quat_norm(v)

#define	gf_mx_init(_obj)
	matrix initialization

#define	gf_mx_is_identity(_obj) ((!(_obj).m[1] && !(_obj).m[2] && !(_obj).m[3] && !(_obj).m[4] && !(_obj).m[6] && !(_obj).m[7] && !(_obj).m[8] && !(_obj).m[9] && !(_obj).m[11] && !(_obj).m[12] && !(_obj).m[13] && !(_obj).m[14] && ((_obj).m[0]==FIX_ONE) && ((_obj).m[5]==FIX_ONE)&& ((_obj).m[10]==FIX_ONE)&& ((_obj).m[15]==FIX_ONE)) ? 1 : 0)

#define	gf_mx_copy(_obj, from)
	matrix copy

Enumerations
enum	{ GF_BBOX_FRONT , GF_BBOX_INTER , GF_BBOX_BACK }

Functions
Fixed	gf_vec_len (GF_Vec v)
	get 3D vector length

Fixed	gf_vec_len_p (GF_Vec *v)
	get 3D vector length

Fixed	gf_vec_lensq (GF_Vec v)
	get 3D vector square length

Fixed	gf_vec_lensq_p (GF_Vec *v)
	get 3D vector square length

Fixed	gf_vec_dot (GF_Vec v1, GF_Vec v2)
	get 3D vector dot product

Fixed	gf_vec_dot_p (GF_Vec v1, GF_Vec v2)
	get 3D vector dot product

void	gf_vec_norm (GF_Vec *v)
	vector normalization

GF_Vec	gf_vec_scale (GF_Vec v, Fixed f)
	vector scaling

GF_Vec	gf_vec_scale_p (GF_Vec *v, Fixed f)
	vector scaling

GF_Vec	gf_vec_cross (GF_Vec v1, GF_Vec v2)
	vector cross product

GF_Vec	gf_vec_cross_p (GF_Vec v1, GF_Vec v2)
	vector cross product

GF_Vec4	gf_quat_to_rotation (GF_Vec4 *quat)
	quaternion to rotation

GF_Vec4	gf_quat_from_rotation (GF_Vec4 rot)
	quaternion from rotation

GF_Vec4	gf_quat_get_inv (GF_Vec4 *quat)

GF_Vec4	gf_quat_multiply (GF_Vec4 q1, GF_Vec4 q2)
	quaternion multiplication

GF_Vec	gf_quat_rotate (GF_Vec4 quat, GF_Vec vec)
	quaternion vector rotating

GF_Vec4	gf_quat_from_axis_cos (GF_Vec axis, Fixed cos_a)
	quaternion from axis and cos

GF_Vec4	gf_quat_slerp (GF_Vec4 q1, GF_Vec4 q2, Fixed frac)
	quaternion interpolation

void	gf_bbox_refresh (GF_BBox *b)

void	gf_bbox_from_rect (GF_BBox box, GF_Rect rc)

void	gf_rect_from_bbox (GF_Rect rc, GF_BBox box)

void	gf_bbox_grow_point (GF_BBox *box, GF_Vec pt)
	bounding box expansion

void	gf_bbox_union (GF_BBox b1, GF_BBox b2)

Bool	gf_bbox_equal (GF_BBox b1, GF_BBox b2)

Bool	gf_bbox_point_inside (GF_BBox box, GF_Vec p)

void	gf_bbox_get_vertices (GF_Vec bmin, GF_Vec bmax, GF_Vec *vecs)
	get box vertices

void	gf_mx_from_mx2d (GF_Matrix mx, GF_Matrix2D mat2D)
	matrix constructor from 2D

Bool	gf_mx_equal (GF_Matrix mx1, GF_Matrix mx2)
	matrix equality testing

void	gf_mx_add_translation (GF_Matrix *mx, Fixed tx, Fixed ty, Fixed tz)
	matrix translation

void	gf_mx_add_scale (GF_Matrix *mx, Fixed sx, Fixed sy, Fixed sz)
	matrix scaling

void	gf_mx_add_rotation (GF_Matrix *mx, Fixed angle, Fixed x, Fixed y, Fixed z)
	matrix rotating

void	gf_mx_add_matrix (GF_Matrix mx, GF_Matrix mul)
	matrices multiplication

void	gf_mx_add_matrix_2d (GF_Matrix mx, GF_Matrix2D mat2D)
	2D matrix multiplication

void	gf_mx_inverse (GF_Matrix *mx)
	affine matrix inversion

void	gf_mx_transpose (GF_Matrix *mx)
	transpose 4x4 matrix

void	gf_mx_apply_vec (GF_Matrix mx, GF_Vec pt)
	matrix point transformation

void	gf_mx_apply_rect (GF_Matrix _this, GF_Rect rc)
	matrix rectangle transformation

