mathlib.c File Reference

math primitives More...

#include "../common/common.h"

Include dependency graph for mathlib.c:

Defines
#define	logf(x) ((float)log((double)(x)))
#define	RT2 0.70710678118654752440084436210485
	cos 45 degree
Functions
int	AngleToDir (int angle)
	Returns the indice of array directionAngles[DIRECTIONS] whose value is the closest to angle.
vec_t	Q_rint (const vec_t in)
	Round to nearest integer.
float	GetDistanceOnGlobe (const vec2_t pos1, const vec2_t pos2)
	Calculate distance on the geoscape.
vec_t	ColorNormalize (const vec3_t in, vec3_t out)
qboolean	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`.
vec_t	VectorNormalize2 (const vec3_t v, vec3_t out)
	Calculated the normal vector for a given vec3_t.
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).
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.
void	GLMatrixAssemble (const vec3_t origin, const vec3_t angles, float *matrix)
	Builds an opengl translation and rotation matrix.
void	GLMatrixMultiply (const float a[16], const float b[16], float c[16])
	Multiply 44 matrix by 44 matrix.
void	GLVectorTransform (const float m[16], const vec4_t in, vec4_t out)
	Multiply 4*4 matrix by 4d vector.
void	VectorRotate (vec3_t m[3], const vec3_t va, vec3_t vb)
	Rotate a vector with a rotation matrix.
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.
vec_t	VectorLength (const vec3_t v)
	Calculate the length of a vector.
void	VectorMix (const vec3_t v1, const vec3_t v2, float mix, vec3_t out)
	Calculate a position on `v1` `v2` line.
void	VectorInverse (vec3_t v)
	Inverse a vector.
void	VectorMidpoint (const vec3_t point1, const vec3_t point2, vec3_t midpoint)
	Calculates the midpoint between two vectors.
float	VectorAngleBetween (const vec3_t vec1, const vec3_t vec2)
	Calculates the angle (in radians) between the two given vectors.
int	Q_log2 (int val)
float	frand (void)
	Return random values between 0 and 1.
float	crand (void)
	Return random values between -1 and 1.
void	gaussrand (float gauss1, float gauss2)
	generate two gaussian distributed random numbers with median at 0 and stdev of 1
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.
qboolean	FrustumVis (const vec3_t origin, int dir, const vec3_t point)
	Checks whether a point is visible from a given position.
static void	ProjectPointOnPlane (vec3_t dst, const vec3_t point, const vec3_t normal)
	Projects a point on a plane passing through the origin.
vec_t	VectorNormalize (vec3_t v)
	Calculate unit vector for a given vec3_t.
void	PerpendicularVector (vec3_t dst, const vec3_t src)
	Finds a vector perpendicular to the source vector.
void	CrossProduct (const vec3_t v1, const vec3_t v2, vec3_t cross)
	binary operation on vectors in a three-dimensional space
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.
void	Print3Vector (const vec3_t v)
	Print a 3D vector.
void	Print2Vector (const vec2_t v)
	Print a 2D vector.
void	PolarToVec (const vec2_t a, vec3_t v)
	Converts longitude and latitude to a 3D vector in Euclidean coordinates.
void	VecToPolar (const vec3_t v, vec2_t a)
	Converts vector coordinates into polar coordinates.
void	VecToAngles (const vec3_t value1, vec3_t angles)
	Converts a vector to an angle vector.
qboolean	Q_IsPowerOfTwo (int i)
	Checks whether i is power of two value.
float	LerpAngle (float a2, float a1, float frac)
	Returns the angle resulting from turning fraction * angle from angle1 to angle2.
float	AngleNormalize360 (float angle)
	returns angle normalized to the range [0 <= angle < 360]
float	AngleNormalize180 (float angle)
	returns angle normalized to the range [-180 < angle <= 180]
void	VectorCenterFromMinsMaxs (const vec3_t mins, const vec3_t maxs, vec3_t center)
	Calculates the center of a bounding box.
void	ClearBounds (vec3_t mins, vec3_t maxs)
	Sets mins and maxs to their starting points before using AddPointToBounds.
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.
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.
void	Orthogonalize (vec3_t v1, const vec3_t v2)
	Grahm-Schmidt orthogonalization.
void	MatrixTranspose (const vec3_t m[3], vec3_t t[3])
	Transposes `m` and stores the result in `t`.
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 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] = { 7, 6, 4, 5, 0, 1, 2, 3 }
const byte	dvleft [CORE_DIRECTIONS] = { 4, 5, 6, 7, 2, 3, 1, 0 }

