math.h

一个用于智能手机的多媒体库适合S60 WinCE的跨平台开发库

 *
 *Returns the smallest pixel-aligned rectangle completely containing a rectangle
 *\param r the rectangle to transform
 *\return the pixel-aligned transformed rectangle
*/
GF_IRect gf_rect_pixelize(GF_Rect *r);


/*!
 *\brief 2D matrix
 *
 *The 2D affine matrix object used by renderers and parsers. The transformation of P(x,y) in P'(X, Y) is:
 \code
	X = m[0]*x + m[1]*y + m[2];
	Y = m[3]*x + m[4]*y + m[5];
 \endcode
*/
typedef struct
{
	Fixed m[6];
} GF_Matrix2D;

/*!\brief matrix initialization
 *\hideinitializer
 *
 *Inits the matrix to the identity matrix
*/
#define gf_mx2d_init(_obj) { memset((_obj).m, 0, sizeof(Fixed)*6); (_obj).m[0] = (_obj).m[4] = FIX_ONE; }
/*!\brief matrix copy
 *\hideinitializer
 *
 *Copies the matrix _from to the matrix _obj
*/
#define gf_mx2d_copy(_obj, from) memcpy((_obj).m, (from).m, sizeof(Fixed)*6)
/*!\brief matrix identity testing
 *\hideinitializer
 *
 *This macro evaluates to 1 if the matrix _obj is the identity matrix, 0 otherwise
*/
#define gf_mx2d_is_identity(_obj) ((!(_obj).m[1] && !(_obj).m[2] && !(_obj).m[3] && !(_obj).m[5] && ((_obj).m[0]==FIX_ONE) && ((_obj).m[4]==FIX_ONE)) ? 1 : 0)

/*!\brief 2D matrix multiplication
 *
 *Multiplies two 2D matrices from*_this
 *\param _this matrix being transformed. Once the function is called, _this contains the result matrix
 *\param from transformation matrix to add
*/
void gf_mx2d_add_matrix(GF_Matrix2D *_this, GF_Matrix2D *from);

/*!\brief 2D matrix pre-multiplication
 *
 *Multiplies two 2D matrices _this*from
 *\param _this matrix being transformed. Once the function is called, _this contains the result matrix
 *\param from transformation matrix to add
*/
void gf_mx2d_pre_multiply(GF_Matrix2D *_this, GF_Matrix2D *from);

/*!\brief matrix translating
 *
 *Translates a 2D matrix
 *\param _this matrix being transformed. Once the function is called, _this contains the result matrix
 *\param cx horizontal translation
 *\param cy vertical translation
*/
void gf_mx2d_add_translation(GF_Matrix2D *_this, Fixed cx, Fixed cy);
/*!\brief matrix rotating
 *
 *Rotates a 2D matrix
 *\param _this matrix being transformed. Once the function is called, _this contains the result matrix
 *\param cx horizontal rotation center coordinate
 *\param cy vertical rotation center coordinate
 *\param angle rotation angle in radians
*/
void gf_mx2d_add_rotation(GF_Matrix2D *_this, Fixed cx, Fixed cy, Fixed angle);
/*!\brief matrix scaling
 *
 *Scales a 2D matrix
 *\param _this matrix being transformed. Once the function is called, _this contains the result matrix
 *\param scale_x horizontal scaling factor
 *\param scale_y vertical scaling factor
*/
void gf_mx2d_add_scale(GF_Matrix2D *_this, Fixed scale_x, Fixed scale_y);
/*!\brief matrix uncentered scaling
 *
 *Scales a 2D matrix with a non-centered scale
 *\param _this matrix being transformed. Once the function is called, _this contains the result matrix
 *\param scale_x horizontal scaling factor
 *\param scale_y vertical scaling factor
 *\param cx horizontal scaling center coordinate
 *\param cy vertical scaling center coordinate
 *\param angle scale orienttion angle in radians
*/
void gf_mx2d_add_scale_at(GF_Matrix2D *_this, Fixed scale_x, Fixed scale_y, Fixed cx, Fixed cy, Fixed angle);
/*!\brief matrix skewing
 *
 *Skews a 2D matrix
 *\param _this matrix being transformed. Once the function is called, _this contains the result matrix
 *\param skew_x horizontal skew factor
 *\param skew_y vertical skew factor
*/
void gf_mx2d_add_skew(GF_Matrix2D *_this, Fixed skew_x, Fixed skew_y);
/*!\brief matrix horizontal skewing
 *
 *Skews a 2D matrix horizontally by a given angle
 *\param _this matrix being transformed. Once the function is called, _this contains the result matrix
 *\param angle horizontal skew angle in radians
*/
void gf_mx2d_add_skew_x(GF_Matrix2D *_this, Fixed angle);
/*!\brief matrix vertical skewing
 *
 *Skews a 2D matrix vertically by a given angle
 *\param _this matrix being transformed. Once the function is called, _this contains the result matrix
 *\param angle vertical skew angle in radians
*/
void gf_mx2d_add_skew_y(GF_Matrix2D *_this, Fixed angle);
/*!\brief matrix inversing
 *
 *Inverses a 2D matrix 
 *\param _this matrix being transformed. Once the function is called, _this contains the result matrix
*/
void gf_mx2d_inverse(GF_Matrix2D *_this);
/*!\brief matrix coordinate transformation
 *
 *Applies a 2D matrix transformation to coordinates
 *\param _this transformation matrix
 *\param x pointer to horizontal coordinate. Once the function is called, x contains the transformed horizontal coordinate
 *\param y pointer to vertical coordinate. Once the function is called, y contains the transformed vertical coordinate
*/
void gf_mx2d_apply_coords(GF_Matrix2D *_this, Fixed *x, Fixed *y);
/*!\brief matrix point transformation
 *
 *Applies a 2D matrix transformation to a 2D point
 *\param _this transformation matrix
 *\param pt pointer to 2D point. Once the function is called, pt contains the transformed point
*/
void gf_mx2d_apply_point(GF_Matrix2D *_this, GF_Point2D *pt);
/*!\brief matrix rectangle transformation
 *
 *Applies a 2D matrix transformation to a rectangle, giving the enclosing rectangle of the transformed one
 *\param _this transformation matrix
 *\param rc pointer to rectangle. Once the function is called, rc contains the transformed rectangle
*/
void gf_mx2d_apply_rect(GF_Matrix2D *_this, GF_Rect *rc);