void	gf_mx_ortho (GF_Matrix *mx, Fixed left, Fixed right, Fixed bottom, Fixed top, Fixed z_near, Fixed z_far)
	ortho matrix construction

void	gf_mx_ortho_reverse_z (GF_Matrix *mx, Fixed left, Fixed right, Fixed bottom, Fixed top, Fixed z_near, Fixed z_far)
	ortho matrix with reverse Z construction

void	gf_mx_perspective (GF_Matrix *mx, Fixed fov, Fixed aspect_ratio, Fixed z_near, Fixed z_far)
	perspective matrix construction

void	gf_mx_perspective_reverse_z (GF_Matrix *mx, Fixed fov, Fixed aspect_ratio, Fixed z_near, Fixed z_far)
	perspective matrix with reverse Z construction

void	gf_mx_lookat (GF_Matrix *mx, GF_Vec position, GF_Vec target, GF_Vec up_vector)
	creates look matrix

void	gf_mx_apply_bbox (GF_Matrix mx, GF_BBox b)
	matrix box transformation

void	gf_mx_apply_bbox_4x4 (GF_Matrix mx, GF_BBox b)
	matrix box transformation

void	gf_mx_apply_bbox_sphere (GF_Matrix mx, GF_BBox box)
	matrix box sphere transformation

void	gf_mx_add_matrix_4x4 (GF_Matrix mat, GF_Matrix mul)
	non-affine matrix multiplication

Bool	gf_mx_inverse_4x4 (GF_Matrix *mx)
	non-affine matrix inversion

void	gf_mx_apply_vec_4x4 (GF_Matrix mx, GF_Vec4 vec)
	matrix 4D vector transformation

void	gf_mx_get_yaw_pitch_roll (GF_Matrix mx, Fixed yaw, Fixed pitch, Fixed roll)
	matrix yaw pitch roll decomposition

void	gf_mx_decompose (GF_Matrix mx, GF_Vec translate, GF_Vec scale, GF_Vec4 rotate, GF_Vec *shear)
	matrix decomposition

void	gf_mx_rotate_vector (GF_Matrix mx, GF_Vec pt)
	matrix vector rotation

void	gf_mx_rotation_matrix_from_vectors (GF_Matrix *mx, GF_Vec x_axis, GF_Vec y_axis, GF_Vec z_axis)
	matrix initialization from vectors

void	gf_mx2d_from_mx (GF_Matrix2D mx2d, GF_Matrix mx)
	matrix to 2D matrix

void	gf_mx_apply_plane (GF_Matrix mx, GF_Plane plane)
	matrix plane transformation

Fixed	gf_plane_get_distance (GF_Plane plane, GF_Vec p)
	point to plane distance

GF_Vec	gf_closest_point_to_line (GF_Vec line_pt, GF_Vec line_vec, GF_Vec pt)
	closest point on a line

u32	gf_plane_get_p_vertex_idx (GF_Plane *p)
	box p-vertex index

Bool	gf_plane_intersect_line (GF_Plane plane, GF_Vec linepoint, GF_Vec linevec, GF_Vec outPoint)
	plane line intersection

u32	gf_bbox_plane_relation (GF_BBox box, GF_Plane p)
	box-plane relation

GF_Ray	gf_ray (GF_Vec start, GF_Vec end)
	ray constructor

void	gf_mx_apply_ray (GF_Matrix mx, GF_Ray r)
	matrix ray transformation

Bool	gf_ray_hit_box (GF_Ray ray, GF_Vec min_edge, GF_Vec max_edge, GF_Vec out_point)
	ray box intersection test

Bool	gf_ray_hit_sphere (GF_Ray ray, GF_Vec center, Fixed radius, GF_Vec *out_point)
	ray sphere intersection test

Bool	gf_ray_hit_triangle (GF_Ray ray, GF_Vec v0, GF_Vec v1, GF_Vec v2, Fixed *dist)
	ray triangle intersection test

Detailed Description

3D Mathematics

This section documents mathematic tools for 3D geometry operations

Data Structure Documentation

◆ GF_Vec

struct GF_Vec

3D point or vector

The 3D point object is used in all the GPAC framework for both point and vector representation.

Data Fields
Fixed	x
Fixed	y
Fixed	z

◆ GF_Vec4

struct GF_Vec4

4D vector

The 4D vector object is used in all the GPAC framework for 4 dimension vectors, VRML Rotations and quaternions representation.

Data Fields
Fixed	x
Fixed	y
Fixed	z
Fixed	q

◆ GF_Matrix

struct GF_Matrix

3D matrix

The 3D matrix object used in GPAC. The matrix is oriented like OpenGL matrices (column-major ordering), with the translation part at the end of the coefficients list.

Note: Unless specified otherwise, the matrix object is always expected to represent an affine transformation.

