math primitives More...

#include "mathlib.h"
#include "../common/common.h"
#include <algorithm>

Macros
#define	logf(x) ((float)log((double)(x)))

#define	RT2 0.70710678118654752440084436210485
	cos 45 degree More...

#define	DIRECTION_EAST 0

#define	DIRECTION_WEST 1

#define	DIRECTION_NORTH 2

#define	DIRECTION_SOUTH 3

#define	DIRECTION_NORTHEAST 4

#define	DIRECTION_SOUTHWEST 5

#define	DIRECTION_NORTHWEST 6

#define	DIRECTION_SOUTHEAST 7

Functions
int	AngleToDir (int angle)
	Returns the index of array directionAngles[DIRECTIONS] whose value is the closest to angle. More...

vec_t	Q_rint (const vec_t in)
	Round to nearest integer. More...

double	GetDistanceOnGlobe (const vec2_t pos1, const vec2_t pos2)
	Calculate distance on the geoscape. More...

vec_t	ColorNormalize (const vec3_t in, vec3_t out)

bool	VectorNearer (const vec3_t v1, const vec3_t v2, const vec3_t comp)
	Checks whether the given vector `v1` is closer to `comp` as the vector `v2`. More...

vec_t	VectorNormalize2 (const vec3_t v, vec3_t out)
	Calculated the normal vector for a given vec3_t. More...

void	VectorMA (const vec3_t veca, const float scale, const vec3_t vecb, vec3_t outVector)
	Sets vector_out (vc) to vevtor1 (va) + scale * vector2 (vb) More...

void	VectorClampMA (vec3_t veca, float scale, const vec3_t vecb, vec3_t vecc)

void	MatrixMultiply (const vec3_t a[3], const vec3_t b[3], vec3_t c[3])
	Multiply 33 matrix by 33 matrix. More...

void	GLMatrixAssemble (const vec3_t origin, const vec3_t angles, float *matrix)
	Builds an opengl translation and rotation matrix. More...

void	GLMatrixMultiply (const float a[16], const float b[16], float c[16])
	Multiply 44 matrix by 44 matrix. More...

void	GLVectorTransform (const float m[16], const vec4_t in, vec4_t out)
	Multiply 4*4 matrix by 4d vector. More...

void	GLPositionTransform (const float m[16], const vec3_t in, vec3_t out)
	Transform position (xyz) vector by OpenGL rules. More...

void	VectorRotate (vec3_t m[3], const vec3_t va, vec3_t vb)
	Rotate a vector with a rotation matrix. More...

int	VectorCompareEps (const vec3_t v1, const vec3_t v2, float epsilon)
	Compare two vectors that may have an epsilon difference but still be the same vectors. More...

vec_t	VectorLength (const vec3_t v)
	Calculate the length of a vector. More...

void	VectorMix (const vec3_t v1, const vec3_t v2, float mix, vec3_t out)
	Calculate a position on `v1` `v2` line. More...

void	VectorInverse (vec3_t v)
	Inverse a vector. More...

void	VectorMidpoint (const vec3_t point1, const vec3_t point2, vec3_t midpoint)
	Calculates the midpoint between two vectors. More...

float	VectorAngleBetween (const vec3_t vec1, const vec3_t vec2)
	Calculates the angle (in radians) between the two given vectors. More...

int	Q_log2 (int val)

float	frand (void)
	Return random values between 0 and 1. More...

float	crand (void)
	Return random values between -1 and 1. More...

void	gaussrand (float gauss1, float gauss2)
	generate two gaussian distributed random numbers with median at 0 and stdev of 1 More...

void	CalculateMinsMaxs (const vec3_t angles, const AABB &relBox, const vec3_t origin, AABB &absBox)
	Calculates the bounding box in absolute coordinates, also for rotating objects. WARNING: do not use this for angles other than 90, 180 or 270 !! More...

void	VectorCreateRotationMatrix (const vec3_t angles, vec3_t matrix[3])

void	VectorRotatePoint (vec3_t point, vec3_t matrix[3])

void	AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
	Create the rotation matrix in order to rotate something. More...

bool	FrustumVis (const vec3_t origin, int dir, const vec3_t point)
	Checks whether a point is visible from a given position. More...

static void	ProjectPointOnPlane (vec3_t dst, const vec3_t point, const vec3_t normal)
	Projects a point on a plane passing through the origin. More...

static float	Q_rsqrtApprox (const float number)

vec_t	VectorNormalize (vec3_t v)
	Calculate unit vector for a given vec3_t. More...

void	VectorNormalizeFast (vec3_t v)
	fast vector normalize routine that does not check to make sure that length != 0, nor does it return length More...

void	PerpendicularVector (vec3_t dst, const vec3_t src)
	Finds a vector perpendicular to the source vector. More...

void	CrossProduct (const vec3_t v1, const vec3_t v2, vec3_t cross)
	binary operation on vectors in a three-dimensional space More...

static void	R_ConcatRotations (float in1[3][3], float in2[3][3], float out[3][3])

void	RotatePointAroundVector (vec3_t dst, const vec3_t dir, const vec3_t point, float degrees)
	Rotate a point around a given vector. More...

void	PolarToVec (const vec2_t a, vec3_t v)
	Converts longitude and latitude to a 3D vector in Euclidean coordinates. More...