/*!\brief matrix decomposition
 *
 *Decomposes a 2D matrix M as M=Scale x Rotation x Translation if possible
 *\param _this transformation matrix
 *\param scale resulting scale part
 *\param rotate resulting rotation part
 *\param translate resulting translation part
 *\return 0 if matrix cannot be decomposed, 1 otherwise
*/
Bool gf_mx2d_decompose(GF_Matrix2D *_this, GF_Point2D *scale, Fixed *rotate, GF_Point2D *translate);

/*! @} */


/*!
 *\addtogroup math3d_grp math3d
 *\ingroup math_grp
 *\brief 3D Mathematics functions
 *
 *This section documents mathematic tools for 3D geometry operations
 *	@{
 */

/*!\brief 3D point or vector
 *
 *The 3D point object is used in all the GPAC framework for both point and vector representation.
*/
typedef struct __vec3f
{
	Fixed x;
	Fixed y;
	Fixed z;
} GF_Vec;

/*base vector operations are MACROs for faster access*/
/*!\hideinitializer macro evaluating to 1 if vectors are equal, 0 otherwise*/
#define gf_vec_equal(v1, v2) (((v1).x == (v2).x) && ((v1).y == (v2).y) && ((v1).z == (v2).z))
/*!\hideinitializer macro reversing a vector v = v*/
#define gf_vec_rev(v) { (v).x = -(v).x; (v).y = -(v).y; (v).z = -(v).z; }
/*!\hideinitializer macro performing the minus operation res = v1 - v2*/
#define gf_vec_diff(res, v1, v2) { (res).x = (v1).x - (v2).x; (res).y = (v1).y - (v2).y; (res).z = (v1).z - (v2).z; }
/*!\hideinitializer macro performing the add operation res = v1 + v2*/
#define gf_vec_add(res, v1, v2) { (res).x = (v1).x + (v2).x; (res).y = (v1).y + (v2).y; (res).z = (v1).z + (v2).z; }

/*!
 *\brief get 3D vector length
 *
 *Gets the length of a 3D vector
 *\return length of the vector
 */
Fixed gf_vec_len(GF_Vec v);
/*!
 *\brief get 3D vector square length
 *
 *Gets the square length of a 3D vector
 *\return square length of the vector
 */
Fixed gf_vec_lensq(GF_Vec v);
/*!
 *\brief get 3D vector dot product
 *
 *Gets the dot product of two vectors
 *\return dot product of the vectors
 */
Fixed gf_vec_dot(GF_Vec v1, GF_Vec v2);
/*!
 *\brief vector normalization
 *
 *Norms the vector, eg make its length equal to \ref FIX_ONE
 *\param v vector to normalize
 */
void gf_vec_norm(GF_Vec *v);
/*!
 *\brief vector scaling
 *
 *Scales a vector by a given amount
 *\param v vector to scale
 *\param f scale factor
 *\return scaled vector
 */
GF_Vec gf_vec_scale(GF_Vec v, Fixed f);
/*!
 *\brief vector cross product
 *
 *Gets the cross product of two vectors
 *\param v1 first vector
 *\param v2 second vector
 *\return cross-product vector
 */
GF_Vec gf_vec_cross(GF_Vec v1, GF_Vec v2);

