gtkradiant/libs/mathlib.h

/*
Copyright (C) 1999-2006 Id Software, Inc. and contributors.
For a list of contributors, see the accompanying CONTRIBUTORS file.

This file is part of GtkRadiant.

GtkRadiant is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.

GtkRadiant is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with GtkRadiant; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
*/

#ifndef __MATHLIB__
#define __MATHLIB__

// mathlib.h
#include <math.h>

#ifdef __cplusplus

// start declarations of functions defined in C library.
extern "C"
{

#endif

#include "bytebool.h"

typedef float vec_t;
typedef vec_t vec3_t[3];
typedef vec_t vec5_t[5];
typedef vec_t vec4_t[4];

#define	SIDE_FRONT		0
#define	SIDE_ON			2
#define	SIDE_BACK		1
#define	SIDE_CROSS		-2

// plane types are used to speed some tests
// 0-2 are axial planes
#define	PLANE_X			0
#define	PLANE_Y			1
#define	PLANE_Z			2
#define	PLANE_NON_AXIAL	3

#define	Q_PI	3.14159265358979323846f

extern const vec3_t vec3_origin;

extern const vec3_t g_vec3_axis_x;
extern const vec3_t g_vec3_axis_y;
extern const vec3_t g_vec3_axis_z;

#define	EQUAL_EPSILON	0.001

#define DotProduct(x,y) ((x)[0]*(y)[0]+(x)[1]*(y)[1]+(x)[2]*(y)[2])
#define VectorSubtract(a,b,c) ((c)[0]=(a)[0]-(b)[0],(c)[1]=(a)[1]-(b)[1],(c)[2]=(a)[2]-(b)[2])
#define VectorAdd(a,b,c) ((c)[0]=(a)[0]+(b)[0],(c)[1]=(a)[1]+(b)[1],(c)[2]=(a)[2]+(b)[2])
#define VectorIncrement(a,b) ((b)[0]+=(a)[0],(b)[1]+=(a)[1],(b)[2]+=(a)[2])
#define VectorCopy(a,b) ((b)[0]=(a)[0],(b)[1]=(a)[1],(b)[2]=(a)[2])
#define VectorSet(v, a, b, c) ((v)[0]=(a),(v)[1]=(b),(v)[2]=(c))
#define VectorScale(a,b,c) ((c)[0]=(b)*(a)[0],(c)[1]=(b)*(a)[1],(c)[2]=(b)*(a)[2])
#define VectorMid(a,b,c) ((c)[0]=((a)[0]+(b)[0])*0.5f,(c)[1]=((a)[1]+(b)[1])*0.5f,(c)[2]=((a)[2]+(b)[2])*0.5f)
#define VectorNegate(a,b) ((b)[0]=-(a)[0],(b)[1]=-(a)[1],(b)[2]=-(a)[2])
#define CrossProduct(a,b,c) ((c)[0]=(a)[1]*(b)[2]-(a)[2]*(b)[1],(c)[1]=(a)[2]*(b)[0]-(a)[0]*(b)[2],(c)[2]=(a)[0]*(b)[1]-(a)[1]*(b)[0])
#define VectorClear(x) ((x)[0]=(x)[1]=(x)[2]=0)

#define FLOAT_SNAP(f,snap) ( (float)( floor( (f) / (snap) + 0.5 ) * (snap) ) )
#define FLOAT_TO_INTEGER(f) ( (float)( floor( (f) + 0.5 ) ) )

#define Q_rint(in) ((vec_t)floor(in+0.5))

qboolean VectorCompare (const vec3_t v1, const vec3_t v2);

vec_t VectorLength(const vec3_t v);

void VectorMA( const vec3_t va, vec_t scale, const vec3_t vb, vec3_t vc );

void _CrossProduct (vec3_t v1, vec3_t v2, vec3_t cross);
vec_t VectorNormalize (const vec3_t in, vec3_t out);
vec_t ColorNormalize( const vec3_t in, vec3_t out );
void VectorInverse (vec3_t v);
void VectorPolar(vec3_t v, float radius, float theta, float phi);

// default snapping, to 1
void VectorSnap(vec3_t v);

