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Vector это C++ класс, который представляет направление и длину отрезка прямой, начинающегося в точке отсчёта(en).

Оси

Каждый вектор содержит три vec_t(en) координаты:

X: +вперёд/-назад
Y: +влево/-вправо
Z: +вверх/-вниз

(1,20,5) означает 1 единица(en) вперёд, 20 единиц влево и 5 единиц 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.
Движение: An entity attempts to move the length of its velocity(en) vector once per second.
Траектории столкновений: A Traceline(en) or -hull(en) is fired from one point to another, detecting what it "hits" along its path.

Операции

Чтобы результат имел смысл, все векторы в операции должны иметь общую точку отсчёта(en). Используется ли локальное или абсолютное начало отсчета, зависит от того, чего вы пытаетесь достичь.

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(произведение)

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 нормирует(en) его. Используйте VectorNormalize() чтобы быстро это сделать.

Нормированное скалярное

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).

Принцип вычисления нормированного скалярное произведения: (2,2) x (-2,0) = (-4,0) = -4; (2,2) x (-2,2) = (-4,4) = 0; (2,2) x (2,2) = (4,4) = 8

Этот код вычисляет скалярное произведение с помощью различных вспомогательных функций Source:

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.

In this code, the expression dot > 0 is true if the angle between the input vectors is < 90°. If you need two vectors to be < x degrees apart, then dot > cos(x°) must be true, where cos(x°) is a constant. Note that this way, the dot product allows to check the angle between two vectors without calling the rather expensive cosine function at runtime.

Важно:There are various entities with keyvalues denoting a maximum angle as a float in the range -1.0 to 1.0, for example the FieldOfView keyvalue of trigger_look. Such a keyvalue commonly refers to a dot product, which means that it is not a linear function of the desired angle. A common mistake would be to set it to a value of 0.5 which is intended to correspond to an angle of 45°, but instead, the correct value would be cos(45°) ≈ 0.707!

Угол между векторами	x°	cos^-1(`dot`)	0°	1°	2°	5°	10°	15°	30°	45°	60°	75°	90°	120°	180°
Нормированное скалярное произведение	cos(x°)	`dot`	1.0	0.99985	0.99939	0.99619	0.98481	0.96593	0.86603	0.70711	0.5	0.25882	0	-0.5	-1.0

Векторное

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: Это используется для недопустимых векторов, например, если результатом функцим станет вектор к точке на пересечении двух параллельных прямых.

Функции пользователя

Длина

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.

Направление

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).

Сравнение

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.

Приведение

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.

Вспомогательные функции

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).