void	VecToPolar (const vec3_t v, vec2_t a)
	Converts vector coordinates into polar coordinates. More...

void	VecToAngles (const vec3_t value1, vec3_t angles)
	Converts a vector to an angle vector. More...

bool	Q_IsPowerOfTwo (int i)
	Checks whether i is power of two value. More...

float	LerpAngle (float a2, float a1, float frac)
	Returns the angle resulting from turning fraction * angle from angle1 to angle2. More...

float	AngleNormalize360 (float angle)
	returns angle normalized to the range [0 <= angle < 360] More...

float	AngleNormalize180 (float angle)
	returns angle normalized to the range [-180 < angle <= 180] More...

void	VectorCalcMinsMaxs (const vec3_t center, const vec3_t size, vec3_t mins, vec3_t maxs)
	Calculates a bounding box from a center and a size. More...

void	ClearBounds (vec3_t mins, vec3_t maxs)
	Sets mins and maxs to their starting points before using AddPointToBounds. More...

void	AddPointToBounds (const vec3_t v, vec3_t mins, vec3_t maxs)
	If the point is outside the box defined by mins and maxs, expand the box to accommodate it. Sets mins and maxs to their new values. More...

void	TangentVectors (const vec3_t normal, const vec3_t sdir, const vec3_t tdir, vec4_t tangent, vec3_t binormal)
	Projects the normalized directional vectors on to the normal's plane. The fourth component of the resulting tangent vector represents sidedness. More...

void	Orthogonalize (vec3_t out, const vec3_t in)
	Grahm-Schmidt orthogonalization. More...

void	MatrixTranspose (const vec3_t m[3], vec3_t t[3])
	Transposes `m` and stores the result in `t`. More...

bool	RayIntersectAABB (const vec3_t start, const vec3_t end, const AABB &aabb)

Variables
const vec2_t	vec2_origin = { 0, 0 }

const vec3_t	vec3_origin = { 0, 0, 0 }

const vec4_t	vec4_origin = { 0, 0, 0, 0 }

const pos3_t	pos3_origin = { 0, 0, 0 }

const vec4_t	dvecs [PATHFINDING_DIRECTIONS]

const float	dvecsn [CORE_DIRECTIONS][2] = { {1, 0}, {-1, 0}, {0, 1}, {0, -1}, {RT2, RT2}, {-RT2, -RT2}, {-RT2, RT2}, {RT2, -RT2} }

const float	directionAngles [CORE_DIRECTIONS] = { 0, 180.0f, 90.0f, 270.0f, 45.0f, 225.0f, 135.0f, 315.0f }

const byte	dvright [CORE_DIRECTIONS]

const byte	dvleft [CORE_DIRECTIONS]

Detailed Description

math primitives

Definition in file mathlib.cpp.

Macro Definition Documentation

#define DIRECTION_EAST 0

Definition at line 107 of file mathlib.cpp.

#define DIRECTION_NORTH 2

Definition at line 109 of file mathlib.cpp.

#define DIRECTION_NORTHEAST 4

Definition at line 111 of file mathlib.cpp.

#define DIRECTION_NORTHWEST 6

Definition at line 113 of file mathlib.cpp.

#define DIRECTION_SOUTH 3

Definition at line 110 of file mathlib.cpp.

#define DIRECTION_SOUTHEAST 7

Definition at line 114 of file mathlib.cpp.

#define DIRECTION_SOUTHWEST 5

Definition at line 112 of file mathlib.cpp.

#define DIRECTION_WEST 1

Definition at line 108 of file mathlib.cpp.

#define logf ( x ) ((float)log((double)(x)))

Definition at line 31 of file mathlib.cpp.

Referenced by gaussrand().

#define RT2 0.70710678118654752440084436210485

cos 45 degree

Definition at line 40 of file mathlib.cpp.

Function Documentation

void AddPointToBounds	(	const vec3_t	v,
		vec3_t	mins,
		vec3_t	maxs
	)

If the point is outside the box defined by mins and maxs, expand the box to accommodate it. Sets mins and maxs to their new values.

Definition at line 1042 of file mathlib.cpp.

References i.

Referenced by SL_BSPSlice(), and WindingBounds().

float AngleNormalize180 ( float angle )

returns angle normalized to the range [-180 < angle <= 180]

Parameters

[in] angle Angle

Definition at line 1004 of file mathlib.cpp.

References AngleNormalize360().

float AngleNormalize360 ( float angle )

returns angle normalized to the range [0 <= angle < 360]

Parameters

[in] angle Angle

See also: VecToAngles

Definition at line 995 of file mathlib.cpp.

References int().

Referenced by AngleNormalize180().

int AngleToDir ( int angle )

Returns the index of array directionAngles[DIRECTIONS] whose value is the closest to angle.

Note: This function allows to know the closest multiple of 45 degree of angle.

Parameters

[in] angle The angle (in degrees) which is tested.

Returns: Corresponding index of array directionAngles[DIRECTIONS].

Definition at line 130 of file mathlib.cpp.

References Com_Printf(), and CORE_DIRECTIONS.

Referenced by AIL_positionwander(), G_Actor2x2Spawn(), G_ActorSpawn(), G_ClientShoot(), G_GetImpactDirection(), G_InitCamera(), and fireDef_s::getShotOrigin().

void AngleVectors	(	const vec3_t	angles,
		vec3_t	forward,
		vec3_t	right,
		vec3_t	up
	)

Create the rotation matrix in order to rotate something.

