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Vector math API documentation

version 1.2.143

Functions for mathematical operations on vectors, matrices and quaternions.

  • The vector types (vmath.vector3 and vmath.vector4) supports addition and subtraction with vectors of the same type. Vectors can be negated and multiplied with numbers (scaled).
  • The quaternion type (vmath.quat) supports multiplication with other quaternions.
  • The matrix type (vmath.matrix4) can be multiplied with numbers, other matrices and vmath.vector4 values.
  • All types performs equality comparison by each component value.

The following components are available for the various types:

vector3
x, y and z. Example: v.y
vector4
x, y, z, and w. Example: v.w
quaternion
x, y, z, and w. Example: q.w
matrix4
m00 to m33 where the first number is the row (starting from 0) and the second number is the column. Columns can be accessed with c0 to c3, returning a vector4. Example: m.m21 which is equal to m.c1.z
vector
indexed by number 1 to the vector length. Example: v[3]

Functions

vmath.conj

calculates the conjugate of a quaternion

vmath.cross

calculates the cross-product of two vectors

vmath.dot

calculates the dot-product of two vectors

vmath.inv

calculates the inverse matrix.

vmath.length

calculates the length of a vector or quaternion

vmath.length_sqr

calculates the squared length of a vector or quaternion

vmath.lerp

lerps between two vectors

vmath.lerp

lerps between two quaternions

vmath.lerp

lerps between two numbers

vmath.matrix4

creates a new identity matrix

vmath.matrix4

creates a new matrix from another existing matrix

vmath.matrix4_axis_angle

creates a matrix from an axis and an angle

vmath.matrix4_from_quat

creates a matrix from a quaternion

vmath.matrix4_frustum

creates a frustum matrix

vmath.matrix4_look_at

creates a look-at view matrix

vmath.matrix4_orthographic

creates an orthographic projection matrix

vmath.matrix4_perspective

creates a perspective projection matrix

vmath.matrix4_rotation_x

creates a matrix from rotation around x-axis

vmath.matrix4_rotation_y

creates a matrix from rotation around y-axis

vmath.matrix4_rotation_z

creates a matrix from rotation around z-axis

vmath.mul_per_elem

performs an element wise multiplication of two vectors

vmath.normalize

normalizes a vector

vmath.ortho_inv

calculates the inverse of an ortho-normal matrix.

vmath.project

projects a vector onto another vector

vmath.quat

creates a new identity quaternion

vmath.quat

creates a new quaternion from another existing quaternion

vmath.quat

creates a new quaternion from its coordinates

vmath.quat_axis_angle

creates a quaternion to rotate around a unit vector

vmath.quat_basis

creates a quaternion from three base unit vectors

vmath.quat_from_to

creates a quaternion to rotate between two unit vectors

vmath.quat_rotation_x

creates a quaternion from rotation around x-axis

vmath.quat_rotation_y

creates a quaternion from rotation around y-axis

vmath.quat_rotation_z

creates a quaternion from rotation around z-axis

vmath.rotate

rotates a vector by a quaternion

vmath.slerp

slerps between two vectors

vmath.slerp

slerps between two quaternions

vmath.vector

create a new vector from a table of values

vmath.vector3

creates a new zero vector

vmath.vector3

creates a new vector from scalar value

vmath.vector3

creates a new vector from another existing vector

vmath.vector3

creates a new vector from its coordinates

vmath.vector4

creates a new zero vector

vmath.vector4

creates a new vector from scalar value

vmath.vector4

creates a new vector from another existing vector

vmath.vector4

creates a new vector from its coordinates

Functions

vmath.conj

vmath.conj(q1)

Calculates the conjugate of a quaternion. The result is a quaternion with the same magnitudes but with the sign of the imaginary (vector) parts changed:

q* = [w, -v]

Parameters

q1

quatertion quaternion of which to calculate the conjugate

q1

quatertion quaternion of which to calculate the conjugate

Returns

q

quatertion the conjugate

q

quatertion the conjugate

Examples

local quat = vmath.quat(1, 2, 3, 4)
print(vmath.conj(quat)) --> vmath.quat(-1, -2, -3, 4)

vmath.cross

vmath.cross(v1, v2)

Given two linearly independent vectors P and Q, the cross product, P × Q, is a vector that is perpendicular to both P and Q and therefore normal to the plane containing them.