Detailed Description

math primitives

Definition in file mathlib.c.

Define Documentation

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

Definition at line 29 of file mathlib.c.

Referenced by gaussrand().

#define RT2 0.70710678118654752440084436210485

cos 45 degree

Definition at line 37 of file mathlib.c.

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 955 of file mathlib.c.

References i.

Referenced by BeginModel(), BoundBrush(), BrushBSP(), BuildNodeChildren(), CalcNodeBounds(), Check_MapSize(), LoadMapFile(), MakeBrushWindings(), MapBrushesBounds(), R_LoadObjModel(), R_ModLoadAliasMD2MeshIndexed(), R_ModLoadAliasMD2MeshUnindexed(), R_ModLoadAliasMD3Model(), SV_ModLoadAliasMD2Model(), and SV_ModLoadAliasMD3Model().

float AngleNormalize180 ( float angle )

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

Parameters:

[in] angle Angle

Definition at line 921 of file mathlib.c.

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 912 of file mathlib.c.

References int().

Referenced by AngleNormalize180().

int AngleToDir ( int angle )

Returns the indice 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 indice of array directionAngles[DIRECTIONS].

Definition at line 112 of file mathlib.c.

References Com_Printf(), and CORE_DIRECTIONS.

Referenced by G_Actor2x2Spawn(), G_ActorSpawn(), and G_ClientShoot().

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 562 of file mathlib.c.

References PITCH, ROLL, torad, and YAW.

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

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 945 of file mathlib.c.

Referenced by AllocTree(), BeginModel(), BoundBrush(), BuildNodeChildren(), CalcNodeBounds(), LoadMapFile(), MakeBrushWindings(), MapBrushesBounds(), ProcessWorldModel(), R_ModLoadAliasMD2Model(), R_ModLoadAliasMD3Model(), and SV_LoadModelMinsMaxs().

vec_t ColorNormalize	(	const vec3_t	in,
		vec3_t	out
	)

Definition at line 172 of file mathlib.c.

References VectorClear, and VectorScale.

Referenced by BuildLights(), and U2M_SetDefaultConfigValues().

float crand ( void )

Return random values between -1 and 1.

See also:: frand; gaussrand

Definition at line 488 of file mathlib.c.

Referenced by AI_HideNeeded(), CL_ParticleFunction(), G_ShootGrenade(), G_ShootSingle(), gaussrand(), and LE_AddGrenade().

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 719 of file mathlib.c.

Referenced by AddBrushBevels(), AIR_GetDestinationWhilePursuing(), BaseWindingForPlane(), Check_EdgeEdgeIntersection(), MAP_AngleOfPath2D(), MAP_AngleOfPath3D(), MAP_MapCalcLine(), PlaneFromPoints(), R_GetSpriteVectors(), R_ModCalcNormalsAndTangents(), R_ModCalcUniqueNormalsAndTangents(), RotatePointAroundVector(), TangentVectors(), TryMergeWinding(), and WindingArea().

float frand ( void )

Return random values between 0 and 1.

See also:: crand; gaussrand

Definition at line 477 of file mathlib.c.

