# Vectors

Last updated: December 17, 2018

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## Vectors

### Intro

Vectors in the wurst standard library refer to the euclidean vector commonly represented as an arrow, connecting point A with point B. They are most commonly used to describe a position in 2d or 3d space, e.g. the position of a unit unit.getPos() returns vec2 or target position on map item.setPos(vec2 pos). vec2 and vec3 are tuples, meaning they have no object id and thus cannot be represented as a single integer. Vectors should be used instead of location or raw primitives. The standard library provides most vector algebra out of the box.

### Basic Usage

// Create footman at (0, 0)
let u = createUnit(DUMMY_PLAYER, UnitIds.footman, ZERO2, angle(0))
let pos = u.getPos()
// Print a unit's position
print(pos.toString())

// Move position right by 128 units
u.setXY(pos + vec2(128, 0))

### Vector algebra

let a = vec2(1, 1)
let b = vec2(2, 2)
let sum = a + b
let difference  = a - b
let scalar = a * 0.5

### Distances

Use distanceTo and distanceToSq to calculate the distance or squared distance between two vectors respectively. Squared distance is often used in range checks to compared with the squared range for a faster calculation (no square root).

let distSq = caster.getPos().distanceToSq(target.getPos())
if distSq < 256 * 256
// in range, deal damage
caster.damageTarget(target, 32.)

Additionally you can calculate a vectors distance to a linesegment and whether it’s contained inside a triangle or polygon.

### Polar Projection

Polar Projection uses trigonometry to project a vector in 2d and 3d space using a distance and angles in which to project. Let’s look at the math real quick.

Given an angle in radians, the Sin and Cos functions return the distance, on the y and x axis respectively, to the point on the outside of the unit circle at that angle. We know that the blue line is of length 1 because it is equal to the radius of the unit circle. Thus we can scale it to our desired distance simply by multiplying the x and y values, resulting in vec2(Cos(this.radians) * len, Sin(this.radians) * len).

Remember that in warcraft 3 a zero xy-angle points east, and a zero z-angle points upwards.

// Blink caster a certain distance in the target direction
let caster = GetSpellAbilityUnit()
let target = getSpellTargetPos()