// integer snapping
void VectorISnap(vec3_t point, int snap);

// Gef:   added snap to float for sub-integer grid sizes
// TTimo: we still use the int version of VectorSnap when possible
//        to avoid potential rounding issues
// TTimo: renaming to VectorFSnap for C implementation
void VectorFSnap(vec3_t point, float snap);

// NOTE: added these from Ritual's Q3Radiant
void ClearBounds (vec3_t mins, vec3_t maxs);
void AddPointToBounds (vec3_t v, vec3_t mins, vec3_t maxs);


#define	PITCH				0		// up / down
#define	YAW					1		// left / right
#define	ROLL				2		// fall over

void AngleVectors (vec3_t angles, vec3_t forward, vec3_t right, vec3_t up);
void VectorToAngles( vec3_t vec, vec3_t angles );

#define ZERO_EPSILON 1.0E-6
#define RAD2DEGMULT 57.29577951308232f
#define DEG2RADMULT 0.01745329251994329f
#define RAD2DEG( a ) ( (a) * RAD2DEGMULT )
#define DEG2RAD( a ) ( (a) * DEG2RADMULT )

void VectorRotate (vec3_t vIn, vec3_t vRotation, vec3_t out);
void VectorRotateOrigin (vec3_t vIn, vec3_t vRotation, vec3_t vOrigin, vec3_t out);

// some function merged from tools mathlib code

qboolean PlaneFromPoints( vec4_t plane, const vec3_t a, const vec3_t b, const vec3_t c );
void NormalToLatLong( const vec3_t normal, byte bytes[2] );
int	PlaneTypeForNormal (vec3_t normal);
void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees );


/*!
\todo
FIXME test calls such as intersect tests should be named test_
*/

typedef vec_t m3x3_t[9];
/*!NOTE 
m4x4 looks like this..

                x  y  z
x axis        ( 0  1  2)
y axis        ( 4  5  6)
z axis        ( 8  9 10)
translation   (12 13 14)
scale         ( 0  5 10)
*/
typedef vec_t m4x4_t[16];

#define M4X4_INDEX(m,row,col) (m[(col<<2)+row])

typedef enum { eXYZ, eYZX, eZXY, eXZY, eYXZ, eZYX } eulerOrder_t;

#define CLIP_PASS 0x00 // 000000
#define CLIP_LT_X 0x01 // 000001
#define CLIP_GT_X 0x02 // 000010
#define CLIP_LT_Y 0x04 // 000100
#define CLIP_GT_Y 0x08 // 001000
#define CLIP_LT_Z 0x10 // 010000
#define CLIP_GT_Z 0x20 // 100000
#define CLIP_FAIL 0x3F // 111111
typedef unsigned char clipmask_t;

extern const m4x4_t g_m4x4_identity;

#define M4X4_COPY(dst,src) (\
(dst)[0]=(src)[0],\
(dst)[1]=(src)[1],\
(dst)[2]=(src)[2],\
(dst)[3]=(src)[3],\
(dst)[4]=(src)[4],\
(dst)[5]=(src)[5],\
(dst)[6]=(src)[6],\
(dst)[7]=(src)[7],\
(dst)[8]=(src)[8],\
(dst)[9]=(src)[9],\
(dst)[10]=(src)[10],\
(dst)[11]=(src)[11],\
(dst)[12]=(src)[12],\
(dst)[13]=(src)[13],\
(dst)[14]=(src)[14],\
(dst)[15]=(src)[15])

typedef enum
{
  eRightHanded = 0,
  eLeftHanded = 1,
} 
m4x4Handedness_t;

m4x4Handedness_t m4x4_handedness(const m4x4_t matrix);

/*! assign other m4x4 to this m4x4 */
void m4x4_assign(m4x4_t matrix, const m4x4_t other);