Parameters

[in]	angles	Contains the three angles PITCH, YAW and ROLL (in degree) of rotation around idle frame ({0, 1, 0}, {0, 0, 1} ,{1, 0, 0}) (in this order!)
[out]	forward	return the first line of the rotation matrix.
[out]	right	return the second line of the rotation matrix.
[out]	up	return the third line of the rotation matrix.

Note: This matrix is the product of the 3 matrixes R*P*Y (in this order!), where R is the rotation matrix around {1, 0, 0} only (angle of rotation is angle[2]), P is the rotation matrix around {0, 1, 0} only, and Y is the rotation matrix around {0, 0, 1}.; Due to z convention for Quake, the z-axis is inverted. Therefore, if you want to use this function in a direct frame, don't forget to inverse the second line (right). Exemple : to rotate v2 into v : AngleVectors(angles, m[0], m[1], m[2]); VectorInverse(m[1]); VectorRotate(m, v2, v);

See also: RotatePointAroundVector : If you need rather "one rotation around a vector you choose" instead of "3 rotations around 3 vectors you don't choose".

Definition at line 631 of file mathlib.cpp.

References PITCH, ROLL, torad, and YAW.

Referenced by BuildLights(), CL_CameraMove(), CM_HintedTransformedBoxTrace(), Door_SlidingUse(), G_ShootGrenade(), G_ShootSingle(), GLMatrixAssemble(), LET_SlideDoor(), R_CullMeshModel(), R_GetSpriteVectors(), R_SetupFrustum(), SEQ_SetCamera(), SP_worldspawn(), U2M_SetDefaultConfigValues(), and VectorCreateRotationMatrix().

void CalculateMinsMaxs	(	const vec3_t	angles,
		const AABB &	relBox,
		const vec3_t	origin,
		AABB &	absBox
	)

Calculates the bounding box in absolute coordinates, also for rotating objects. WARNING: do not use this for angles other than 90, 180 or 270 !!

Definition at line 546 of file mathlib.cpp.

References AABB::getCenter(), m, AABB::maxs, AABB::set(), AABB::shift(), VectorAdd, VectorCreateRotationMatrix(), VectorNotEmpty, VectorRotate(), and VectorSubtract.

Referenced by CM_GetInlineModelAABB(), Grid_RecalcRouting(), LE_AddEdictHighlight(), and SV_LinkEdict().

void ClearBounds	(	vec3_t	mins,
		vec3_t	maxs
	)

Sets mins and maxs to their starting points before using AddPointToBounds.

See also: AddPointToBounds

Definition at line 1032 of file mathlib.cpp.

Referenced by WindingBounds().

vec_t ColorNormalize	(	const vec3_t	in,
		vec3_t	out
	)

Definition at line 190 of file mathlib.cpp.

References EQUAL, f, VectorClear, and VectorScale.

Referenced by BuildLights(), SP_worldspawn(), and U2M_SetDefaultConfigValues().

float crand ( void )

Return random values between -1 and 1.

See also: frand; gaussrand

Definition at line 517 of file mathlib.cpp.

Referenced by AI_HideNeeded(), AIR_PilotSurvivedCrash(), CL_ParticleFunction(), G_ClientShoot(), G_ShootSingle(), gaussrand(), LE_AddGrenade(), and Weather::update().

void CrossProduct	(	const vec3_t	v1,
		const vec3_t	v2,
		vec3_t	cross
	)

binary operation on vectors in a three-dimensional space

Note: also known as the vector product or outer product; It differs from the dot product in that it results in a vector rather than in a scalar; Its main use lies in the fact that the cross product of two vectors is orthogonal to both of them.

Parameters

[in]	v1	directional vector
[in]	v2	directional vector
[out]	cross	output

Note: you have the right and forward values of an axis, their cross product will; be a properly oriented "up" direction

See also: DotProduct; VectorNormalize2

Definition at line 820 of file mathlib.cpp.

Referenced by AddBrushBevels(), AIR_GetDestinationWhilePursuing(), BaseWindingForPlane(), Check_EdgeEdgeIntersection(), GEO_AngleOfPath2D(), GEO_AngleOfPath3D(), GEO_CalcLine(), PlaneFromPoints(), R_GenerateGrass(), R_GetSpriteVectors(), R_ModCalcNormalsAndTangents(), R_ModCalcUniqueNormalsAndTangents(), R_PlantGrass(), RotatePointAroundVector(), TangentVectors(), TryMergeWinding(), and WindingArea().

float frand ( void )

Return random values between 0 and 1.

See also: crand; gaussrand

Definition at line 506 of file mathlib.cpp.