Смотри также

@@ Line 1: / Line 1: @@
-{{lang|Vector:ru|Вектор}}
+{{LanguageBar|title = Вектор (Vector)}}
+{{translate}}
 {{toc-right}}
-'''<code>Вектор</code>''' это C++ класс который представляет направление и имеет длину, начинающийся с [[origin|нулевой точки]] объекта. Каждый вектор содержит три <code>[[vec_t]]</code> координаты:
+'''<code>Vector</code>''' это C++ класс, который представляет направление и длину отрезка прямой, начинающегося в {{L|origin|точке отсчёта}}.
-* '''X''' +вперёд/-назад
+== Оси ==
-* '''Y''' +лево/-право
+Каждый вектор содержит три <code>{{L|vec_t}}</code> координаты:
-* '''Z''' +вверх/-вниз
-<code>(1,20,5)</code> означает 1 [[unit:ru|юнит]] вперёд, 20 юнитов влево и 5 юнитов вверх.
+;X
+:+вперёд/-назад
+;Y
+:+влево/-вправо
+;Z
+:+вверх/-вниз
-{{note|Source's vector class is geometric and ''very'' different from [[Wikipedia:Vector (C++)|the Standard Template Library's]], which is a type of [[Wikipedia:Array|array]]. The STL-style vector has been renamed <code>[[CUtlVector]]</code> in Source.}}
+<code>(1,20,5)</code> означает 1 {{L|unit|единица}} вперёд, 20 единиц влево и 5 единиц вверх.
-== Declaration ==
+{{Note|Класс вектора в движке Source является геометрическим понятием и сильно отличается от вектора из [[Wikipedia:Vector (C++)|STL]], который является массивом [[Wikipedia:Array|массивом]]. STL вектор в коде движка был переименован в <code>{{L|CUtlVector}}</code>.}}
+== Объявление ==
   Vector vecMyVector = Vector(1,20,5);
-* The classname <code>Vector</code> is case-sensitive.
+* Класс вектора пишется как <code>Vector</code>, а не vector.
-* You can construct it by defining the X, Y and Z member variables separately, pass a single value for all three or copying the data of another Vector.
+* Вы можете определять значения X, Y и Z отдельно.
-* The prefix <code>vec</code> (or sometimes just <code>v</code>) identifies the variable as a vector.
+* Префикс <code>vec</code> (или просто <code>v</code>) определяет переменную как вектор.
-== Orientation ==
+== Направление ==
-A vector does not have an orientation; that is determined by the code that uses it.
+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'''.
@@ Line 29: / Line 36: @@
 There is no way of telling which interpretation will be used from the variable, so check for function comments when in doubt. Use [[#Helper functions|<code>VectorRotate()</code>]] and [[#Helper functions|<code>VectorIRotate()</code>]] to translate between alignments.
-== Uses ==
+== Использование ==
-; Positioning
+; Позиционирование
-: Every entity's position ('origin') is stored as a vector relative to its [[parent]]: you are likely to be familiar with this idea already as [[coordinates|Cartesian grid coordinates]]. See <code>[[GetAbsOrigin()]]</code> for more details.
+: Every entity's position ('origin') is stored as a vector relative to its {{L|parent}}: you are likely to be familiar with this idea already as {{L|coordinates|Cartesian grid coordinates}}. See <code>{{L|GetAbsOrigin()}}</code> for more details.
-; Movement
+; Движение
-: An entity attempts to move the length of its [[velocity]] vector once per second.
+: An entity attempts to move the length of its {{L|velocity}} vector once per second.
-; Collision Traces
+; Траектории столкновений
-: A [[UTIL_TraceLine|Traceline]] or [[UTIL_TraceHull|-hull]] is fired from one point to another, detecting what it "hits" along its path.
+: A {{L|UTIL_TraceLine|Traceline}} or {{L|UTIL_TraceHull|-hull}} is fired from one point to another, detecting what it "hits" along its path.
-== Operations ==
+== Операции ==
-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.
+Чтобы результат имел смысл, все векторы в операции должны иметь общую {{L|origin|точку отсчёта}}. Используется ли локальное или абсолютное начало отсчета, зависит от того, чего вы пытаетесь достичь.
-=== Addition ===
+=== Сложение ===
-Adding two (or more) vectors '''combines''' them. You have already experienced vector addition if you've ever pushed an object with two hands!
+Сложение двух (или более) векторов '''складывает''' их значения. Вы уже складывали векторы, если толкали что либо двумя руками!
-[[File:Vector_add.png|center|Vector addition: (4,1) + (-3,1) = (1,2)]]
+[[File:Vector_add.png|center|Сложение векторов: (4,1) + (-3,1) = (1,2)]]
-=== Subtraction ===
+=== Вычитание ===
-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.