// constructors
/*! create m4x4 as identity matrix */
void m4x4_identity(m4x4_t matrix);
/*! create m4x4 as a translation matrix, for a translation vec3 */
void m4x4_translation_for_vec3(m4x4_t matrix, const vec3_t translation);
/*! create m4x4 as a rotation matrix, for an euler angles (degrees) vec3 */
void m4x4_rotation_for_vec3(m4x4_t matrix, const vec3_t euler, eulerOrder_t order);
/*! create m4x4 as a scaling matrix, for a scale vec3 */
void m4x4_scale_for_vec3(m4x4_t matrix, const vec3_t scale);
/*! create m4x4 as a rotation matrix, for a quaternion vec4 */
void m4x4_rotation_for_quat(m4x4_t matrix, const vec4_t rotation);
/*! create m4x4 as a rotation matrix, for an axis vec3 and an angle (radians) */
void m4x4_rotation_for_axisangle(m4x4_t matrix, const vec3_t axis, double angle);
/*! generate a perspective matrix by specifying the view frustum */
void m4x4_frustum(m4x4_t matrix, vec_t left, vec_t right, vec_t bottom, vec_t top, vec_t nearval, vec_t farval);

// a valid m4x4 to access is always first argument
/*! extract translation vec3 from matrix */
void m4x4_get_translation_vec3(const m4x4_t matrix, vec3_t translation);
/*! extract euler rotation angles from a rotation-only matrix */
void m4x4_get_rotation_vec3(const m4x4_t matrix, vec3_t euler, eulerOrder_t order);
/*! extract scale vec3 from matrix */
void m4x4_get_scale_vec3(const m4x4_t matrix, vec3_t scale);
/*! extract translation/euler/scale from an orthogonal matrix. NOTE: requires right-handed axis-base */
void m4x4_get_transform_vec3(const m4x4_t matrix, vec3_t translation, vec3_t euler, eulerOrder_t order, vec3_t scale);

// a valid m4x4 to be modified is always first argument
/*! translate m4x4 by a translation vec3 */
void m4x4_translate_by_vec3(m4x4_t matrix, const vec3_t translation);
/*! rotate m4x4 by a euler (degrees) vec3 */
void m4x4_rotate_by_vec3(m4x4_t matrix, const vec3_t euler, eulerOrder_t order);
/*! scale m4x4 by a scaling vec3 */
void m4x4_scale_by_vec3(m4x4_t matrix, const vec3_t scale);
/*! rotate m4x4 by a quaternion vec4 */
void m4x4_rotate_by_quat(m4x4_t matrix, const vec4_t rotation);
/*! rotate m4x4 by an axis vec3 and an angle (radians) */
void m4x4_rotate_by_axisangle(m4x4_t matrix, const vec3_t axis, double angle);
/*! transform m4x4 by translation/eulerZYX/scaling vec3 (transform = scale * eulerZ * eulerY * eulerX * translation) */
void m4x4_transform_by_vec3(m4x4_t matrix, const vec3_t translation, const vec3_t euler, eulerOrder_t order, const vec3_t scale);
/*! rotate m4x4 around a pivot point by eulerZYX vec3 */
void m4x4_pivoted_rotate_by_vec3(m4x4_t matrix, const vec3_t euler, eulerOrder_t order, const vec3_t pivotpoint);
/*! scale m4x4 around a pivot point by scaling vec3 */
void m4x4_pivoted_scale_by_vec3(m4x4_t matrix, const vec3_t scale, const vec3_t pivotpoint);
/*! transform m4x4 around a pivot point by translation/eulerZYX/scaling vec3 */
void m4x4_pivoted_transform_by_vec3(m4x4_t matrix, const vec3_t translation, const vec3_t euler, eulerOrder_t order, const vec3_t scale, const vec3_t pivotpoint);
/*! transform m4x4 around a pivot point by translation/rotation/scaling vec3 */
void m4x4_pivoted_transform_by_rotation(m4x4_t matrix, const vec3_t translation, const m4x4_t rotation, const vec3_t scale, const vec3_t pivotpoint);
/*! rotate m4x4 around a pivot point by quaternion vec4 */
void m4x4_pivoted_rotate_by_quat(m4x4_t matrix, const vec4_t quat, const vec3_t pivotpoint);
/*! rotate m4x4 around a pivot point by axis vec3 and angle (radians) */
void m4x4_pivoted_rotate_by_axisangle(m4x4_t matrix, const vec3_t axis, double angle, const vec3_t pivotpoint);