Referenced by AI_CheckUsingDoor(), AI_CivilianCalcActionScore(), AI_FighterCalcActionScore(), AI_FindBestFiredef(), AI_InitPlayer(), AI_PanicCalcActionScore(), AI_SetStats(), AIRFIGHT_BaseShoot(), AIRFIGHT_ExecuteActions(), AIRFIGHT_InstallationShoot(), AIRFIGHT_MissTarget(), AM_CheckFire(), AM_FillTeamFromBattleParams(), AM_UpdateSurivorsAfterBattle(), B_BuildFromTemplate(), B_Destroy_AntimaterStorage_f(), Weather::changeTo(), CHRSH_CharGenAbilitySkills(), CL_AddMapParticle(), CL_ParticleFunction(), CL_RunMapParticles(), CP_BaseAttackChooseBase(), CP_CheckNewMissionDetectedOnGeoscape(), CP_ChooseNation(), CP_CreateBattleParameters(), CP_GetRandomPosOnGeoscape(), CP_GetRandomPosOnGeoscapeWithParameters(), CP_InterceptChooseInstallation(), CP_InterceptMissionSet(), CP_MissionChooseUFO(), CP_ReconMissionChoose(), CP_ReconMissionNewGroundMission(), CP_SelectNewMissionType(), CP_SpawnNewMissions(), Date_Random(), E_InitialEmployees(), InventoryInterface::EquipActorNormal(), G_GetStartingTeam(), G_MoraleBehaviour(), G_MoraleStopPanic(), G_MoraleStopRage(), BodyData::getHitBodyPart(), BodyData::getRandomBodyPart(), TerrainDefs::getWeather(), ReactionFire::isEnemy(), MIS_IsSpawnedFromGround(), R_AddClump(), R_GenerateGrass(), R_PlantGrass(), RADAR_CheckUFOSensored(), Weather::setDefaults(), Weather::update(), and UR_DialogInitSell_f().

bool FrustumVis	(	const vec3_t	origin,
		int	dir,
		const vec3_t	point
	)

Checks whether a point is visible from a given position.

Parameters

[in]	origin	Origin to test from
[in]	dir	Direction to test into
[in]	point	This is the point we want to check the visibility for

Definition at line 666 of file mathlib.cpp.

References DIRECTIONS, dvecsn, and VectorNormalizeFast().

Referenced by G_FrustumVis().

void gaussrand	(	float *	gauss1,
		float *	gauss2
	)

generate two gaussian distributed random numbers with median at 0 and stdev of 1

Parameters

[out]	gauss1	First gaussian distributed random number
[out]	gauss2	Second gaussian distributed random number

See also: crand; frand

Definition at line 529 of file mathlib.cpp.

References crand(), and logf.

Referenced by G_ShootGrenade(), G_ShootSingle(), and UFO_SetRandomDestAround().

double GetDistanceOnGlobe	(	const vec2_t	pos1,
		const vec2_t	pos2
	)

Calculate distance on the geoscape.

Parameters

[in]	pos1	Position at the start.
[in]	pos2	Position at the end.

Returns: Distance from pos1 to pos2.

Note: distance is an angle! This is the angle (in degrees) between the 2 vectors starting at earth's center and ending at pos1 or pos2. (if you prefer distance, this is also the distance on a globe of radius 180 / pi = 57)

Definition at line 171 of file mathlib.cpp.

References todeg, and torad.

Referenced by AB_SetAlienBasePosition(), AB_UpdateStealthForOneBase(), AIR_AircraftHasEnoughFuel(), AIR_AircraftHasEnoughFuelOneWay(), AIR_GetDestinationWhilePursuing(), AIR_SortByDistance(), AIRFIGHT_BaseShoot(), AIRFIGHT_ChooseWeapon(), AIRFIGHT_InstallationShoot(), AIRFIGHT_MissTarget(), AIRFIGHT_ProjectileReachedTarget(), BDEF_AutoTarget(), CL_DisplayPopupInterceptMission(), CP_DrawXVIOverlayPixel(), GEO_GetAircraftText(), GEO_PositionCloseToBase(), PR_CalculateTotalFrames(), RADAR_AddDetectedUFOToEveryRadar(), RADAR_CheckRadarSensored(), RADAR_CheckUFOSensored(), TR_TransferStart(), UFO_CampaignCheckEvents(), UFO_SearchAircraftTarget(), UFO_UpdateAlienInterestForOneBase(), UFO_UpdateAlienInterestForOneInstallation(), and US_GetClosestStoredUFO().

void GLMatrixAssemble	(	const vec3_t	origin,
		const vec3_t	angles,
		float *	matrix
	)

Builds an opengl translation and rotation matrix.

Parameters

origin	The translation vector
angles	The angle vector that is used to calculate the rotation part of the matrix
matrix	The resulting matrix, must be of dimension 16

Definition at line 325 of file mathlib.cpp.

References AngleVectors(), and VectorInverse().

Referenced by CL_ActorGetMuzzle(), and R_CalcTransform().

void GLMatrixMultiply	(	const float	a[16],
		const float	b[16],
		float	c[16]
	)

Multiply 4*4 matrix by 4*4 matrix.

See also: MatrixMultiply

Parameters

[out]	c	The result of the multiplication matrix = `a` * `b` (not the same as `b` * `a` as matrix multiplication is not commutative)
[in]	a	First matrix.
[in]	b	Second matrix.

Definition at line 350 of file mathlib.cpp.

References i.

Referenced by CL_ActorGetMuzzle(), and R_CalcTransform().

void GLPositionTransform	(	const float	m[16],
		const vec3_t	in,
		vec3_t	out
	)

Transform position (xyz) vector by OpenGL rules.

Note: Equivalent to calling GLVectorTransfrom with (x y z 1) vector and taking first 3 components of result

Parameters

[out]	out	the result of the multiplication = `m` * `in`.
[in]	m	4*4 matrix
[in]	in	3d vector.

See also: GLVectorTransform

Definition at line 380 of file mathlib.cpp.

