Vector

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Revision as of 15:50, 15 April 2009 by TomEdwards (talk | contribs) (Orientation)

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Vector is a C++ class that represents a line with direction and length, starting at the current origin.

Each vector contains three vec_t 'ordinates'. (0,20,5) means 20 units in front of and 5 units above the current origin.

Note:Source's vector class is geometric and very different from the Standard Template Library's, which is a type of array. The STL-style vector has been renamed CUtlVector in Source.

Declaration

Vector vecMyVector = Vector(0,20,5);
  • The classname Vector is case-sensitive.
  • You could also assign to the X, Y and Z member variables separately.
  • vec (or sometimes just v) identifies the variable as a Vector.

Orientation

A vector does not have an orientation; that is determined by the code that uses it.

In the vast majority of cases a vector will be interpreted as world axis aligned regardless of an entity's rotation, but there are few cases (e.g. applying physics forces), where they are considered object axis aligned.

There is no way of telling which interpretation will be used from the variable, so check for function comments when in doubt. Use VectorRotate() and VectorIRotate() to translate between alignments.

Uses

Positioning

Every entity's position is stored as a vector relative to its parent. You are likely to be familiar with this idea already as Cartesian grid coordinates.

The parent-relative vector stored by the entity is 'local'; calculating an 'absolute' vector relative to the world requires extra work. The two Abs functions below do that work for you, but are more expensive.

Movement

An entity attempts to move the length of its velocity vector once per second. The code looks something like this:

Vector velocity = Vector(0,5,0); // 5 units/second in the +Y direction

Vector vecNewOrigin = GetAbsOrigin() + velocity * gpGlobals->frametime; // frametime is in seconds, e.g. 0.033

SetAbsOrigin(vecNewOrigin);

Notice how frametime is used to regulate the entity's speed regardless of how long each frame takes to calculate. See scalar multiplication for more detail on the operation.

As with the origin, velocity is stored relative to the parent. AbsVelocity represents the velocity relative to the rest frame of the world, and is the more commonly used method.

Tracelines

Main article: TraceLines

Tracing is the process of going from a point A towards another point B, and finding out the first thing that we "hit" on our way from A to B (TraceLine).

Operations

All vectors in an operation must have the same origin for the result to make sense. Whether a local or absolute origin is used depends on what you're trying to achieve.

Addition

Adding two (or more) vectors combines them. You have already experienced vector addition if you've ever pushed an object with two hands!

Vector addition: (4,1) + (-3,1) = (1,2)

Subtraction

Subtracting one vector from another produces the difference between the two - in other words, how to get to the first location from the second. The result is local to the second vector.

Vector subtraction: (2,3) - (-2,1) = (4,2)
Tip:The order in which you subtract defines the direction of the vector.

Multiplication

Scalar

Multiplying or dividing a vector by a scalar (i.e. an int or float) will change its length (sometimes called "magnitude") without affecting its direction.

Vector-scalar multiplication: (1,2) x 2 = (2,4)
Tip:Dividing a vector by its length normalises it. Use VectorNormalize() to do this quickly.

Dot product

Multiplying two vectors then adding the result's ordinates produces a dot product, which when both vectors have been normalised (see above) is equal to the cosine of the angle between the two vectors.

One use of a dot product is to tell how closely the two vectors align. +1 means a match, 0 means they are perpendicular to each other, and -1 means they are opposed.

Note:True dot products are only produced when the length of both vectors is 1. The normalisation step has been skipped in the following demonstration to make its equations simpler (but the positive/zero/negative rule still applies).
Vector dot products: (2,2) x (-2,0) = (-4,0) = -4; (2,2) x (-2,2) = (-4,4) = 0; (2,2) x (2,2) = (4,4) = 8

This code calculates a dot product with the aid of Source's various helper functions:

Vector vecTarget = GetAbsOrigin() - pTarget->GetAbsOrigin();	// Get local vector to target
VectorNormalize(vecTarget);	// Normalisation needs to be done beforehand

Vector vecFacing;
AngleVectors(GetLocalAngles(),&vecFacing);	// Convert facing angle to equivalent vector (arrives normalised)

float result = DotProduct(vecTarget,vecFacing);	// Get the dot product.

if (result > 0)
	Msg("pTarget is in front of me!\n");
Tip:There is no need to normalise if you only care about whether one location is in front of another.

Cross product

A cross product is a vector perpendicular to two input vectors. It's used to extrapolate a third dimension from just two: the cross product of a vector pointing down the X-axis and a vector pointing down the Y-axis is a vector pointing down the Z-axis.

The equation is fiddly and doesn't have to be learnt; just use CrossProduct(vecA,vecB,&vecResult). There generally isn't any need to normalise the input vectors. Most modders will likely only use cross products rarely, if ever - but if required, be aware that a moderate amount of math is required to properly understand this operation.

Member functions

Length

vec_t Length()
vec_t LengthSqr()
Length() returns the vector's length in units. It's faster to use LengthSqr() and square the value for comparison, however.
bool IsLengthGreaterThan(flValue)
bool IsLengthLessThan(flValue)
Helpers that perform fast length checks using LengthSqr().
void Zero()
Guess what?

Direction

void Init(vec_t X, Y, Z)
Quickly set an existing vector's ordinates.
void Random(vec_t minVal,vec_t maxVal)
Randomises all three ordinates within the given range.
void Negate()
Reverses the vector's direction without affecting its length.
Vector Max(vOther)
Vector Min(vOther)
Clamps the vector's ordinates either above or below the given values. The ordinates won't stay in proportion (i.e. direction might change).

Comparison

vec_t DistTo(vOther)
vec_t DistToSqr(vOther)
Returns the distance between the current vector and vOther as a scalar. As ever, the squared flavour is faster.
vec_t Dot(vOther)
Returns the dot product of the current vector and vOther.
Vector Cross(vOther)
Returns the cross product of the current vector and vOther.
bool WithinAABox(vecBoxmin,vecBoxmax)
Does the vector end within this box? Argument vectors are local.

Casts

Vector2D AsVector2D()
Casts to Vector2D.
vec_t Length2D()
vec_t Length2DSqr()
As their standard equivalents, but ignoring the Z-axis.
Base()
Casts to vec_t. To do: What does that achieve?

Helper functions

vec_t DotProduct(vecA,vecB)
See #Dot product.
void CrossProduct(const Vector& a, const Vector& b, Vector& result )
See #Cross product.

See also