Data Fields
Fixed	m[16]

◆ GF_BBox

struct GF_BBox

3D Bounding Box

The 3D Bounding Box is a 3D Axis-Aligned Bounding Box used to in various tools of the GPAC framework for bounds estimation of a 3D object. It features an axis-aligned box and a sphere bounding volume for fast intersection tests.

Collaboration diagram for GF_BBox:

Data Fields
GF_Vec	min_edge	minimum x, y, and z of the object
GF_Vec	max_edge	maximum x, y, and z of the object
GF_Vec	center	center of the bounding box. Note this is computed from min_edge and max_edge
Fixed	radius	radius of the bounding sphere for this box. Note this is computed from min_edge and max_edge
Bool	is_set	the bbox center and radius are valid

◆ GF_Plane

struct GF_Plane

Plane object.

Collaboration diagram for GF_Plane:

Data Fields
GF_Vec	normal	normal vector to the plane
Fixed	d	distance from origin of the plane

◆ GF_Ray

struct GF_Ray

3D Ray

The 3D ray object is used in GPAC for all collision and mouse interaction tests

Collaboration diagram for GF_Ray:

Data Fields
GF_Vec	orig	origin point of the ray
GF_Vec	dir	normalized direction vector of the ray

Macro Definition Documentation

◆ gf_vec_equal

#define gf_vec_equal	(	v1,
		v2
	)

macro evaluating to 1 if vectors are equal, 0 otherwise

◆ gf_vec_rev

#define gf_vec_rev ( v )

macro reversing a vector v = v

◆ gf_vec_diff

#define gf_vec_diff	(	res,
		v1,
		v2
	)

macro performing the minus operation res = v1 - v2

◆ gf_vec_add

#define gf_vec_add	(	res,
		v1,
		v2
	)

macro performing the add operation res = v1 + v2

◆ gf_quat_len

#define gf_quat_len ( v )

gets the len of a quaternion

◆ gf_quat_norm

#define gf_quat_norm ( v )

normalizes a quaternion

◆ gf_mx_init

#define gf_mx_init ( _obj )

matrix initialization

Inits the matrix to the identity matrix

◆ gf_mx_is_identity

#define gf_mx_is_identity ( _obj ) ((!(_obj).m[1] && !(_obj).m[2] && !(_obj).m[3] && !(_obj).m[4] && !(_obj).m[6] && !(_obj).m[7] && !(_obj).m[8] && !(_obj).m[9] && !(_obj).m[11] && !(_obj).m[12] && !(_obj).m[13] && !(_obj).m[14] && ((_obj).m[0]==FIX_ONE) && ((_obj).m[5]==FIX_ONE)&& ((_obj).m[10]==FIX_ONE)&& ((_obj).m[15]==FIX_ONE)) ? 1 : 0)

macro to check if a matrix is the identity matrix

◆ gf_mx_copy

#define gf_mx_copy	(	_obj,
		from
	)

matrix copy

Copies the matrix _from to the matrix _obj

Enumeration Type Documentation

◆ anonymous enum

anonymous enum

Classification types for box/plane position used in gf_bbox_plane_relation

Enumerator
GF_BBOX_FRONT	box is in front of the plane
GF_BBOX_INTER	box intersects the plane
GF_BBOX_BACK	box is back of the plane

Function Documentation

◆ gf_vec_len()

Fixed gf_vec_len ( GF_Vec v )

get 3D vector length

Gets the length of a 3D vector

Parameters

v	the target vector

Returns: length of the vector

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◆ gf_vec_len_p()

Fixed gf_vec_len_p ( GF_Vec * v )

get 3D vector length

Gets the length of a 3D vector

Parameters

v	the target vector

Returns: length of the vector

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◆ gf_vec_lensq()

Fixed gf_vec_lensq ( GF_Vec v )

get 3D vector square length

Gets the square length of a 3D vector

Parameters

v	the target vector

Returns: square length of the vector

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◆ gf_vec_lensq_p()

Fixed gf_vec_lensq_p ( GF_Vec * v )

get 3D vector square length

Gets the square length of a 3D vector

Parameters

v	the target vector

Returns: square length of the vector

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◆ gf_vec_dot()

Fixed gf_vec_dot	(	GF_Vec	v1,
		GF_Vec	v2
	)

get 3D vector dot product

Gets the dot product of two vectors

Parameters

v1	first vector
v2	second vector

Returns: dot product of the vectors

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◆ gf_vec_dot_p()

Fixed gf_vec_dot_p	(	GF_Vec *	v1,
		GF_Vec *	v2
	)

get 3D vector dot product

Gets the dot product of two vectors

Parameters

v1	first vector
v2	second vector

Returns: dot product of the vectors

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◆ gf_vec_norm()

void gf_vec_norm ( GF_Vec * v )

vector normalization

Normalize the vector, eg make its length equal to FIX_ONE

Parameters

v	vector to normalize

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◆ gf_vec_scale()