Referenced by AI_CheckUsingDoor(), AI_CivilianCalcBestAction(), AI_InitPlayer(), AI_SearchBestTarget(), AIRFIGHT_BaseShoot(), AIRFIGHT_ExecuteActions(), AIRFIGHT_InstallationShoot(), AIRFIGHT_MissTarget(), B_BuildFromTemplate(), B_Destroy_AntimaterStorage_f(), CHRSH_CharGenAbilitySkills(), CL_AddMapParticle(), CL_GameAutoGo(), CL_ParticleFunction(), CL_RunMapParticles(), CP_BaseAttackChooseBase(), CP_CheckNewMissionDetectedOnGeoscape(), CP_ChooseNation(), CP_CreateBattleParameters(), CP_GetRandomPosOnGeoscape(), CP_GetRandomPosOnGeoscapeWithParameters(), CP_InterceptChooseInstallation(), CP_InterceptMissionAvailableUFOs(), CP_MissionChooseUFO(), CP_ReconMissionChoose(), CP_ReconMissionNewGroundMission(), CP_SelectNewMissionType(), CP_SpawnNewMissions(), Date_Random(), E_InitialEmployees(), G_GetStartingTeam(), G_MoraleBehaviour(), G_MoraleStopPanic(), G_MoraleStopRage(), G_ReactionFireIsPossible(), I_EquipActor(), RADAR_CheckUFOSensored(), SP_alien_start(), and UR_DialogInitSell_f().

qboolean 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 597 of file mathlib.c.

References byte, DIRECTIONS, dvecsn, qfalse, qtrue, and VectorNormalize().

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 500 of file mathlib.c.

References crand(), and logf.

Referenced by G_ShootSingle(), and UFO_SetRandomDestAround().

float 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 154 of file mathlib.c.

References todeg, and torad.

Referenced by AB_SetAlienBasePosition(), AB_UpdateStealthForOneBase(), AIR_AircraftHasEnoughFuel(), AIR_AircraftHasEnoughFuelOneWay(), AIR_GetDestinationWhilePursuing(), AIRFIGHT_BaseShoot(), AIRFIGHT_ChooseWeapon(), AIRFIGHT_InstallationShoot(), AIRFIGHT_MissTarget(), AIRFIGHT_ProjectileReachedTarget(), BDEF_AutoTarget(), CL_DisplayPopupInterceptMission(), CP_DrawXVIOverlayPixel(), MAP_GetAircraftText(), MAP_PositionCloseToBase(), PR_CalculateProductionPercentDone(), RADAR_AddDetectedUFOToEveryRadar(), RADAR_CheckRadarSensored(), RADAR_CheckUFOSensored(), TR_TransferAlienAfterMissionStart(), 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 307 of file mathlib.c.

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 332 of file mathlib.c.

References i.

Referenced by CL_ActorGetMuzzle(), and R_CalcTransform().

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 350 of file mathlib.c.

References i.

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

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

Definition at line 898 of file mathlib.c.

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 286 of file mathlib.c.

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 1017 of file mathlib.c.

References i.

void Orthogonalize	(	vec3_t	v1,
		const vec3_t	v2
	)

Grahm-Schmidt orthogonalization.

Parameters:

`[out]`	v1
`[in]`	v2

Definition at line 1004 of file mathlib.c.

References DotProduct, VectorMul, VectorNormalize(), 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-NULL pointers and src is normalized

See also:: ProjectPointOnPlane

Definition at line 680 of file mathlib.c.

References i, pos, ProjectPointOnPlane(), and VectorNormalize().

Referenced by MAP_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 827 of file mathlib.c.

References torad, and VectorSet.

Referenced by AIR_GetDestinationWhilePursuing(), AIRFIGHT_GetNextPointInPathFromVector(), MAP_3DMapToScreen(), MAP_AngleOfPath2D(), MAP_AngleOfPath3D(), MAP_MapCalcLine(), and MAP_MapDrawEquidistantPoints().

void Print2Vector ( const vec2_t v )

Print a 2D vector.