/*!\brief 4D vector
 *
 *The 4D vector object is used in all the GPAC framework for 4 dimension vectors, VRML Rotations and quaternions representation.
*/
typedef struct __vec4f
{
	Fixed x;
	Fixed y;
	Fixed z;
	Fixed q;
} GF_Vec4;


/*!\brief 3D matrix
 *
 *The 3D matrix object used by renderers and parsers. 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.
 */
typedef struct
{
	Fixed m[16];
} GF_Matrix;


/*!\hideinitializer gets the len of a quaternion*/
#define gf_quat_len(v) gf_sqrt(gf_mulfix((v).q,(v).q) + gf_mulfix((v).x,(v).x) + gf_mulfix((v).y,(v).y) + gf_mulfix((v).z,(v).z))
/*!\hideinitializer normalizes a quaternion*/
#define gf_quat_norm(v) { \
	Fixed __mag = gf_quat_len(v);	\
	(v).x = gf_divfix((v).x, __mag); (v).y = gf_divfix((v).y, __mag); (v).z = gf_divfix((v).z, __mag); (v).q = gf_divfix((v).q, __mag);	\
	}	\

/*!\brief 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
 *\param quat the quaternion to transform
 *\return the rotation value
 */
GF_Vec4 gf_quat_to_rotation(GF_Vec4 *quat);
/*!\brief quaternion from rotation
 *
 *Transforms a Rotation to a quaternion
 *\param rot the rotation to transform
 *\return the quaternion value
 */
GF_Vec4 gf_quat_from_rotation(GF_Vec4 rot);
/*!inverses a quaternion*/
GF_Vec4 gf_quat_get_inv(GF_Vec4 *quat);
/*!\brief quaternion multiplication
 *
 *Multiplies two quaternions
 *\param q1 the first quaternion
 *\param q2 the second quaternion
 *\return the resulting quaternion
 */
GF_Vec4 gf_quat_multiply(GF_Vec4 *q1, GF_Vec4 *q2);
/*!\brief quaternion vector rotating
 *
 *Rotates a vector with a quaternion 
 *\param quat the quaternion modelizing the rotation
 *\param vec the vector to rotate
 *\return the resulting vector
 */
GF_Vec gf_quat_rotate(GF_Vec4 *quat, GF_Vec *vec);
/*!\brief quaternion from axis and cos
 *
 *Constructs a quaternion from an axis and a cosinus value (shortcut to \ref gf_quat_from_rotation)
 *\param axis the rotation axis
 *\param cos_a the rotation cosinus value
 *\return the resulting quaternion
 */
GF_Vec4 gf_quat_from_axis_cos(GF_Vec axis, Fixed cos_a);
/*!\brief quaternion interpolation
 *
 *Interpolates two quaternions using spherical linear interpolation
 *\param q1 the first quaternion
 *\param q2 the second quaternion
 *\param frac the fraction of the interpolation, between 0 and \ref FIX_ONE
 *\return the interpolated quaternion
 */
GF_Vec4 gf_quat_slerp(GF_Vec4 q1, GF_Vec4 q2, Fixed frac);

/*!\brief 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.
 */
typedef struct
{
	/*!minimum x, y, and z of the object*/
	GF_Vec min_edge;
	/*!maximum x, y, and z of the object*/
	GF_Vec max_edge;

	/*!center of the bounding box.\note this is computed from min_edge and max_edge*/
	GF_Vec center;
	/*!radius of the bounding sphere for this box.\note this is computed from min_edge and max_edge*/
	Fixed radius;
	/*!the bbox center and radius are valid*/
	Bool is_set;
} GF_BBox;
/*!updates information of the bounding box based on the edge information*/
void gf_bbox_refresh(GF_BBox *b);
/*!builds a bounding box from a 2D rectangle*/
void gf_bbox_from_rect(GF_BBox *box, GF_Rect *rc);
/*!builds a rectangle from a 3D bounding box.\note The z dimension is lost and no projection is performed*/