3D Mathematics functions More...
Classes | |
struct | __vec3f |
3D point or vector More... | |
struct | __vec4f |
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... | |
Defines | |
#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_copy(_obj, from) |
matrix copy | |
Typedefs | |
typedef struct __vec3f | GF_Vec |
3D point or vector | |
typedef struct __vec4f | GF_Vec4 |
4D vector | |
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_lensq (GF_Vec v) |
get 3D vector square length | |
Fixed | gf_vec_dot (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_cross (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 identity 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_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_perspective (GF_Matrix *mx, Fixed foc, Fixed aspect_ratio, Fixed z_near, Fixed z_far) |
perspective matrix 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_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_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 | |
Bool | gf_ray_hit_triangle_backcull (GF_Ray *ray, GF_Vec *v0, GF_Vec *v1, GF_Vec *v2, Fixed *dist) |
ray triangle intersection test |
This section documents mathematic tools for 3D geometry operations
#define gf_vec_equal | ( | v1, | |||
v2 | ) |
macro evaluating to 1 if vectors are equal, 0 otherwise
#define gf_vec_rev | ( | v | ) |
macro reversing a vector v = v
#define gf_vec_diff | ( | res, | |||
v1, | |||||
v2 | ) |
macro performing the minus operation res = v1 - v2
#define gf_vec_add | ( | res, | |||
v1, | |||||
v2 | ) |
macro performing the add operation res = v1 + v2
#define gf_quat_len | ( | v | ) |
gets the len of a quaternion
#define gf_quat_norm | ( | v | ) |
normalizes a quaternion
#define gf_mx_init | ( | _obj | ) |
Inits the matrix to the identity matrix
#define gf_mx_copy | ( | _obj, | |||
from | ) |
Copies the matrix _from to the matrix _obj
The 3D point object is used in all the GPAC framework for both point and vector representation.
The 4D vector object is used in all the GPAC framework for 4 dimension vectors, VRML Rotations and quaternions representation.
anonymous enum |
Classification types for box/plane position used in gf_bbox_plane_relation
Gets the square length of a 3D vector
Gets the dot product of two vectors
void gf_vec_norm | ( | GF_Vec * | v | ) |
Norms the vector, eg make its length equal to FIX_ONE
v | vector to normalize |
Scales a vector by a given amount
v | vector to scale
|
Gets the cross product of two vectors
v1 | first vector
|
Transforms a quaternion to a Rotation, expressed as a 4 dimension vector with x,y,z for axis and q for rotation angle
quat | the quaternion to transform
|
Transforms a Rotation to a quaternion
rot | the rotation to transform
|
Multiplies two quaternions
q1 | the first quaternion
|
Rotates a vector with a quaternion
quat | the quaternion modelizing the rotation
|
Constructs a quaternion from an axis and a cosinus value (shortcut to gf_quat_from_rotation)
axis | the rotation axis
|
Interpolates two quaternions using spherical linear interpolation
q1 | the first quaternion
|
void gf_bbox_refresh | ( | GF_BBox * | b | ) |
updates information of the bounding box based on the edge information
builds a rectangle from a 3D bounding box.
Checks if a point is inside a bounding box and updates the bounding box to include it if not the case
box | the bounding box object
|
checks if a point is inside a bounding box or not
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
bmin | minimum edge of the box
|
void gf_mx_from_mx2d | ( | GF_Matrix * | mx, | |
GF_Matrix2D * | mat2D | |||
) |
Initializes a 3D matrix from a 2D matrix.
Tests if two matrices are equal or not.
Translates a matrix
mx | the matrix being transformed. Once the function is called, contains the result matrix
|
Scales a matrix
mx | the matrix being transformed. Once the function is called, contains the result matrix
|
Rotates a matrix
mx | the matrix being transformed. Once the function is called, contains the result matrix
|
Multiplies a matrix with another one mx = mx*mul
mx | the matrix being transformed. Once the function is called, contains the result matrix
|
void gf_mx_add_matrix_2d | ( | GF_Matrix * | mx, | |
GF_Matrix2D * | mat2D | |||
) |
Adds a 2D affine matrix to a matrix
mx | the matrix
|
void gf_mx_inverse | ( | GF_Matrix * | mx | ) |
Inverses an affine matrix.
mx | the matrix to inverse |
Applies a 3D matrix transformation to a 3D point
mx | transformation matrix
|
Applies a 3D matrix transformation to a rectangle, giving the enclosing rectangle of the transformed one.
_this | transformation matrix
|
void gf_mx_ortho | ( | GF_Matrix * | mx, | |
Fixed | left, | |||
Fixed | right, | |||
Fixed | bottom, | |||
Fixed | top, | |||
Fixed | z_near, | |||
Fixed | z_far | |||
) |
Creates an orthogonal projection matrix
mx | matrix to initialize
|
Creates a perspective projection matrix
mx | matrix to initialize
|
Creates a transformation matrix looking at a given direction from a given point (camera matrix).
mx | matrix to initialize
|
Applies a 3D matrix transformation to a bounding box, giving the enclosing box of the transformed one
mx | transformation matrix
|
Applies a 3D matrix transformation to a bounding box, computing only the enclosing sphere of the transformed one.
mx | transformation matrix
|
Multiplies two non-affine matrices mx = mx*mul
Bool gf_mx_inverse_4x4 | ( | GF_Matrix * | mx | ) |
Inverses a non-affine matrices
Applies a 3D non-affine matrix transformation to a 4 dimension vector
mx | transformation matrix
|
void gf_mx_decompose | ( | GF_Matrix * | mx, | |
GF_Vec * | translate, | |||
GF_Vec * | scale, | |||
GF_Vec4 * | rotate, | |||
GF_Vec * | shear | |||
) |
Decomposes a matrix into translation, scale, shear and rotate
mx | the matrix to decompose
|
Rotates a vector with a given matrix, ignoring any translation.
mx | transformation matrix
|
void gf_mx_rotation_matrix_from_vectors | ( | GF_Matrix * | mx, | |
GF_Vec | x_axis, | |||
GF_Vec | y_axis, | |||
GF_Vec | z_axis | |||
) |
Inits a matrix to rotate the local axis in the given vectors
mx | matrix to initialize
|
void gf_mx2d_from_mx | ( | GF_Matrix2D * | mx2d, | |
GF_Matrix * | mx | |||
) |
Inits a 2D matrix by removing all depth info from a 3D matrix
mx2d | 2D matrix to initialize
|
Transorms a plane by a given matrix
mx | the matrix to use
|
Gets the distance between a point and a plne
plane | the plane to use
|
Gets the closest point on a line from a given point in space
line_pt | a point of the line to test
|
u32 gf_plane_get_p_vertex_idx | ( | GF_Plane * | p | ) |
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
p | the plane to check
|
Bool gf_plane_intersect_line | ( | GF_Plane * | plane, | |
GF_Vec * | linepoint, | |||
GF_Vec * | linevec, | |||
GF_Vec * | outPoint | |||
) |
Checks for the intersection of a plane and a line
plane | plane to test
|
Gets the spatial relation between a box and a plane
box | the box to check
|
Constructs a ray object
start | starting point of the ray
|
Transforms a ray by a given transformation matrix
mx | the matrix to use
|
Checks if a ray intersects a box or not
ray | the ray to check
|
Checks if a ray intersects a box or not
ray | the ray to check
|
Checks if a ray intersects a triangle or not
ray | the ray to check
|