References i.

Referenced by R_EnableModelLights(), and R_EnableWorldLights().

void GLVectorTransform	(	const float	m[16],
		const vec4_t	in,
		vec4_t	out
	)

Multiply 4*4 matrix by 4d vector.

Parameters

[out]	out	the result of the multiplication = `m` * `in`.
[in]	m	4*4 matrix
[in]	in	4d vector.

See also: VectorRotate

Definition at line 366 of file mathlib.cpp.

References i.

Referenced by R_InitModelProgram(), and R_UseModelProgram().

float LerpAngle	(	float	a2,
		float	a1,
		float	frac
	)

Returns the angle resulting from turning fraction * angle from angle1 to angle2.

Definition at line 981 of file mathlib.cpp.

void MatrixMultiply	(	const vec3_t	a[3],
		const vec3_t	b[3],
		vec3_t	c[3]
	)

Multiply 3*3 matrix by 3*3 matrix.

Parameters

[out]	c	The result of the multiplication matrix = `a` * `b` (not the same as `b` * `a` !)
[in]	a	First matrix.
[in]	b	Second matrix.

See also: GLMatrixMultiply

Definition at line 304 of file mathlib.cpp.

void MatrixTranspose	(	const vec3_t	m[3],
		vec3_t	t[3]
	)

Transposes m and stores the result in t.

Parameters

[in]	m	The matrix to transpose
[out]	t	The transposed matrix

Definition at line 1101 of file mathlib.cpp.

References i.

void Orthogonalize	(	vec3_t	out,
		const vec3_t	in
	)

Grahm-Schmidt orthogonalization.

Parameters

[out]	out	Orthogonalized vector
[in]	in	Reference vector

Definition at line 1088 of file mathlib.cpp.

References DotProduct, VectorMul, VectorNormalizeFast(), and VectorSubtract.

Referenced by R_ModCalcNormalsAndTangents(), and R_ModCalcUniqueNormalsAndTangents().

void PerpendicularVector	(	vec3_t	dst,
		const vec3_t	src
	)

Finds a vector perpendicular to the source vector.

Parameters

[in]	src	The source vector
[out]	dst	A vector perpendicular to `src`

Note: dst is a perpendicular vector to src such that it is the closest to one of the three axis: {1,0,0}, {0,1,0} and {0,0,1} (chosen in that order in case of equality)

Precondition: non-nullptr pointers and src is normalized

See also: ProjectPointOnPlane

Definition at line 780 of file mathlib.cpp.

References i, ProjectPointOnPlane(), and VectorNormalizeFast().

Referenced by GEO_MapDrawEquidistantPoints(), and RotatePointAroundVector().

void PolarToVec	(	const vec2_t	a,
		vec3_t	v
	)

Converts longitude and latitude to a 3D vector in Euclidean coordinates.

Parameters

[in]	a	The longitude and latitude in a 2D vector
[out]	v	The resulting normal 3D vector

See also: VecToPolar

Definition at line 910 of file mathlib.cpp.

References torad, and VectorSet.

Referenced by AIR_GetDestinationWhilePursuing(), AIRFIGHT_GetNextPointInPathFromVector(), GEO_3DMapToScreen(), GEO_AngleOfPath2D(), GEO_AngleOfPath3D(), GEO_CalcLine(), GEO_MapDrawEquidistantPoints(), and R_PlantGrass().

static void ProjectPointOnPlane	(	vec3_t	dst,
		const vec3_t	point,
		const vec3_t	normal
	)

inlinestatic

Projects a point on a plane passing through the origin.

Parameters

[in]	point	Coordinates of the point to project
[in]	normal	The normal vector of the plane
[out]	dst	Coordinates of the projection on the plane

Precondition: Non-null pointers and a normalized normal vector.

< closest distance from the point to the plane

Definition at line 692 of file mathlib.cpp.

References DotProduct.

Referenced by PerpendicularVector().

bool Q_IsPowerOfTwo ( int i )

Checks whether i is power of two value.

Definition at line 972 of file mathlib.cpp.

Referenced by CIN_ROQ_DecodeInfo(), and R_CvarCheckMaxLightmap().

int Q_log2 ( int val )

Definition at line 492 of file mathlib.cpp.

vec_t Q_rint ( const vec_t in )

Round to nearest integer.

Definition at line 156 of file mathlib.cpp.

Referenced by GetVertexnum(), and SnapPlane().

static float Q_rsqrtApprox ( const float number )

inlinestatic

Definition at line 716 of file mathlib.cpp.

References f, and i.

Referenced by VectorNormalizeFast().

static void R_ConcatRotations	(	float	in1[3][3],
		float	in2[3][3],
		float	out[3][3]
	)

inlinestatic

Definition at line 827 of file mathlib.cpp.

Referenced by RotatePointAroundVector().

bool RayIntersectAABB	(	const vec3_t	start,
		const vec3_t	end,
		const AABB &	aabb
	)

Definition at line 1110 of file mathlib.cpp.

References f, i, AABB::maxs, AABB::mins, and VectorSubtract.

Referenced by G_SmokeVis(), and G_TeamPointVis().

void RotatePointAroundVector	(	vec3_t	dst,
		const vec3_t	dir,
		const vec3_t	point,
		float	degrees
	)

Rotate a point around a given vector.

