Src/idlib/math/vectors.h (source file)

From modwiki

The Doom 3 engine uses vectors for many things, including forces of movement, direction of view, and even plain variable storage in some cases. In the engine, a vector can be represented as

 idVec2 - x,y
 idVec3 - x,y,z
 idVec4 - x,y,z,w
 idVec5 - x,y,z,s,t
 idVec6 - p[0],p[1],p[2],p[3],p[4],p[5]
 idVecX - p[0]-p[x-1]

Where idVec 2-6 represents 2d-6d vectors, respectively, and idVecX is an arbitrarily sized vector.

The components of the vector are public floats, so accessing them is easy enough:

 
  idVec3 myvector;
    myvector.x = 1.4;
    myvector.y = 2;
    myvector.z = 25.99;

The vectors all have overloaded operators, although some (namely idVec5) seem to use only a few. Here is a table describing the arguments, function, and datatype of operators used with idVec2 and idVec3, the more frequently used vector types:

operator	Arguments	Description	Returns
[ ]	int index	Returns component index	float&
-	none	Multiply all components by -1	idVecN
*	const idVecN &a	Multiply vector components together	float
/	const float a	Divide all components of the vector by a	idVecN
+	const idVecN &a	Add components of the vectors together	idVecN
-	const idVecN &a	Subtract components from a from current vector (x - a.x, etc.)	idVecN
+ =	const idVecN &a	Add components of the vectors together	idVecN &
- =	const idVecN &a	Subtract components from a from current vector (x - a.x, etc.)	idVecN &
/ =	const idVecN &a	Divide components from current vector by components in a	idVecN &
/ =	const float a	Divide all components in current vector by a	idVecN &
* =	const float a	Multiply all components in current vector by a	idVecN &
*	const float a, const idVecN b	Multiply all components of b by a	idVecN
= =	const idVecN &a	Non-epsilon comparison of current vector to a	bool
! =	const idVecN &a	Non-epsilon inverse comparison of current vector to a	bool

And, for your enjoyment, here is a table with all vector types, applicable functions, and descriptions of the functions.

	idVec2	idVec3	idVec4	idVec5	idVec6	idVecX	Description
Set	X	X	X	X			Sets the components of the vector. (float args)
Zero	X	X	X	X	X	X	Sets all components to 0.
Compare	X	X	X	X	X	X	Compares two vectors. (optional epsilon comparison)
Length	X	X	X		X	X	Returns the modulus of a vector.
LengthFast	X	X	X		X	X	Returns the modulus. (less accurate)
LengthSqr	X	X	X		X	X	Returns the sum of the squares of the components. (modulus squared)
Normalize	X	X	X		X	X	Brings the components into 0-1 range, modulus = 1.
NormalizeFast	X	X	X		X	X	Normalizes, but less accurate.
Truncate	X	X					Shortens modulus to new value if applicable.
Clamp	X	X				X	Bumps the vectors components into the supplied min-max.
Snap	X	X					Rounds the components of the vector to integers.
SnapInt	X	X					Converts the components to ints, then back to floats.
GetDimension	X	X	X	X	X	X	Returns the dimension of the vector. (2,3,4,5,6,x)
ToFloatPtr	X	X	X	X	X	X	Returns &x. (&p for idVecX)
ToString	X	X	X	X	X	X	Returns the vector in string format.
Lerp	X	X	X	X			Linearly inperpolates one vector to another.
ToYaw		X					Returns yaw value. (x and y)
ToPitch		X					Returns pitch value. (x, y, z)
ToAngles		X					Returns angles value. (-pitch, yaw, 0)
ToPolar		X					Returns polar value. ((vx²+y²+z²), yaw, -pitch)
ToMat3		X					Returns a 3x1 matrix. (xyz)
ToVec2		X	X				Reinterpret_cast to idVec2. (only x/y?)
NormalVectors		X
OrthagonalBasis		X
ProjectOntoPlane		X
ProjectAlongPlane		X
ProjectSelfOntoSphere		X
SLerp		X
FixDegenerateNormal		X
FixDenormals		X
Cross		X
SetSize						X	Set size(dimension) of idVecX.
ChangeSize						X	Change size of idVecX. (expand makes new components 0)
GetSize						X	Returns the size(dimension) of idVecX.
SetData						X	Set 16 byte-aligned data. (?)
Random						X	Randomize all current elements. (or a list to the specified length)
Negate						X	Multiply all elements by -1.
SwapElements						X	Switches index of two elements.
SubVec3						X	Convert to idVec3.
SubVec6						X	Convert to idVec6.