+Вычитание одного вектора из другого это '''разница''' между ними - другими словами, как добраться из первого вектора в другой.
-[[File:Vector_subtraction.png|center|Vector subtraction: (2,3) - (-2,1) = (4,2)]]
+[[File:Vector_subtraction.png|center|Вычитание векторов: (2,3) - (-2,1) = (4,2)]]
-{{tip|The order in which you subtract defines the direction of the vector.}}
+{{tip|От порядка векторов зависит направление получившегося вектора}}
-=== Multiplication ===
+=== Умножение(произведение) ===
-==== Scalar ====
+==== Скалярное ====
-Multiplying or dividing a vector by a [[Wikipedia:Scalar|scalar]] (i.e. an [[int]] or [[float]]) will change its '''length''' (sometimes called "magnitude") without affecting its direction.
+Умножение или деление вектора [[Wikipedia:Scalar|скалярно]] (то есть на {{L|int}} или {{L|float}}) изменит '''длину''' вектора не изменяя его направления.
-[[File:Vector-scalar_multiply.png|center|Vector-scalar multiplication: (1,2) x 2 = (2,4)]]
+[[File:Vector-scalar_multiply.png|center|Скалярное произведение векторов: (1,2) x 2 = (2,4)]]
-{{tip|Dividing a vector by its length [[normal]]ises it. Use <code>VectorNormalize()</code> to do this quickly.}}
+{{tip|Делениние вектора на его длину {{L|normal|нормирует}} его. Используйте <code>VectorNormalize()</code> чтобы быстро это сделать.}}
-==== Dot product ====
+==== Нормированное скалярное ====
-Multiplying two vectors then adding the result's ordinates produces a dot product, which when both vectors have been [[normal]]ised is equal to the '''cosine''' of the angle between the two vectors.
+Multiplying two vectors then adding the result's ordinates produces a dot product, which when both vectors have been {{L|normal}}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.
-{{note|''True dot products are only produced when the length of both vectors is 1.'' The [[normal]]isation step has been skipped in the following demonstration to make its equations simpler (but the positive/zero/negative rule still applies).}}
+{{note|''True dot products are only produced when the length of both vectors is 1.'' The {{L|normal}}isation step has been skipped in the following demonstration to make its equations simpler (but the positive/zero/negative rule still applies).}}
-[[File:Vector_dotproduct.png|center|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]]
+[[File:Vector_dotproduct.png|center|Принцип вычисления нормированного скалярное произведения: (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:
+Этот код вычисляет скалярное произведение с помощью различных вспомогательных функций Source:
 <source lang=cpp>
@@ Line 93: / Line 100: @@
 {{tip|There is no need to normalise if you only care about whether one location is in front of another.}}
-==== Cross product ====
+In this code, the expression {{code|dot &gt; 0}} is true if the angle between the input vectors is &lt; 90°. If you need two vectors to be &lt; x degrees apart, then {{code|dot &gt; cos(x°)}} must be true, where cos(x°) is a constant. Note that this way, the dot product allows to check the angle between two vectors without calling the rather expensive cosine function at runtime.
+{{important|1=There are various entities with keyvalues denoting a maximum angle as a float in the range -1.0 to 1.0, for example the <tt>FieldOfView</tt> keyvalue of {{ent|trigger_look}}. Such a keyvalue commonly refers to a dot product, which means that it is <b style=white-space:nowrap>not a linear</b> function of the desired angle. A common mistake would be to set it to a value of 0.5 which is intended to correspond to an angle of 45°, but instead, the correct value would be cos(45°) &asymp; 0.707!}}
+{| class=wikitable
+!style=background:#333| Угол между векторами
+|     x°  || cos<sup>-1</sup>(<tt>dot</tt>) ||  0° ||      1° ||      2° ||      5° ||     10° ||     15° ||     30° ||     45° || 60° ||     75° || 90° || 120° || 180°
+|-
+!style=background:#333| Нормированное скалярное произведение
+| cos(x°) ||                  <tt>dot</tt>  || 1.0 || 0.99985 || 0.99939 || 0.99619 || 0.98481 || 0.96593 || 0.86603 || 0.70711 || 0.5 || 0.25882 ||  0  || -0.5 || -1.0
+|}
+==== Векторное ====
 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.
@@ Line 99: / Line 118: @@
 The equation is fiddly and doesn't have to be learnt; just use <code>CrossProduct(vecA,vecB,&vecResult)</code>. 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 [http://mathworld.wolfram.com/CrossProduct.html moderate amount of math] is required to [[Wikipedia:Cross product|properly understand]] this operation.