/*! postmultiply m4x4 by another m4x4 */
void m4x4_multiply_by_m4x4(m4x4_t matrix, const m4x4_t matrix_src);
/*! premultiply m4x4 by another m4x4 */
void m4x4_premultiply_by_m4x4(m4x4_t matrix, const m4x4_t matrix_src);
/*! postmultiply orthogonal m4x4 by another orthogonal m4x4 */
void m4x4_orthogonal_multiply_by_m4x4(m4x4_t matrix, const m4x4_t matrix_src);
/*! premultiply orthogonal m4x4 by another orthogonal m4x4 */
void m4x4_orthogonal_premultiply_by_m4x4(m4x4_t matrix, const m4x4_t matrix_src);

/*! multiply a point (x,y,z,1) by matrix */
void m4x4_transform_point(const m4x4_t matrix, vec3_t point);
/*! multiply a normal (x,y,z,0) by matrix */
void m4x4_transform_normal(const m4x4_t matrix, vec3_t normal);
/*! multiply a vec4 (x,y,z,w) by matrix */
void m4x4_transform_vec4(const m4x4_t matrix, vec4_t vector);

/*! multiply a point (x,y,z,1) by matrix */
void m4x4_transform_point(const m4x4_t matrix, vec3_t point);
/*! multiply a normal (x,y,z,0) by matrix */
void m4x4_transform_normal(const m4x4_t matrix, vec3_t normal);

/*! transpose a m4x4 */
void m4x4_transpose(m4x4_t matrix);
/*! invert an orthogonal 4x3 subset of a 4x4 matrix */
int m4x4_orthogonal_invert(m4x4_t matrix);
/*! invert any m4x4 using Kramer's rule.. return 1 if matrix is singular, else return 0 */
int m4x4_invert(m4x4_t matrix);

/*! clip a point (x,y,z,1) by canonical matrix */
clipmask_t m4x4_clip_point(const m4x4_t matrix, const vec3_t point, vec4_t clipped);
/*! device-space polygon for clipped triangle */
unsigned int m4x4_clip_triangle(const m4x4_t matrix, const vec3_t p0, const vec3_t p1, const vec3_t p2, vec4_t clipped[9]);
/*! device-space line for clipped line  */
unsigned int m4x4_clip_line(const m4x4_t matrix, const vec3_t p0, const vec3_t p1, vec4_t clipped[2]);


//! quaternion identity
void quat_identity(vec4_t quat);
//! quaternion from two unit vectors
void quat_for_unit_vectors(vec4_t quat, const vec3_t from, const vec3_t to);
//! quaternion from axis and angle (radians)
void quat_for_axisangle(vec4_t quat, const vec3_t axis, double angle);
//! concatenates two rotations.. equivalent to m4x4_multiply_by_m4x4 .. postmultiply.. the right-hand side is the first rotation performed
void quat_multiply_by_quat(vec4_t quat, const vec4_t other);
//! negate a quaternion
void quat_conjugate(vec4_t quat);
//! normalise a quaternion
void quat_normalise(vec4_t quat);



/*!
\todo object/ray intersection functions should maybe return a point rather than a distance?
*/

/*!
aabb_t -  "axis-aligned" bounding box... 
  origin: centre of bounding box... 
  extents: +/- extents of box from origin... 
*/
typedef struct aabb_s
{
  vec3_t origin;
  vec3_t extents;
} aabb_t;

extern const aabb_t g_aabb_null;

/*!
bbox_t - oriented bounding box... 
  aabb: axis-aligned bounding box... 
  axes: orientation axes... 
*/
typedef struct bbox_s
{
  aabb_t aabb;
  vec3_t axes[3];
  vec_t radius;
} bbox_t;

/*!
ray_t - origin point and direction unit-vector
*/
typedef struct ray_s
{
  vec3_t origin;
  vec3_t direction;
} ray_t;

/*!
line_t - centre point and displacement of end point from centre
*/
typedef struct line_s
{
  vec3_t origin;
  vec3_t extents;
} line_t;


/*! Generate line from start/end points. */
void line_construct_for_vec3(line_t* line, const vec3_t start, const vec3_t end);
/*! Return 2 if line is behind plane, else return 1 if line intersects plane, else return 0. */
int line_test_plane(const line_t* line, const vec4_t plane);

