Vectors

Note that because they're objects all their methods except for new need to be called with ":" between the object and the method (e.g. v:length()).

Vector2

Vector2 is a 2D vector object.

Vector2 Constants

It's got six constants that are pre-defined vectors:

key	x	y
ONE	1	1
UP	0	-1
DOWN	0	1
LEFT	-1	0
RIGHT	1	0
ZERO	0	0

Vector2 Methods

Vector2 : new( number : x, number : y )

Returns a new Vector2 that points to (x; y).

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)

-- Printing the vector (Note: tostring(v1) will return v1:string(0),
--  if you want more precision you should use v1:string(decimal_digits))
print(v1)

Vector2 : duplicate()

Returns a new Vector2 that has the same x, y as the original Vector2.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)
-- Creating a reference to v1
local v2 = v1
-- Making a duplicate of v1
local v3 = v1:duplicate()

-- Changing the x value on
--  The reference to v1
v2.x = 5
--  The duplicate of v1
v3.x = 2

-- Printing all 3 vectors to show the difference between
--  A referenced vector and a duplicate one
print(v1)
print(v2)
print(v3)

number : length_sq()

Returns the squared length of the vector (It's much faster than doing length if you need to compare lengths).

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)

-- Printing its squared length
print(v1:length_sq())

number : length()

Returns the length of the vector.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)

-- Printing its length
print(v1:length())

Vector2 : unit()

Returns the unit vector of the vector.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)
-- Getting the unit vector of v1
local v1_unit = v1:unit()

-- Printing it with string method to get more decimal digits
--  (If nothing is specified it will have 6 decimal digits the default for string.format("%f"))
print(v1_unit:string())

number : dot( Vector2 : other )

Returns the dot product between the vector and the specified vector.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)
-- Creating a second Vector
local v2 = math_utils.Vector2.new(3, 2)

-- Printing the dot product between the two vectors
print(v1:dot(v2))

number : cross( Vector2 : other )

Returns the cross product between the vector and the specified vector.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)
-- Creating a second Vector
local v2 = math_utils.Vector2.new(3, 2)

-- Printing the cross product between the two vectors
print(v1:cross(v2))

Vector2 : rotate( number : angle )

Returns a Vector2 that is the vector rotated by angle (in radians).

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)

-- Printing the vector rotated by 180°
print(v1:rotate(math.pi))

string : string( number : precision )

Returns a string that is equal to ("(%f; %f)"):format(v.x, v.y) if precision is specified then the string will show vector's x and y with precision decimal digits.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)

-- Printing the vector with 10 decimal digits
print(v1:string(10))

Vector2 Metamethods

If you don't know what metamethods are you can go to this link to learn more.

Creating a new Vector2

Vector2 implements the __call metamethod, which means that doing math_utils.Vector2.new() is the same as math_utils.Vector2().

It's still better using .new() because only one function is called instead of two, but it can be done both ways.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)
-- Creating a second Vector
local v2 = math_utils.Vector2(3, 2)

-- Printing the two vectors
print(v1, v2)

tostring(Vector2)

Vector2 implements the __tostring metamethod, which means that doing tostring(Vector2) will return Vector2:string(0).

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)

-- Converting v1 into string
local v1_string = tostring(v1)

-- Printing v1's string
print(v1_string)

Length of Vector2

Note: This only works on ComputerCraft version 1.87+.