-== Rotation ==
+== Поворот ==
-Rotating a Vector requires a [[matrix3x4_t|matrix]], so can't be done with an operation like those above. Thankfully you don't need to get involved in the gritty details: just call <code>VectorRotate(Vector in, QAngle in, Vector& out)</code>.
+Для поворота вектора нужна {{L|matrix3x4_t|матрица}}, это нельзя сделать также легко как умножение. К счастью не нужно в это вникать: можно просто вызвать <code>VectorRotate(Vector in, QAngle in, Vector& out)</code>.
-== Special Vectors ==
+== Специальные вектора ==
-Source defines two special Vectors:
+в Source есть два вида специальных векторов:
 ; <code>vec3_origin</code>
 : Vector(0,0,0).
 ; <code>vec3_invalid</code>
-: This is used for invalid Vectors, e.g. if you need to return a Vector in a function, but something is not possible (such as the intersection-point of two parallel straight lines).
+: Это используется для недопустимых векторов, например, если результатом функцим станет вектор к точке на пересечении двух параллельных прямых.
-== Member functions ==
+== Функции пользователя ==
-=== Length ===
+=== Длина ===
-; <code>[[vec_t]] Length()</code>
+; <code>{{L|vec_t}} Length()</code>
 ; <code>vec_t LengthSqr()</code>
-: <code>Length()</code> returns the vector's length in [[unit]]s. It's faster to use <code>LengthSqr()</code> and square the other value being compared.
+: <code>Length()</code> returns the vector's length in {{L|unit}}s. It's faster to use <code>LengthSqr()</code> and square the other value being compared.
-; <code>[[bool]] IsLengthGreaterThan(flValue)</code>
+; <code>{{L|boolean|bool}} IsLengthGreaterThan(flValue)</code>
 ; <code>bool IsLengthLessThan(flValue)</code>
 : Helpers that perform fast length checks using <code>LengthSqr()</code>.
@@ Line 124: / Line 143: @@
 : Sets all elements to 0.
-=== Direction ===
+=== Направление ===
 ; <code>void Init(vec_t X, Y, Z)</code>
@@ Line 136: / Line 155: @@
 : 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 ===
+=== Сравнение ===
 ; <code>vec_t DistTo(vOther)</code>
@@ Line 148: / Line 167: @@
 : Tests whether the Vector ends within the given box. Box min/max values are local to the Vector.
-=== Casts ===
+=== Приведение ===
 ; <code>Vector2D AsVector2D()</code>
-: Casts to [[Vector2D]].
+: Casts to {{L|Vector2D}}.
 ; <code>vec_t Length2D()</code>
 ; <code>vec_t Length2DSqr()</code>
 : As their standard equivalents, but ignoring the Z-axis.
 ; <code>Base()</code>
-: Casts to [[vec_t]]*, basically the same as &vec.x or (float*)&vec.
+: Casts to {{L|vec_t}}*, basically the same as &vec.x or (float*)&vec.
-== Helper functions ==
+== Вспомогательные функции ==
 These globals are all available through <code>cbase.h</code>.
-; <code>[[float]] VectorNormalize(vec)</code>
+; <code>{{L|float}} VectorNormalize(vec)</code>
-: Divides the vector by its length, [[normal]]ising it. Modifies the Vector and returns the old length.
+: Divides the vector by its length, {{L|normal}}ising it. Modifies the Vector and returns the old length.
-; <code>[[vec_t]] DotProduct(vecA,vecB)</code>
+; <code>{{L|vec_t}} DotProduct(vecA,vecB)</code>
 : See [[#Dot product]].
 ; <code>void CrossProduct(vecA,vecB,vecResult)</code>
 : See [[#Cross product]].
 ; <code>void VectorTransform(Vector in1, matrix3x4_t in2, Vector out)</code>
-: See [[matrix3x4_t]].
+: See {{L|matrix3x4_t}}.
-* [[UTIL_VecToYaw()|<code>UTIL_VecToYaw()</code> / <code>UTIL_VecToPitch()</code>]]
+* {{L|UTIL_VecToYaw()|<code>UTIL_VecToYaw()</code> / <code>UTIL_VecToPitch()</code>}}
-* [[AngleVectors()|<code>AngleVectors()</code> / <code>VectorAngles()</code>]]
+* {{L|AngleVectors()|<code>AngleVectors()</code> / <code>VectorAngles()</code>}}
-== See also ==
+== Смотри также ==
 * [[Wikipedia:Euclidean vector]]
-* <code>[[vec_t]]</code>
+* <code>{{L|vec_t}}</code>
-* <code>[[Vector2D]]</code>
+* <code>{{L|Vector2D}}</code>
-* <code>[[QAngle]]</code>
+* <code>{{L|QAngle}}</code>
-* <code>[[matrix3x4_t]]</code>
+* <code>{{L|matrix3x4_t}}</code>
-* <code>[[CUtlVector]]</code>
+* <code>{{L|CUtlVector}}</code>
-[[Category:Glossary]]
+{{ACategory|Source class}}
-[[Category:Variables]]
+{{ACategory|Helpers}}
-[[Category:Helpers]]
+{{ACategory|Glossary}}
+{{ACategory|Variables}}
+{{ACategory|Helpers}}

Ru/Vector: Difference between revisions

Latest revision as of 14:20, 27 May 2025

Contents

Оси

Объявление

Направление

Использование