Parameters:

[in] v The vector to be printed

Definition at line 815 of file mathlib.c.

References Com_Printf().

void Print3Vector ( const vec3_t v )

Print a 3D vector.

Parameters:

[in] v The vector to be printed

Definition at line 806 of file mathlib.c.

References Com_Printf().

Referenced by Check_SidesOverlap().

static void ProjectPointOnPlane	(	vec3_t	dst,
		const vec3_t	point,
		const vec3_t	normal
	)			`[inline, static]`

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 623 of file mathlib.c.

References DotProduct.

Referenced by PerpendicularVector().

qboolean Q_IsPowerOfTwo ( int i )

Checks whether i is power of two value.

Definition at line 889 of file mathlib.c.

Referenced by CIN_ROQ_DecodeInfo(), and R_CvarCheckMaxLightmap().

int Q_log2 ( int val )

Definition at line 463 of file mathlib.c.

vec_t Q_rint ( const vec_t in )

Round to nearest integer.

Definition at line 138 of file mathlib.c.

Referenced by GetVertexnum(), and SnapPlane().

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

Definition at line 726 of file mathlib.c.

Referenced by RotatePointAroundVector().

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 748 of file mathlib.c.

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

Referenced by AIR_GetDestinationWhilePursuing(), AIRFIGHT_GetNextPointInPathFromVector(), MAP3D_ScreenToMap(), MAP_3DMapToScreen(), MAP_AngleOfPath2D(), MAP_AngleOfPath3D(), MAP_MapDrawEquidistantPoints(), R_SetupFrustum(), and RotateCelestialBody().

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 973 of file mathlib.c.

References CrossProduct(), DotProduct, VectorCopy, VectorMA(), VectorNormalize(), 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 851 of file mathlib.c.

References int(), PITCH, ROLL, todeg, 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 839 of file mathlib.c.

References todeg.

Referenced by AIR_GetDestinationWhilePursuing(), AIRFIGHT_GetNextPointInPathFromVector(), MAP3D_ScreenToMap(), MAP_MapCalcLine(), and MAP_MapDrawEquidistantPoints().

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 455 of file mathlib.c.

References DotProduct.

void VectorCenterFromMinsMaxs	(	const vec3_t	mins,
		const vec3_t	maxs,
		vec3_t	center
	)

Calculates the center of a bounding box.

Parameters:

`[in]`	mins	The lower end of the bounding box
`[in]`	maxs	The upper end of the bounding box
`[out]`	center	The target center vector calculated from `mins` and `maxs`

Definition at line 935 of file mathlib.c.

References VectorAdd, and VectorScale.

Referenced by CL_CenterCameraIntoMap_f(), CM_CalculateBoundingBox(), Destroy_Breakable(), G_BuildForbiddenListForEntity(), G_SplashDamage(), Grid_RecalcRouting(), ParseBrush(), R_ModelAutoScale(), R_SetSurfaceExtents(), SV_LinkEdict(), SV_StartSound(), and TR_BoxTrace().

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

Definition at line 250 of file mathlib.c.

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 385 of file mathlib.c.

References VectorSubtract.

Referenced by CP_InterceptAttackInstallation(), CP_InterceptMissionLeave(), MAP_MapCalcLine(), 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 523 of file mathlib.c.

References AngleVectors(), and VectorInverse().

Referenced by Grid_RecalcRouting(), R_DrawBrushModel(), and SV_LinkEdict().

void VectorInverse ( vec3_t v )

Inverse a vector.

Parameters:

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

Definition at line 431 of file mathlib.c.

Referenced by GLMatrixAssemble(), 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 406 of file mathlib.c.