GF_Vec gf_vec_scale	(	GF_Vec	v,
		Fixed	f
	)

vector scaling

Scales a vector by a given amount

Parameters

v	vector to scale
f	scale factor

Returns: scaled vector

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◆ gf_vec_scale_p()

GF_Vec gf_vec_scale_p	(	GF_Vec *	v,
		Fixed	f
	)

vector scaling

Scales a vector by a given amount

Parameters

v	vector to scale
f	scale factor

Returns: scaled vector

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◆ gf_vec_cross()

GF_Vec gf_vec_cross	(	GF_Vec	v1,
		GF_Vec	v2
	)

vector cross product

Gets the cross product of two vectors

Parameters

v1	first vector
v2	second vector

Returns: cross-product vector

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◆ gf_vec_cross_p()

GF_Vec gf_vec_cross_p	(	GF_Vec *	v1,
		GF_Vec *	v2
	)

vector cross product

Gets the cross product of two vectors

Parameters

v1	first vector
v2	second vector

Returns: cross-product vector

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◆ gf_quat_to_rotation()

GF_Vec4 gf_quat_to_rotation ( GF_Vec4 * quat )

quaternion to rotation

Transforms a quaternion to a Rotation, expressed as a 4 dimension vector with x,y,z for axis and q for rotation angle

Parameters

quat	the quaternion to transform

Returns: the rotation value

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◆ gf_quat_from_rotation()

GF_Vec4 gf_quat_from_rotation ( GF_Vec4 rot )

quaternion from rotation

Transforms a Rotation to a quaternion

Parameters

rot	the rotation to transform

Returns: the quaternion value

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◆ gf_quat_get_inv()

GF_Vec4 gf_quat_get_inv ( GF_Vec4 * quat )

Inverses a quaternion

Parameters

quat	the quaternion to inverse

Returns: the inverted quaternion

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◆ gf_quat_multiply()

GF_Vec4 gf_quat_multiply	(	GF_Vec4 *	q1,
		GF_Vec4 *	q2
	)

quaternion multiplication

Multiplies two quaternions

Parameters

q1	the first quaternion
q2	the second quaternion

Returns: the resulting quaternion

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◆ gf_quat_rotate()

GF_Vec gf_quat_rotate	(	GF_Vec4 *	quat,
		GF_Vec *	vec
	)

quaternion vector rotating

Rotates a vector with a quaternion

Parameters

quat	the quaternion modelizing the rotation
vec	the vector to rotate

Returns: the resulting vector

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◆ gf_quat_from_axis_cos()

GF_Vec4 gf_quat_from_axis_cos	(	GF_Vec	axis,
		Fixed	cos_a
	)

quaternion from axis and cos

Constructs a quaternion from an axis and a cosinus value (shortcut to gf_quat_from_rotation)

Parameters

axis	the rotation axis
cos_a	the rotation cosinus value

Returns: the resulting quaternion

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◆ gf_quat_slerp()

GF_Vec4 gf_quat_slerp	(	GF_Vec4	q1,
		GF_Vec4	q2,
		Fixed	frac
	)

quaternion interpolation

Interpolates two quaternions using spherical linear interpolation

Parameters

q1	the first quaternion
q2	the second quaternion
frac	the fraction of the interpolation, between 0 and FIX_ONE

Returns: the interpolated quaternion

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◆ gf_bbox_refresh()

void gf_bbox_refresh ( GF_BBox * b )

updates information of the bounding box based on the edge information

Parameters

b	the target bounding box

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◆ gf_bbox_from_rect()

void gf_bbox_from_rect	(	GF_BBox *	box,
		GF_Rect *	rc
	)

builds a bounding box from a 2D rectangle

Parameters

box	the bounding box to build
rc	the source rectangle

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◆ gf_rect_from_bbox()

void gf_rect_from_bbox	(	GF_Rect *	rc,
		GF_BBox *	box
	)

builds a rectangle from a 3D bounding box.

Note: The z dimension is lost and no projection is performed

Parameters

rc	the destination rectangle
box	the source bounding box

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◆ gf_bbox_grow_point()

void gf_bbox_grow_point	(	GF_BBox *	box,
		GF_Vec	pt
	)

bounding box expansion

Checks if a point is inside a bounding box and updates the bounding box to include it if not the case

Parameters

box	the bounding box object
pt	the 3D point to check

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◆ gf_bbox_union()

void gf_bbox_union	(	GF_BBox *	b1,
		GF_BBox *	b2
	)

performs the union of two bounding boxes

Parameters

b1	the first bounding box
b2	the bounding box to add

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◆ gf_bbox_equal()

Bool gf_bbox_equal	(	GF_BBox *	b1,
		GF_BBox *	b2
	)

checks if two bounding boxes are equal or not

Parameters

b1	the first bounding box
b2	the second bounding box

Returns: GF_TRUE if equal

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◆ gf_bbox_point_inside()

