/* 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 #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__ */