Vector2 implements the __len metamethod, which means that #Vector2 works.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)

-- Printing the length of the vector
print(#v1)

Sum of Vector2

Vector2 implements the __add metamethod, which means that Vector2 + Vector2 works.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)
-- Creating a second Vector
local v2 = math_utils.Vector2.new(3, 2)

-- Printing the sum between the two vectors
print(v1 + v2)

Subtraction of Vector2

Vector2 implements the __sub metamethod, which means that Vector2 - Vector2 works.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)
-- Creating a second Vector
local v2 = math_utils.Vector2.new(3, 2)

-- Printing the subtraction between the two vectors
print(v1 - v2)

Multiplying a Vector2 by a number

Vector2 implements the __mul metamethod, which means that Vector2 * Number works.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)

-- Printing the multiplication between a Vector2 and a number
print(v1 * 10)

Dividing a Vector2 by a number

Vector2 implements the __div metamethod, which means that Vector2 / Number works.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)

-- Printing the division between a Vector2 and a number
print(v1 / 2)

Checking if two Vector2 are equal

NOTE: To check if two vectors have the same length do v1:length_sq() == v2:length_sq().

Vector2 implements the __eq metamethod, which means that Vector2 == Vector2 works.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)
-- Creating a second Vector
local v2 = math_utils.Vector2.new(10, 2)

-- Printing if the two vectors are equal
print(v1 == v2)

Checking if a Vector2's length is greater than another Vector2's length

Vector2 implements the __lt metamethod, which means that Vector2 < Vector2 and Vector2 > Vector2 work.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)
-- Creating a second Vector
local v2 = math_utils.Vector2.new(3, 2)

-- Printing if the length of the first vector is greater than the second one
print(v1 > v2)
-- Printing if the length of the first vector is lower than the second one
print(v1 < v2)

Checking if a Vector2's length is greater or equal to another Vector2's length

Vector2 implements the __le metamethod, which means that Vector2 <= Vector2 and Vector2 >= Vector2 work.

-- Creating a new Vector
local v1 = math_utils.Vector2.new(10, 2)
-- Creating a second Vector
local v2 = math_utils.Vector2.new(3, 2)
-- Creating a third vector
local v3 = math_utils.Vector2.new(2, 10)

-- Printing if the length of the first vector is greater or equal to the second one
print(v1 >= v2)
-- Printing if the length of the first vector is lower or equal to the third one
print(v1 <= v3)

Vector3

Vector3 is a 3D vector object.

Vector3 Constants

It's got eight constants that are pre-defined vectors:

key	x	y	z
ONE	1	1	1
UP	0	1	0
DOWN	0	-1	0
LEFT	-1	0	0
RIGHT	1	0	0
FORWARD	0	0	1
BACK	0	0	-1
ZERO	0	0	0

Vector3 Methods

Vector3 : new( number : x, number : y, number : z )

Returns a new Vector3 that points to (x; y; z).

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)

-- Printing the vector (Note: tostring(v1) will return v1:string(0),
--  if you want more precision you should use v1:string(decimal_digits))
print(v1)

Vector3 : duplicate()

Returns a new Vector3 that has the same x, y, z as the original Vector3.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)
-- Creating a reference to v1
local v2 = v1
-- Making a duplicate of v1
local v3 = v1:duplicate()

-- Changing the x value on
--  The reference to v1
v2.x = 5
--  The duplicate of v1
v3.x = 2

-- Printing all 3 vectors to show the difference between
--  A referenced vector and a duplicate one
print(v1)
print(v2)
print(v3)

number : length_sq()

Returns the squared length of the vector (It's much faster than doing length if you need to compare lengths).

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)

-- Printing its squared length
print(v1:length_sq())

number : length()

Returns the length of the vector.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)

-- Printing its length
print(v1:length())

Vector3 : unit()

Returns the unit vector of the vector.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)
-- Getting the unit vector of v1
local v1_unit = v1:unit()

-- Printing it with string method to get more decimal digits
--  (If nothing is specified it will have 6 decimal digits the default for string.format("%f"))
print(v1_unit:string())

number : dot( Vector3 : other )

Returns the dot product between the vector and the specified vector.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)
-- Creating a second Vector
local v2 = math_utils.Vector3.new(3, 2, 10)

-- Printing the dot product between the two vectors
print(v1:dot(v2))

Vector3 : cross( Vector3 : other )

Returns the cross product between the vector and the specified vector.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)
-- Creating a second Vector
local v2 = math_utils.Vector3.new(3, 2, 10)