Bool gf_bbox_point_inside	(	GF_BBox *	box,
		GF_Vec *	p
	)

checks if a point is inside a bounding box or not

Parameters

box	the bounding box
p	the point to check

Returns: GF_TRUE if point is inside

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◆ gf_bbox_get_vertices()

void gf_bbox_get_vertices	(	GF_Vec	bmin,
		GF_Vec	bmax,
		GF_Vec *	vecs
	)

get box vertices

Returns the 8 bounding box vertices given the minimum and maximum edge. Vertices are ordered to respect "p-vertex indexes", (vertex from a box closest to plane) and so that n-vertex (vertex from a box farthest from plane) is 7-p_vx_idx

Parameters

bmin	minimum edge of the box
bmax	maximum edge of the box
vecs	list of 8 3D points used to store the vertices.

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◆ gf_mx_from_mx2d()

void gf_mx_from_mx2d	(	GF_Matrix *	mx,
		GF_Matrix2D *	mat2D
	)

matrix constructor from 2D

Initializes a 3D matrix from a 2D matrix.

Note: all z-related coefficients will be set to default.

Parameters

mx	the target matrix to initialize
mat2D	the source 2D matrix

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◆ gf_mx_equal()

Bool gf_mx_equal	(	GF_Matrix *	mx1,
		GF_Matrix *	mx2
	)

matrix equality testing

Tests if two matrices are equal or not.

Parameters

mx1	the first matrix
mx2	the first matrix

Returns: GF_TRUE if matrices are same, GF_FALSE otherwise

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◆ gf_mx_add_translation()

void gf_mx_add_translation	(	GF_Matrix *	mx,
		Fixed	tx,
		Fixed	ty,
		Fixed	tz
	)

matrix translation

Translates a matrix

Parameters

mx	the matrix being transformed. Once the function is called, contains the result matrix
tx	horizontal translation
ty	vertical translation
tz	depth translation

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◆ gf_mx_add_scale()

void gf_mx_add_scale	(	GF_Matrix *	mx,
		Fixed	sx,
		Fixed	sy,
		Fixed	sz
	)

matrix scaling

Scales a matrix

Parameters

mx	the matrix being transformed. Once the function is called, contains the result matrix
sx	horizontal translation scaling
sy	vertical translation scaling
sz	depth translation scaling

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◆ gf_mx_add_rotation()

void gf_mx_add_rotation	(	GF_Matrix *	mx,
		Fixed	angle,
		Fixed	x,
		Fixed	y,
		Fixed	z
	)

matrix rotating

Rotates a matrix

Parameters

mx	the matrix being transformed. Once the function is called, contains the result matrix
angle	rotation angle in radians
x	horizontal coordinate of rotation axis
y	vertical coordinate of rotation axis
z	depth coordinate of rotation axis

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◆ gf_mx_add_matrix()

void gf_mx_add_matrix	(	GF_Matrix *	mx,
		GF_Matrix *	mul
	)

matrices multiplication

Multiplies a matrix with another one mx = mx*mul

Parameters

mx	the matrix being transformed. Once the function is called, contains the result matrix
mul	the matrix to add

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◆ gf_mx_add_matrix_2d()

void gf_mx_add_matrix_2d	(	GF_Matrix *	mx,
		GF_Matrix2D *	mat2D
	)

2D matrix multiplication

Adds a 2D affine matrix to a matrix

Parameters

mx	the matrix
mat2D	the matrix to premultiply

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◆ gf_mx_inverse()

void gf_mx_inverse ( GF_Matrix * mx )

affine matrix inversion

Inverses an affine matrix.

Warning: Results are undefined if the matrix is not an affine one

Parameters

mx	the matrix to inverse

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◆ gf_mx_transpose()

void gf_mx_transpose ( GF_Matrix * mx )

transpose 4x4 matrix

Transposes a 4x4 matrix

Parameters

mx	the matrix to transpose

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◆ gf_mx_apply_vec()

void gf_mx_apply_vec	(	GF_Matrix *	mx,
		GF_Vec *	pt
	)

matrix point transformation

Applies a 3D matrix transformation to a 3D point

Parameters

mx	transformation matrix
pt	pointer to 3D point. Once the function is called, pt contains the transformed point

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◆ gf_mx_apply_rect()

void gf_mx_apply_rect	(	GF_Matrix *	_this,
		GF_Rect *	rc
	)

matrix rectangle transformation

Applies a 3D matrix transformation to a rectangle, giving the enclosing rectangle of the transformed one.

Note: all depth information are discarded.