Parameters

[in]	dir	The vector around which to rotate
[in]	point	The point to be rotated
[in]	degrees	How many degrees to rotate the point by
[out]	dst	The point after rotation

Note: Warning: dst must be different from point (otherwise the result has no meaning)

Precondition: dir must be normalized

Definition at line 849 of file mathlib.cpp.

References CrossProduct(), DotProduct, i, m, OBJZERO, PerpendicularVector(), R_ConcatRotations(), and torad.

Referenced by AIR_GetDestinationWhilePursuing(), AIRFIGHT_GetNextPointInPathFromVector(), GEO_3DMapToScreen(), GEO_AngleOfPath2D(), GEO_AngleOfPath3D(), GEO_MapDrawEquidistantPoints(), R_PlantGrass(), R_RotateCelestialBody(), R_SetupFrustum(), and uiGeoscapeNode::screenTo3DMap().

void TangentVectors	(	const vec3_t	normal,
		const vec3_t	sdir,
		const vec3_t	tdir,
		vec4_t	tangent,
		vec3_t	binormal
	)

Projects the normalized directional vectors on to the normal's plane. The fourth component of the resulting tangent vector represents sidedness.

Definition at line 1057 of file mathlib.cpp.

References CrossProduct(), DotProduct, VectorCopy, VectorMA(), VectorNormalizeFast(), and VectorScale.

Referenced by BuildFacelights(), and R_LoadBspVertexArrays().

void VecToAngles	(	const vec3_t	value1,
		vec3_t	angles
	)

Converts a vector to an angle vector.

Parameters

[in]	value1
[in]	angles	Target vector for pitch, yaw, roll

See also: anglemod

Definition at line 934 of file mathlib.cpp.

References EQUAL, f, PITCH, ROLL, todeg, Vector2Empty, and YAW.

Referenced by G_ShootGrenade(), G_ShootSingle(), LE_AddProjectile(), and LET_Projectile().

void VecToPolar	(	const vec3_t	v,
		vec2_t	a
	)

Converts vector coordinates into polar coordinates.

See also: PolarToVec

Definition at line 922 of file mathlib.cpp.

References todeg.

Referenced by AIR_GetDestinationWhilePursuing(), AIRFIGHT_GetNextPointInPathFromVector(), GEO_CalcLine(), GEO_MapDrawEquidistantPoints(), and uiGeoscapeNode::screenTo3DMap().

float VectorAngleBetween	(	const vec3_t	vec1,
		const vec3_t	vec2
	)

Calculates the angle (in radians) between the two given vectors.

Note: Both vectors must be normalized.

Returns: the angle in radians.

Definition at line 484 of file mathlib.cpp.

References DotProduct.

Referenced by G_GetImpactDirection().

void VectorCalcMinsMaxs	(	const vec3_t	center,
		const vec3_t	size,
		vec3_t	mins,
		vec3_t	maxs
	)

Calculates a bounding box from a center and a size.

Parameters

[in]	center	The center vector
[in]	size	The size vector to calculate the bbox
[out]	mins	The lower end of the bounding box
[out]	maxs	The upper end of the bounding box

Definition at line 1019 of file mathlib.cpp.

References i, and length.

void VectorClampMA	(	vec3_t	veca,
		float	scale,
		const vec3_t	vecb,
		vec3_t	vecc
	)

Definition at line 268 of file mathlib.cpp.

References f, i, and VectorMA().

int VectorCompareEps	(	const vec3_t	v1,
		const vec3_t	v2,
		float	epsilon
	)

Compare two vectors that may have an epsilon difference but still be the same vectors.

Parameters

[in]	v1	vector to compare with v2
[in]	v2	vector to compare with v1
[in]	epsilon	The epsilon the vectors may differ to still be the same

Returns: 1 if the 2 vectors are the same (less than epsilon difference).

Note: This is not an exact calculation (should use a sqrt). Use this function only if you want to know if both vectors are the same with a precison that is roughly epsilon (the difference should be lower than sqrt(3) * epsilon).

Definition at line 413 of file mathlib.cpp.

References VectorSubtract.

Referenced by CL_CameraRoute(), CP_InterceptAttackInstallation(), CP_InterceptMissionLeave(), PTL_Trace(), TR_TestLineDM(), and TR_TileTestLineDM().

void VectorCreateRotationMatrix	(	const vec3_t	angles,
		vec3_t	matrix[3]
	)

Parameters

angles	The angles to calulcate the rotation matrix for
matrix	The resulting rotation matrix. The `right` part of this matrix is inversed because of the coordinate system we are using internally.

See also: AnglesVectors; VectorRotatePoint

Definition at line 592 of file mathlib.cpp.

References AngleVectors(), and VectorInverse().

Referenced by CalculateMinsMaxs(), Grid_RecalcRouting(), and AABB::rotateAround().

void VectorInverse ( vec3_t v )

Inverse a vector.

Parameters

[in,out] v Vector to inverse. Output value is -v.

Definition at line 460 of file mathlib.cpp.

Referenced by GLMatrixAssemble(), R_PlantGrass(), and VectorCreateRotationMatrix().

vec_t VectorLength ( const vec3_t v )

Calculate the length of a vector.

Parameters

[in] v Vector to calculate the length of

See also: VectorNormalize

Returns: Vector length as vec_t

Definition at line 434 of file mathlib.cpp.

References DotProduct.

