Vectors Library

This library adds an interface for working with arbitrary-sized vectors (in the mathematical sense). It provides various functions for creating vectors, and common operators to work with them.

All the functions that return a vector create a copy and never modify the same vector. I.e. v:negate() would return the negative of the provided vector, but leave the passed in vector unchanged.

Usage

require('vectors')

Functions

V(coords, dimension)

vector = V(coords, dimension)

• vector table - The resulting vector

• coords table - A table containing the coordinates (numerically indexed, contiguous starting from 1)

• dimension number [optional] - An integer describing the dimension of the vector

Constructor for vectors. Optionally provide dimension dimension, to avoid computing the dimension from the table. Can be used on a literal table like the similar one capital letter functions in other libraries. I.e. T{1,2,3}, S{1,2,3} and, in this case, V{1,2,3}.

vectors.zero(dimension)

vector = vectors.zero(dimension)

• vector table - The resulting vector

• dimension number - The length of the vector

Creates a zero-vector of dimension dimension.

vectors.fill(dimension, value)

vector = vectors.fill(dimension, value)

• vector table - The resulting vector

• dimension number - The dimension of the vector

• value any - The element to fill the vector with

Creates a vector of dimension dimension with all values set to value.

vectors.unit(dimension, position)

vector = vectors.unit(dimension, position)

• vector table - The resulting vector

• dimension number - The dimension of the vector

• position number - The position of the 1 element

Creates a euclidean unit vector of dimension dimension for axis position.

vectors.length(vector)

length = vectors.length(vector)

• length number - The resulting absolute length of the vector

• vector table - The vector whose length is to be measured

Returns the length of vector measured from 0.

vectors.normalize(vector)

normvector = vectors.normalize(vector)

• normvector table - The resulting normalized vector

• vector table - The vector that is meant to be normalized

Returns a vector in the same direction as vector, normalized to length one.

vectors.dimension(vector)

dimension = vectors.dimension(vector)

• dimension number - The dimension of the provided vector

• vector table - The vector that is meant to be normalized

Returns the dimension of vector. Constant.

vectors.dot(vector1, vector2)

dotvector = vectors.dot(vector1, vector2)

• dotvector table - The vector resulting from the operation

• vector1 table - The first operand vector

• vector2 table - The second operand vector

Returns the dot product between two vectors.

vectors.cross(vector1, vector2)

crossvector = vectors.cross(vector1, vector2)

• crossvector table - The vector resulting from the operation

• vector1 table - The first operand vector

• vector2 table - The second operand vector

Returns the cross product of two R^3 vectors.

vectors.scale(vector, factor)

scaledvector = vectors.scale(vector, factor)

• scaledvector table - The resulting scaled vector

• vector table - The vector to scale

• factor number - The factor to scale it with

Returns vector multiplied by factor, i.e. all elements multiplied by the same factor.

vectors.negate(vector)

negvector = vectors.negate(vector)

• negvector table - The resulting negated vector

• vector table - The vector to negate

Returns the vector pointing in the opposite direction of vector with the same length.

vectors.add(vector1, vector2)

sumvector = vectors.add(vector1, vector2)

• sumvector table - The vector resulting from the operation

• vector1 table - The first operand vector

• vector2 table - The second operand vector

Returns vector1 added to vector2.

vectors.subtract(vector1, vector2)

subvector = vectors.subtract(vector1, vector2)

• subvector table - The vector resulting from the operation

• vector1 table - The first operand vector

• vector2 table - The second operand vector

Returns vector1 subtracted by vector2.

vectors.angle(vector1, vector2)

angle = vectors.angle(vector1, vector2)

• angle number - The resulting angle

• vector1 table - The first operand vector

• vector2 table - The second operand vector

Returns the angle described by two vectors (in radians).

vectors.from_radian(angle)

vector = vectors.from_radian(angle)

• vector table - The resulting vector

• angle number - The radian to compute it from

Returns a 2D vector from a radian value. Note that this goes against mathematical convention, which commonly makes the radian go counter-clockwise. This function, instead, goes clockwise, i.e. it will return (0, -1) for π/2. This is done to match the game's internal representation, which has the X axis pointing east and the Y axis pointing south.

vectors.to_radian(vector)

radian = vectors.to_radian(vector)

• angle number - The resulting radian

• vector table - The vector to compute it from

Returns the radian that describes the direction of the vector.

Operators

addvector

addvector = vector1 + vector2

Calls vector.add.

subvector

subvector = vector1 - vector2

Calls vector.subtract.

dotvector

dotvector = vector1 * vector2

Calls vector.dot.

scaledvector

scaledvector = vector * scalar

Calls vector.scale.

negvector

negvector = -vector

Calls vector.negate.

V

vector = +vector

Calls V, which results in a copy of the same vector.