Parameters

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

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◆ gf_mx_ortho()

void gf_mx_ortho	(	GF_Matrix *	mx,
		Fixed	left,
		Fixed	right,
		Fixed	bottom,
		Fixed	top,
		Fixed	z_near,
		Fixed	z_far
	)

ortho matrix construction

Creates an orthogonal projection matrix. This assume the NDC Z lies in [-1,1]

Parameters

mx	matrix to initialize
left	min horizontal coordinate of viewport
right	max horizontal coordinate of viewport
bottom	min vertical coordinate of viewport
top	max vertical coordinate of viewport
z_near	min depth coordinate of viewport
z_far	max depth coordinate of viewport

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◆ gf_mx_ortho_reverse_z()

void gf_mx_ortho_reverse_z	(	GF_Matrix *	mx,
		Fixed	left,
		Fixed	right,
		Fixed	bottom,
		Fixed	top,
		Fixed	z_near,
		Fixed	z_far
	)

ortho matrix with reverse Z construction

Creates an orthogonal projection matrix with reverse Z. This assume the NDC Z lies in [0,1], not [-1,1]

Parameters

mx	matrix to initialize
left	min horizontal coordinate of viewport
right	max horizontal coordinate of viewport
bottom	min vertical coordinate of viewport
top	max vertical coordinate of viewport
z_near	min depth coordinate of viewport
z_far	max depth coordinate of viewport

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◆ gf_mx_perspective()

void gf_mx_perspective	(	GF_Matrix *	mx,
		Fixed	fov,
		Fixed	aspect_ratio,
		Fixed	z_near,
		Fixed	z_far
	)

perspective matrix construction

Creates a perspective projection matrix. This assume the NDC Z lies in [-1,1]

Parameters

mx	matrix to initialize
fov	camera field of view angle in radian
aspect_ratio	viewport aspect ratio
z_near	min depth coordinate of viewport
z_far	max depth coordinate of viewport

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◆ gf_mx_perspective_reverse_z()

void gf_mx_perspective_reverse_z	(	GF_Matrix *	mx,
		Fixed	fov,
		Fixed	aspect_ratio,
		Fixed	z_near,
		Fixed	z_far
	)

perspective matrix with reverse Z construction

Creates a perspective projection matrix with reverse Z. This assume the NDC Z lies in [0,1]

Parameters

mx	matrix to initialize
fov	camera field of view angle in radian
aspect_ratio	viewport aspect ratio
z_near	min depth coordinate of viewport
z_far	max depth coordinate of viewport

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◆ gf_mx_lookat()

void gf_mx_lookat	(	GF_Matrix *	mx,
		GF_Vec	position,
		GF_Vec	target,
		GF_Vec	up_vector
	)

creates look matrix

Creates a transformation matrix looking at a given direction from a given point (camera matrix).

Parameters

mx	matrix to initialize
position	position
target	look direction
up_vector	vector describing the up direction

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◆ gf_mx_apply_bbox()

void gf_mx_apply_bbox	(	GF_Matrix *	mx,
		GF_BBox *	b
	)

matrix box transformation

Applies a 3D matrix transformation to a bounding box, giving the enclosing box of the transformed one

Parameters

mx	transformation matrix
b	pointer to bounding box. Once the function is called, contains the transformed bounding box

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◆ gf_mx_apply_bbox_4x4()

void gf_mx_apply_bbox_4x4	(	GF_Matrix *	mx,
		GF_BBox *	b
	)

matrix box transformation

Applies a 3D matrix transformation using perspective division to a bounding box, giving the enclosing box of the transformed one

Parameters

mx	transformation matrix
b	pointer to bounding box. Once the function is called, contains the transformed bounding box

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◆ gf_mx_apply_bbox_sphere()

void gf_mx_apply_bbox_sphere	(	GF_Matrix *	mx,
		GF_BBox *	box
	)

matrix box sphere transformation

Applies a 3D matrix transformation to a bounding box, computing only the enclosing sphere of the transformed one.

Parameters

mx	transformation matrix
box	pointer to bounding box. Once the function is called, contains the transformed bounding sphere

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◆ gf_mx_add_matrix_4x4()

void gf_mx_add_matrix_4x4	(	GF_Matrix *	mat,
		GF_Matrix *	mul
	)

non-affine matrix multiplication

Multiplies two non-affine matrices mx = mx*mul

Parameters

mat	the target matrix
mul	the matrix we multiply with

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◆ gf_mx_inverse_4x4()

Bool gf_mx_inverse_4x4 ( GF_Matrix * mx )

non-affine matrix inversion

Inverses a non-affine matrices

Parameters

mx	the target matrix

Returns: 1 if inversion was done, 0 if inversion not possible.