Referenced by BuildVertexNormals(), CalcLightinfoVectors(), Check_EdgeEdgeIntersection(), Check_EdgePlaneIntersection(), Check_SidesOverlap(), CL_CameraMove(), CL_CameraRoute(), CL_TargetingGrenade(), Com_GrenadeTarget(), CreateNewFloatPlane(), FixWinding(), G_FindRadius(), G_ShootGrenade(), G_ShotMorale(), GEO_AngleOfPath2D(), GEO_AngleOfPath3D(), GEO_StartCenter(), LE_AddProjectile(), LE_FindRadius(), R_CreateSurfaceFlare(), R_GenerateGrass(), R_GetLevelOfDetailForModel(), R_RadiusFromBounds(), R_UpdateLightList(), Weather::render(), S_LoopSample(), SampleNormal(), uiGeoscapeNode::smoothRotate(), TestEdge(), UI_GeoscapeNodeScroll_f(), VectorNearer(), WindingArea(), and WindingIsTiny().

void VectorMA	(	const vec3_t	veca,
		const float	scale,
		const vec3_t	vecb,
		vec3_t	outVector
	)

Sets vector_out (vc) to vevtor1 (va) + scale * vector2 (vb)

Parameters

[in]	veca	Position to start from
[in]	scale	Speed of the movement
[in]	vecb	Movement direction
[out]	outVector	Target vector

Definition at line 261 of file mathlib.cpp.

Referenced by BaseWindingForPlane(), BuildFacelights(), BuildPatch(), CalcLightinfoVectors(), CL_ActorVis(), CL_BattlescapeMouseDragging(), CL_CameraMove(), CL_GetWorldCoordsUnderMouse(), CL_ParticleRun2(), CL_TargetingStraight(), FinishSubdividePatch(), G_ActorVis(), G_ClientShoot(), G_ShootGrenade(), G_ShootSingle(), G_SplashDamage(), GatherSampleLight(), GatherSampleSunlight(), LE_AddProjectile(), LET_PathMove(), NudgeSamplePosition(), R_CreateSurfaceFlare(), R_DrawAliasTags(), R_DrawBspNormals(), R_DrawSprite(), R_GenerateGrass(), R_ModLoadAliasMD2MeshIndexed(), R_ModLoadAliasMD2MeshUnindexed(), R_PlantGrass(), R_UpdateLightList(), SEQ_Render3D(), SEQ_SetCamera(), SV_ModLoadAliasMD2Model(), TangentVectors(), TestEdge(), UI_DrawModelNode(), and VectorClampMA().

void VectorMidpoint	(	const vec3_t	point1,
		const vec3_t	point2,
		vec3_t	midpoint
	)

Calculates the midpoint between two vectors.

Parameters

[in]	point1	vector of first point.
[in]	point2	vector of second point.
[out]	midpoint	calculated midpoint vector.

Definition at line 473 of file mathlib.cpp.

References f, VectorAdd, and VectorScale.

void VectorMix	(	const vec3_t	v1,
		const vec3_t	v2,
		float	mix,
		vec3_t	out
	)

Calculate a position on v1 v2 line.

Parameters

[in]	v1	First point of the line.
[in]	v2	Second point of the line.
[in]	mix	Position on the line. If 0 < `mix` < 1, `out` is between `v1` and `v2` . if `mix` < 0, `out` is outside `v1` and `v2` , on `v1` side.
[out]	out	The resulting point

Definition at line 447 of file mathlib.cpp.

Referenced by FinalLightFace(), GatherSampleLight(), GatherSampleSunlight(), and S_LoopSample().

bool VectorNearer	(	const vec3_t	v1,
		const vec3_t	v2,
		const vec3_t	comp
	)

Checks whether the given vector v1 is closer to comp as the vector v2.

Parameters

[in]	v1	Vector to check whether it's closer to `comp` as `v2`
[in]	v2	Vector to check against
[in]	comp	The vector to check the distance from

Returns: Returns true if v1 is closer to comp as v2

Definition at line 219 of file mathlib.cpp.

References VectorLength(), and VectorSubtract.

Referenced by TR_TestLineDist_r(), TR_TestLineDM(), and TR_TileTestLineDM().

vec_t VectorNormalize ( vec3_t v )

Calculate unit vector for a given vec3_t.

Parameters

[in] v Vector to normalize

See also: VectorNormalize2

Returns: vector length as vec_t

Definition at line 745 of file mathlib.cpp.

References DotProduct, and length.

Referenced by AddBrushBevels(), AIR_GetDestinationWhilePursuing(), BaseWindingForPlane(), BuildFacelights(), BuildLights(), BuildVertexNormals(), CalcLightinfoVectors(), Check_EdgeEdgeIntersection(), CL_ActorVis(), CL_CameraMove(), CL_CameraRoute(), CL_TargetingStraight(), FixFaceEdges(), G_GetImpactDirection(), GatherSampleLight(), GEO_AngleOfPath2D(), GEO_AngleOfPath3D(), GEO_CalcLine(), NudgeSamplePosition(), PlaneFromPoints(), R_DrawFlareSurfaces(), RemoveColinearPoints(), S_SpatializeChannel(), uiGeoscapeNode::screenTo3DMap(), SL_SliceTheWorld(), SubdivideFace(), and TryMergeWinding().

vec_t VectorNormalize2	(	const vec3_t	v,
		vec3_t	out
	)

Calculated the normal vector for a given vec3_t.