Referenced by BuildVertexNormals(), CalcLightinfoVectors(), Check_EdgeEdgeIntersection(), Check_EdgePlaneIntersection(), Check_SidesOverlap(), CL_CameraMove(), CL_CameraRoute(), CL_TargetingGrenade(), Com_GrenadeTarget(), CreateNewFloatPlane(), FixWinding(), G_FindRadius(), G_ShootGrenade(), LE_AddProjectile(), LE_FindRadius(), MAP3D_SmoothRotate(), MAP_AngleOfPath2D(), MAP_AngleOfPath3D(), MAP_Scroll_f(), MAP_StartCenter(), R_CreateSurfaceFlare(), R_GetLevelOfDetailForModel(), R_RadiusFromBounds(), R_StageColor(), S_LoopSample(), SampleNormal(), TestEdge(), 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 243 of file mathlib.c.

Referenced by BaseWindingForPlane(), BuildPatch(), CalcLightinfoVectors(), CL_ActorMouseTrace(), CL_ActorVis(), CL_CameraMove(), 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_DrawBspNormals(), R_DrawSprite(), R_ModLoadAliasMD2MeshIndexed(), R_ModLoadAliasMD2MeshUnindexed(), SEQ_Render3D(), SEQ_SetCamera(), SV_ModLoadAliasMD2Model(), TangentVectors(), TestEdge(), 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 444 of file mathlib.c.

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 419 of file mathlib.c.

References i.

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

qboolean 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 201 of file mathlib.c.

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

Note:: - Embedding the assignments into the expressions provides huge performance increases when compiled with optimizations. The value of an assignment is retained for the comparison or evaluation, saving time for a function that is called 471342268 times in 2 minutes.

< Assign and compare the result

Todo:

< Assign and use the result

Definition at line 653 of file mathlib.c.

References DotProduct.

Referenced by AddBrushBevels(), AI_CheckFF(), AI_FindHerdLocation(), AIR_GetDestinationWhilePursuing(), BaseWindingForPlane(), BuildFacelights(), BuildLights(), BuildVertexNormals(), CalcLightinfoVectors(), Check_EdgeEdgeIntersection(), CL_ActorVis(), CL_CameraMove(), CL_CameraRoute(), CL_TargetingStraight(), Com_GrenadeTarget(), FixFaceEdges(), FrustumVis(), G_ActorVis(), G_ShootSingle(), GatherSampleLight(), MAP3D_ScreenToMap(), MAP_AngleOfPath2D(), MAP_AngleOfPath3D(), MAP_MapCalcLine(), NudgeSamplePosition(), Orthogonalize(), PerpendicularVector(), PlaneFromPoints(), R_DrawFlareSurfaces(), R_DrawSprite(), R_GetSpriteVectors(), R_InterpolateTransform(), R_ModCalcNormalsAndTangents(), R_ModCalcUniqueNormalsAndTangents(), R_StageTexCoord(), RemoveColinearPoints(), S_SpatializeChannel(), SubdivideFace(), TangentVectors(), 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 219 of file mathlib.c.

References DotProduct.

Referenced by CL_CameraMove(), and R_SphereGenerate().

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 367 of file mathlib.c.

Referenced by Grid_RecalcRouting(), and SV_LinkEdict().

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 534 of file mathlib.c.

References DotProduct, and VectorCopy.

Referenced by R_DrawBrushModel().

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 100 of file mathlib.c.

Referenced by CL_ActorAppear(), CL_ActorDoTurn(), 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 53 of file mathlib.c.

Referenced by CMod_RerouteMap(), Grid_MoveMark(), 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 97 of file mathlib.c.

Referenced by FrustumVis().

const byte dvleft[CORE_DIRECTIONS] = { 4, 5, 6, 7, 2, 3, 1, 0 }

Definition at line 103 of file mathlib.c.

Referenced by G_ActorDoTurn().

const byte dvright[CORE_DIRECTIONS] = { 7, 6, 4, 5, 0, 1, 2, 3 }

Definition at line 102 of file mathlib.c.

Referenced by G_ActorDoTurn().

const vec2_t vec2_origin = { 0, 0 }