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◆ gf_mx_apply_vec_4x4()

void gf_mx_apply_vec_4x4	(	GF_Matrix *	mx,
		GF_Vec4 *	vec
	)

matrix 4D vector transformation

Applies a 3D non-affine matrix transformation to a 4 dimension vector

Parameters

mx	transformation matrix
vec	pointer to the vector. Once the function is called, contains the transformed vector

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◆ gf_mx_get_yaw_pitch_roll()

void gf_mx_get_yaw_pitch_roll	(	GF_Matrix *	mx,
		Fixed *	yaw,
		Fixed *	pitch,
		Fixed *	roll
	)

matrix yaw pitch roll decomposition

Extracts yaw, pitch and roll info from a matrix

Parameters

mx	the matrix to decompose
yaw	the extracted yaw angle in radians
pitch	the extracted pitch angle in radians
roll	the extracted roll angle in radians

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◆ gf_mx_decompose()

void gf_mx_decompose	(	GF_Matrix *	mx,
		GF_Vec *	translate,
		GF_Vec *	scale,
		GF_Vec4 *	rotate,
		GF_Vec *	shear
	)

matrix decomposition

Decomposes a matrix into translation, scale, shear and rotate

Parameters

mx	the matrix to decompose
translate	the decomposed translation part
scale	the decomposed scaling part
rotate	the decomposed rotation part, expressed as a Rotataion (axis + angle)
shear	the decomposed shear part

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◆ gf_mx_rotate_vector()

void gf_mx_rotate_vector	(	GF_Matrix *	mx,
		GF_Vec *	pt
	)

matrix vector rotation

Rotates a vector with a given matrix, ignoring any translation.

Parameters

mx	transformation matrix
pt	pointer to 3D vector. Once the function is called, pt contains the transformed vector

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◆ gf_mx_rotation_matrix_from_vectors()

void gf_mx_rotation_matrix_from_vectors	(	GF_Matrix *	mx,
		GF_Vec	x_axis,
		GF_Vec	y_axis,
		GF_Vec	z_axis
	)

matrix initialization from vectors

Inits a matrix to rotate the local axis in the given vectors

Parameters

mx	matrix to initialize
x_axis	target normalized X axis
y_axis	target normalized Y axis
z_axis	target normalized Z axis

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◆ gf_mx2d_from_mx()

void gf_mx2d_from_mx	(	GF_Matrix2D *	mx2d,
		GF_Matrix *	mx
	)

matrix to 2D matrix

Inits a 2D matrix by removing all depth info from a 3D matrix

Parameters

mx2d	2D matrix to initialize
mx	3D matrix to use

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◆ gf_mx_apply_plane()

void gf_mx_apply_plane	(	GF_Matrix *	mx,
		GF_Plane *	plane
	)

matrix plane transformation

Transorms a plane by a given matrix

Parameters

mx	the matrix to use
plane	pointer to 3D plane. Once the function is called, plane contains the transformed plane

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◆ gf_plane_get_distance()

Fixed gf_plane_get_distance	(	GF_Plane *	plane,
		GF_Vec *	p
	)

point to plane distance

Gets the distance between a point and a plne

Parameters

plane	the plane to use
p	pointer to ^point to check

Returns: the distance between the place and the point

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◆ gf_closest_point_to_line()

GF_Vec gf_closest_point_to_line	(	GF_Vec	line_pt,
		GF_Vec	line_vec,
		GF_Vec	pt
	)

closest point on a line

Gets the closest point on a line from a given point in space

Parameters

line_pt	a point of the line to test
line_vec	the normalized direction vector of the line
pt	the point to check

Returns: the closest point on the line to the desired point

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◆ gf_plane_get_p_vertex_idx()

u32 gf_plane_get_p_vertex_idx ( GF_Plane * p )

box p-vertex index

Gets the p-vertex index for a given plane. The p-vertex index is the index of the closest vertex of a bounding box to the plane. The vertices of a box are always ordered in GPAC? cf gf_bbox_get_vertices

Parameters

p	the plane to check

Returns: the p-vertex index value, ranging from 0 to 7

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◆ gf_plane_intersect_line()

Bool gf_plane_intersect_line	(	GF_Plane *	plane,
		GF_Vec *	linepoint,
		GF_Vec *	linevec,
		GF_Vec *	outPoint
	)

plane line intersection

Checks for the intersection of a plane and a line

Parameters

plane	plane to test
linepoint	a point on the line to test
linevec	normalized direction vector of the line to test
outPoint	optional pointer to retrieve the intersection point, NULL otherwise

Returns: 1 if line and plane intersect, 0 otherwise

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◆ gf_bbox_plane_relation()

u32 gf_bbox_plane_relation	(	GF_BBox *	box,
		GF_Plane *	p
	)

box-plane relation

Gets the spatial relation between a box and a plane

Parameters

box	the box to check
p	the plane to check

Returns: the relation type

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◆ gf_ray()

GF_Ray gf_ray	(	GF_Vec	start,
		GF_Vec	end
	)

ray constructor

Constructs a ray object

Parameters

start	starting point of the ray
end	end point of the ray, or any point on the ray