/*! Generate AABB from min/max. */
void aabb_construct_for_vec3(aabb_t* aabb, const vec3_t min, const vec3_t max);
/*! Initialise AABB to negative size. */
void aabb_clear(aabb_t* aabb);

/*! Extend AABB to include point. */
void aabb_extend_by_point(aabb_t* aabb, const vec3_t point);
/*! Extend AABB to include aabb_src. */
void aabb_extend_by_aabb(aabb_t* aabb, const aabb_t* aabb_src);
/*! Extend AABB by +/- extension vector. */
void aabb_extend_by_vec3(aabb_t* aabb, vec3_t extension);

/*! Return 2 if point is inside, else 1 if point is on surface, else 0. */
int aabb_test_point(const aabb_t* aabb, const vec3_t point);
/*! Return 2 if aabb_src intersects, else 1 if aabb_src touches exactly, else 0. */
int aabb_test_aabb(const aabb_t* aabb, const aabb_t* aabb_src);
/*! Return 2 if aabb is behind plane, else 1 if aabb intersects plane, else 0. */
int aabb_test_plane(const aabb_t* aabb, const float* plane);
/*! Return 1 if aabb intersects ray, else 0... dist = closest intersection. */
int aabb_intersect_ray(const aabb_t* aabb, const ray_t* ray, vec3_t intersection);
/*! Return 1 if aabb intersects ray, else 0. Faster, but does not provide point of intersection */
int aabb_test_ray(const aabb_t* aabb, const ray_t* ray);

/*! Return 2 if oriented aabb is behind plane, else 1 if aabb intersects plane, else 0. */
int aabb_oriented_intersect_plane(const aabb_t* aabb, const m4x4_t transform, const vec_t* plane);

/*! Calculate the corners of the aabb. */
void aabb_corners(const aabb_t* aabb, vec3_t corners[8]);

/*! (deprecated) Generate AABB from oriented bounding box. */
void aabb_for_bbox(aabb_t* aabb, const bbox_t* bbox);
/*! (deprecated) Generate AABB from 2-dimensions of min/max, specified by axis. */
void aabb_for_area(aabb_t* aabb, vec3_t area_tl, vec3_t area_br, int axis);
/*! Generate AABB to contain src*  transform. NOTE: transform must be orthogonal */
void aabb_for_transformed_aabb(aabb_t* dst, const aabb_t* src, const m4x4_t transform);

/*! Update bounding-sphere radius. */
void bbox_update_radius(bbox_t* bbox);
/*! Generate oriented bounding box from AABB and transformation matrix. */
/*!\todo Remove need to specify eulerZYX/scale. */
void bbox_for_oriented_aabb(bbox_t* bbox, const aabb_t* aabb,
                    const m4x4_t matrix, const vec3_t eulerZYX, const vec3_t scale);
/*! Return 2 if bbox is behind plane, else return 1 if bbox intersects plane, else return 0. */
int bbox_intersect_plane(const bbox_t* bbox, const vec_t* plane);


/*! Generate a ray from an origin point and a direction unit-vector */
void ray_construct_for_vec3(ray_t* ray, const vec3_t origin, const vec3_t direction);
  
/*! Transform a ray */
void ray_transform(ray_t* ray, const m4x4_t matrix);

/*! distance from ray origin in ray direction to point. FLT_MAX if no intersection. */
vec_t ray_intersect_point(const ray_t* ray, const vec3_t point, vec_t epsilon, vec_t divergence);
/*! distance from ray origin in ray direction to triangle. FLT_MAX if no intersection. */
vec_t ray_intersect_triangle(const ray_t* ray, qboolean bCullBack, const vec3_t vert0, const vec3_t vert1, const vec3_t vert2);
/*! distance from ray origin in ray direction to plane. */
vec_t ray_intersect_plane(const ray_t* ray, const vec3_t normal, vec_t dist);


int plane_intersect_planes(const vec4_t plane1, const vec4_t plane2, const vec4_t plane3, vec3_t intersection);


#ifdef __cplusplus
}
#endif

#endif /* __MATHLIB__ */