Parameters

[in]	v	Vector to normalize
[out]	out	The normalized vector

See also: VectorNormalize

Returns: vector length as vec_t

See also: CrossProduct

Todo:

Definition at line 237 of file mathlib.cpp.

References DotProduct, EQUAL, f, and length.

Referenced by CL_CameraMove(), and R_SphereGenerate().

void VectorNormalizeFast ( vec3_t v )

fast vector normalize routine that does not check to make sure that length != 0, nor does it return length

Definition at line 762 of file mathlib.cpp.

References DotProduct, and Q_rsqrtApprox().

Referenced by AI_CheckFF(), AI_FindHerdLocation(), Com_GrenadeTarget(), FrustumVis(), G_ActorVis(), G_ShootSingle(), Orthogonalize(), PerpendicularVector(), R_DrawSprite(), R_GetSpriteVectors(), R_InterpolateTransform(), R_ModCalcNormalsAndTangents(), R_ModCalcUniqueNormalsAndTangents(), R_PlantGrass(), R_StageTexCoord(), and TangentVectors().

void VectorRotate	(	vec3_t	m[3],
		const vec3_t	va,
		vec3_t	vb
	)

Rotate a vector with a rotation matrix.

Parameters

[out]	vb	The result of multiplication (ie vector `va` after rotation).
[in]	m	The 3*3 matrix (rotation matrix in case of a rotation).
[in]	va	The vector that should be multiplied (ie rotated in case of rotation).

Note: Basically, this is just the multiplication of m * va: this is the same than GLVectorTransform in 3D. This can be used for other applications than rotation.

See also: GLVectorTransform

Definition at line 395 of file mathlib.cpp.

Referenced by CalculateMinsMaxs(), Grid_RecalcRouting(), R_PlantGrass(), and AABB::rotateAround().

void VectorRotatePoint	(	vec3_t	point,
		vec3_t	matrix[3]
	)

Parameters

[out]	point	The vector to rotate around and the location of the rotated vector
[in]	matrix	The input rotation matrix

See also: VectorCreateRotationMatrix

Definition at line 603 of file mathlib.cpp.

References DotProduct, and VectorCopy.

Variable Documentation

const float directionAngles[CORE_DIRECTIONS] = { 0, 180.0f, 90.0f, 270.0f, 45.0f, 225.0f, 135.0f, 315.0f }

Note: if you change directionAngles[PATHFINDING_DIRECTIONS], you must also change function AngleToDV

Definition at line 105 of file mathlib.cpp.

Referenced by CL_ActorAppear(), CL_ActorDoTurn(), CL_CameraAppear(), G_ActorDoTurn(), LE_DoPathMove(), and UI_RadarNodeDrawActor().

const vec4_t dvecs[PATHFINDING_DIRECTIONS]

Note: DIRECTIONS straight 0 = x+1, y 1 = x-1, y 2 = x , y+1 3 = x , y-1 diagonal 4 = x+1, y+1 5 = x-1, y-1 6 = x-1, y+1 7 = x+1, y-1; (change in x, change in y, change in z, change in height status)

Definition at line 58 of file mathlib.cpp.

Referenced by Step::calcNewPos(), CMod_RerouteMap(), G_GetImpactDirection(), fireDef_s::getShotOrigin(), and RT_UpdateConnectionColumn().

const float dvecsn[CORE_DIRECTIONS][2] = { {1, 0}, {-1, 0}, {0, 1}, {0, -1}, {RT2, RT2}, {-RT2, -RT2}, {-RT2, RT2}, {RT2, -RT2} }

Definition at line 102 of file mathlib.cpp.

Referenced by FrustumVis().

const byte dvleft[CORE_DIRECTIONS]

Initial value:

= { DIRECTION_NORTHEAST, DIRECTION_SOUTHWEST,
        DIRECTION_NORTHWEST, DIRECTION_SOUTHEAST, DIRECTION_NORTH,
        DIRECTION_SOUTH, DIRECTION_WEST, DIRECTION_EAST }

Definition at line 119 of file mathlib.cpp.

Referenced by AIL_positionwander(), and G_ActorDoTurn().

const byte dvright[CORE_DIRECTIONS]

Initial value:

= { DIRECTION_SOUTHEAST,
        DIRECTION_NORTHWEST, DIRECTION_NORTHEAST, DIRECTION_SOUTHWEST,
        DIRECTION_EAST, DIRECTION_WEST, DIRECTION_NORTH, DIRECTION_SOUTH }

Definition at line 116 of file mathlib.cpp.

Referenced by AIL_positionwander(), and G_ActorDoTurn().

const pos3_t pos3_origin = { 0, 0, 0 }

Definition at line 37 of file mathlib.cpp.

Referenced by AiAreaSearch::AiAreaSearch().

const vec2_t vec2_origin = { 0, 0 }

Definition at line 34 of file mathlib.cpp.

Referenced by GEO_GetGeoscapeAngle().

const vec3_t vec3_origin = { 0, 0, 0 }

const vec4_t vec4_origin = { 0, 0, 0, 0 }

Definition at line 36 of file mathlib.cpp.

Referenced by R_DrawModelDirect(), and R_DrawModelParticle().

Macros

Functions

Variables

Detailed Description

Macro Definition Documentation

Function Documentation

Variable Documentation