Returns: the ray object

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◆ gf_mx_apply_ray()

void gf_mx_apply_ray	(	GF_Matrix *	mx,
		GF_Ray *	r
	)

matrix ray transformation

Transforms a ray by a given transformation matrix

Parameters

mx	the matrix to use
r	pointer to the ray. Once the function is called, contains the transformed ray

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◆ gf_ray_hit_box()

Bool gf_ray_hit_box	(	GF_Ray *	ray,
		GF_Vec	min_edge,
		GF_Vec	max_edge,
		GF_Vec *	out_point
	)

ray box intersection test

Checks if a ray intersects a box or not

Parameters

ray	the ray to check
min_edge	the minimum edge of the box to check
max_edge	the maximum edge of the box to check
out_point	optional location of a 3D point to store the intersection, NULL otherwise.

Returns: retuns 1 if the ray intersects the box, 0 otherwise

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◆ gf_ray_hit_sphere()

Bool gf_ray_hit_sphere	(	GF_Ray *	ray,
		GF_Vec *	center,
		Fixed	radius,
		GF_Vec *	out_point
	)

ray sphere intersection test

Checks if a ray intersects a box or not

Parameters

ray	the ray to check
center	the center of the sphere to check. If NULL, the origin (0,0,0)is used
radius	the radius of the sphere to check
out_point	optional location of a 3D point to store the intersection, NULL otherwise

Returns: retuns 1 if the ray intersects the sphere, 0 otherwise

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◆ gf_ray_hit_triangle()

Bool gf_ray_hit_triangle	(	GF_Ray *	ray,
		GF_Vec *	v0,
		GF_Vec *	v1,
		GF_Vec *	v2,
		Fixed *	dist
	)

ray triangle intersection test

Checks if a ray intersects a triangle or not

Parameters

ray	the ray to check
v0	first vertex of the triangle
v1	second vertex of the triangle
v2	third vertex of the triangle
dist	optional location of a fixed number to store the intersection distance from ray origin if any, NULL otherwise

Returns: retuns 1 if the ray intersects the triangle, 0 otherwise

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Data Structures

Macros

Enumerations

Functions

Detailed Description

Data Structure Documentation

◆ GF_Vec

◆ GF_Vec4

◆ GF_Matrix

◆ GF_BBox

◆ GF_Plane

◆ GF_Ray

Macro Definition Documentation

◆ gf_vec_equal

◆ gf_vec_rev

◆ gf_vec_diff

◆ gf_vec_add

◆ gf_quat_len

◆ gf_quat_norm

◆ gf_mx_init

◆ gf_mx_is_identity

◆ gf_mx_copy

Enumeration Type Documentation

◆ anonymous enum

Function Documentation

◆ gf_vec_len()

◆ gf_vec_len_p()

◆ gf_vec_lensq()

◆ gf_vec_lensq_p()

◆ gf_vec_dot()

◆ gf_vec_dot_p()

◆ gf_vec_norm()

◆ gf_vec_scale()

◆ gf_vec_scale_p()

◆ gf_vec_cross()

◆ gf_vec_cross_p()

◆ gf_quat_to_rotation()

◆ gf_quat_from_rotation()

◆ gf_quat_get_inv()

◆ gf_quat_multiply()

◆ gf_quat_rotate()

◆ gf_quat_from_axis_cos()

◆ gf_quat_slerp()

◆ gf_bbox_refresh()

◆ gf_bbox_from_rect()

◆ gf_rect_from_bbox()

◆ gf_bbox_grow_point()

◆ gf_bbox_union()

◆ gf_bbox_equal()

◆ gf_bbox_point_inside()

◆ gf_bbox_get_vertices()

◆ gf_mx_from_mx2d()

◆ gf_mx_equal()

◆ gf_mx_add_translation()

◆ gf_mx_add_scale()

◆ gf_mx_add_rotation()

◆ gf_mx_add_matrix()

◆ gf_mx_add_matrix_2d()

◆ gf_mx_inverse()

◆ gf_mx_transpose()

◆ gf_mx_apply_vec()

◆ gf_mx_apply_rect()

◆ gf_mx_ortho()

◆ gf_mx_ortho_reverse_z()

◆ gf_mx_perspective()

◆ gf_mx_perspective_reverse_z()

◆ gf_mx_lookat()

◆ gf_mx_apply_bbox()

◆ gf_mx_apply_bbox_4x4()

◆ gf_mx_apply_bbox_sphere()

◆ gf_mx_add_matrix_4x4()

◆ gf_mx_inverse_4x4()

◆ gf_mx_apply_vec_4x4()

◆ gf_mx_get_yaw_pitch_roll()

◆ gf_mx_decompose()

◆ gf_mx_rotate_vector()

◆ gf_mx_rotation_matrix_from_vectors()

◆ gf_mx2d_from_mx()

◆ gf_mx_apply_plane()

◆ gf_plane_get_distance()