-- Printing the cross product between the two vectors
print(v1:cross(v2))

Vector3 : rotate( Vector3 : axis, number : angle )

Returns a Vector3 that is the vector rotated by angle (in radians) on the specified axis, you can use Vector3 constants as axis.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)

-- Printing the vector rotated by 180° on the y axis
print(v1.UP, v1:rotate(math.pi))

string : string( number : precision )

Returns a string that is equal to ("(%f; %f; %f)"):format(v.x, v.y, v.z) if precision is specified then the string will show vector's x, y and z with precision decimal digits.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)

-- Printing the vector with 10 decimal digits
print(v1:string(10))

Vector3 Metamethods

If you don't know what metamethods are you can go to this link to learn more.

Creating a new Vector3

Vector3 implements the __call metamethod, which means that doing math_utils.Vector3.new() is the same as math_utils.Vector3().

It's still better using .new() because only one function is called instead of two, but it can be done both ways.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)
-- Creating a second Vector
local v2 = math_utils.Vector3(3, 2, 10)

-- Printing the two vectors
print(v1, v2)

tostring(Vector3)

Vector3 implements the __tostring metamethod, which means that doing tostring(Vector3) will return Vector3:string(0).

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)

-- Converting v1 into string
local v1_string = tostring(v1)

-- Printing v1's string
print(v1_string)

Length of Vector3

Note: This only works on ComputerCraft version 1.87+.

Vector3 implements the __len metamethod, which means that #Vector3 works.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)

-- Printing the length of the vector
print(#v1)

Sum of Vector3

Vector3 implements the __add metamethod, which means that Vector3 + Vector3 works.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)
-- Creating a second Vector
local v2 = math_utils.Vector3.new(3, 2, 10)

-- Printing the sum between the two vectors
print(v1 + v2)

Subtraction of Vector3

Vector3 implements the __sub metamethod, which means that Vector3 - Vector3 works.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)
-- Creating a second Vector
local v2 = math_utils.Vector3.new(3, 2, 10)

-- Printing the subtraction between the two vectors
print(v1 - v2)

Multiplying a Vector3 by a number

Vector3 implements the __mul metamethod, which means that Vector3 * Number works.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)

-- Printing the multiplication between a Vector3 and a number
print(v1 * 10)

Dividing a Vector3 by a number

Vector3 implements the __div metamethod, which means that Vector3 / Number works.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)

-- Printing the division between a Vector3 and a number
print(v1 / 2)

Checking if two Vector3 are equal

NOTE: To check if two vectors have the same length do v1:length_sq() == v2:length_sq().

Vector3 implements the __eq metamethod, which means that Vector3 == Vector3 works.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)
-- Creating a second Vector
local v2 = math_utils.Vector3.new(10, 2, 5)

-- Printing if the two vectors are equal
print(v1 == v2)

Checking if a Vector3's length is greater than another Vector3's length

Vector3 implements the __lt metamethod, which means that Vector3 < Vector3 and Vector3 > Vector3 work.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)
-- Creating a second Vector
local v2 = math_utils.Vector3.new(3, 2, 10)

-- Printing if the length of the first vector is greater than the second one
print(v1 > v2)
-- Printing if the length of the first vector is lower than the second one
print(v1 < v2)

Checking if a Vector3's length is greater or equal to another Vector3's length

Vector3 implements the __le metamethod, which means that Vector3 <= Vector3 and Vector3 >= Vector3 work.

-- Creating a new Vector
local v1 = math_utils.Vector3.new(10, 2, 5)
-- Creating a second Vector
local v2 = math_utils.Vector3.new(3, 2, 10)
-- Creating a third vector
local v3 = math_utils.Vector3.new(2, 10, 5)

-- Printing if the length of the first vector is greater or equal to the second one
print(v1 >= v2)
-- Printing if the length of the first vector is lower or equal to the third one
print(v1 <= v3)