Вектор

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Вектор это C++ класс который представляет направление и имеет длину, начинающийся с нулевой точки(en) объекта. Каждый вектор содержит три vec_t(en) координаты:

• X +вперёд/-назад
• Y +лево/-право
• Z +вверх/-вниз

(1,20,5) означает 1 юнит(en) вперёд, 20 юнитов влево и 5 юнитов вверх.

Примечание:Класс вектора в движке Source является геометрическим понятием и сильно отличается от вектора из STL, который является массивом массивом. STL вектор в коде движка был переименован в CUtlVector(en).

Объявление

Vector vecMyVector = Vector(1,20,5);

• Класс вектора пишется как Vector, а не vector.
• Вы можете определять значения X, Y и Z отдельно.
• Префикс vec (или просто v) определяет переменную как вектор.

Направление

У вектора нет направления; это определяется кодом, который используется.

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.

Использование

Позиционирование

Every entity's position ('origin') is stored as a vector relative to its parent(en): you are likely to be familiar with this idea already as Cartesian grid coordinates(en). See GetAbsOrigin()(en) for more details.

Movement

An entity attempts to move the length of its velocity(en) vector once per second.

Collision Traces

A Traceline(en) or -hull(en) is fired from one point to another, detecting what it "hits" along its path.

Операции

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

Сложение

Сложение двух (или более) векторов складывает их значения. Вы уже складывали векторы, если толкали что либо двумя руками!

Вычитание

Вычитание одного вектора из другого это разница между ними - другими словами, как добраться из первого вектора в другой.

Совет:От порядка векторов зависит направление получившегося вектора

Умножение

Скалярное

Умножение или деление вектора скалярно (то есть на int(en) или float(en)) изменит длину вектора не изменяя его направления.

Совет:Делениние вектора на его длину нормализует(en) его. Используйте VectorNormalize() чтобы быстро это сделать.

Dot product

Multiplying two vectors then adding the result's ordinates produces a dot product, which when both vectors have been normal(en)ised 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.

Примечание:True dot products are only produced when the length of both vectors is 1. The normal(en)isation step has been skipped in the following demonstration to make its equations simpler (but the positive/zero/negative rule still applies).

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

Vector vecTarget = pTarget->GetAbsOrigin() - 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");

Совет: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.

Поворот

Для поворота вектора нужна матрица(en), это нельзя сделать также легко как умножение. К счастью не нужно в это вникать: можно просто вызвать VectorRotate(Vector in, QAngle in, Vector& out).

Специальные вектора

в Source есть два вида специальных векторов:

vec3_origin

Vector(0,0,0).

vec3_invalid

Для неверных векторов

Member functions

Length

vec_t(en) Length()

vec_t LengthSqr()

Length() returns the vector's length in unit(en)s. It's faster to use LengthSqr() and square the other value being compared.

bool(en) IsLengthGreaterThan(flValue)

bool IsLengthLessThan(flValue)

Helpers that perform fast length checks using LengthSqr().

void Zero()

Sets all elements to 0.

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)

Tests whether the Vector ends within the given box. Box min/max values are local to the Vector.

Casts

Vector2D AsVector2D()

Casts to Vector2D(en).

vec_t Length2D()

vec_t Length2DSqr()

As their standard equivalents, but ignoring the Z-axis.

Base()

Casts to vec_t(en)*, basically the same as &vec.x or (float*)&vec.

Helper functions

These globals are all available through cbase.h.

float(en) VectorNormalize(vec)

Divides the vector by its length, normal(en)ising it. Modifies the Vector and returns the old length.

vec_t(en) DotProduct(vecA,vecB)

See #Dot product.

void CrossProduct(vecA,vecB,vecResult)

See #Cross product.

void VectorTransform(Vector in1, matrix3x4_t in2, Vector out)

See matrix3x4_t(en).

• UTIL_VecToYaw() / UTIL_VecToPitch()(en)
• AngleVectors() / VectorAngles()(en)

See also

• Wikipedia:Euclidean vector
• vec_t(en)
• Vector2D(en)
• QAngle(en)
• matrix3x4_t(en)
• CUtlVector(en)