If the two vectors have the same direction (or have the exact opposite direction from one another, i.e. are not linearly independent) or if either one has zero length, then their cross product is zero.

Parameters

v1

vector3 first vector

v2

vector3 second vector

v1

vector3 first vector

v2

vector3 second vector

Returns

v

vector3 a new vector representing the cross product

v

vector3 a new vector representing the cross product

Examples

local vec1 = vmath.vector3(1, 0, 0)
local vec2 = vmath.vector3(0, 1, 0)
print(vmath.cross(vec1, vec2)) --> vmath.vector3(0, 0, 1)
local vec3 = vmath.vector3(-1, 0, 0)
print(vmath.cross(vec1, vec3)) --> vmath.vector3(0, -0, 0)

vmath.dot

vmath.dot(v1, v2)

The returned value is a scalar defined as:

P ⋅ Q = |P| |Q| cos θ

where θ is the angle between the vectors P and Q.

  • If the dot product is positive then the angle between the vectors is below 90 degrees.
  • If the dot product is zero the vectors are perpendicular (at right-angles to each other).
  • If the dot product is negative then the angle between the vectors is more than 90 degrees.

Parameters

v1

vector3 | vector4 first vector

v2

vector3 | vector4 second vector

v1

vector3 | vector4 first vector

v2

vector3 | vector4 second vector

Returns

n

number dot product

n

number dot product

Examples

if vmath.dot(vector1, vector2) == 0 then
    -- The two vectors are perpendicular (at right-angles to each other)
    ...
end

vmath.inv

vmath.inv(m1)

The resulting matrix is the inverse of the supplied matrix.

For ortho-normal matrices, e.g. regular object transformation, use vmath.ortho_inv() instead. The specialized inverse for ortho-normalized matrices is much faster than the general inverse.

Parameters

m1

matrix4 matrix to invert

m1

matrix4 matrix to invert

Returns

m

matrix4 inverse of the supplied matrix

m

matrix4 inverse of the supplied matrix

Examples

local mat1 = vmath.matrix4_rotation_z(3.141592653)
local mat2 = vmath.inv(mat1)
-- M * inv(M) = identity matrix
print(mat1 * mat2) --> vmath.matrix4(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1)

vmath.length

vmath.length(v)

Returns the length of the supplied vector or quaternion.

If you are comparing the lengths of vectors or quaternions, you should compare the length squared instead as it is slightly more efficient to calculate (it eliminates a square root calculation).

Parameters

v

vector3 | vector4 | quat value of which to calculate the length

v

vector3 | vector4 | quat value of which to calculate the length

Returns

n

number length

n

number length

Examples

if vmath.length(self.velocity) < max_velocity then
    -- The speed (velocity vector) is below max.

    -- TODO: max_velocity can be expressed as squared
    -- so we can compare with length_sqr() instead.
    ...
end

vmath.length_sqr

vmath.length_sqr(v)

Returns the squared length of the supplied vector or quaternion.

Parameters

v

vector3 | vector4 | quat value of which to calculate the squared length

v

vector3 | vector4 | quat value of which to calculate the squared length

Returns

n

number squared length

n

number squared length

Examples

if vmath.length_sqr(vector1) < vmath.length_sqr(vector2) then
    -- Vector 1 has less magnitude than vector 2
    ...
end

vmath.lerp

vmath.lerp(t, v1, v2)

Linearly interpolate between two vectors. The function treats the vectors as positions and interpolates between the positions in a straight line. Lerp is useful to describe transitions from one place to another over time.

The function does not clamp t between 0 and 1.

Parameters

t

number interpolation parameter, 0-1

v1

vector3 | vector4 vector to lerp from

v2

vector3 | vector4 vector to lerp to

t

number interpolation parameter, 0-1

v1

vector3 | vector4 vector to lerp from

v2

vector3 | vector4 vector to lerp to

Returns

v

vector3 | vector4 the lerped vector

v

vector3 | vector4 the lerped vector

Examples

function init(self)
    self.t = 0
end

function update(self, dt)
    self.t = self.t + dt
    if self.t <= 1 then
        local startpos = vmath.vector3(0, 600, 0)
        local endpos = vmath.vector3(600, 0, 0)
        local pos = vmath.lerp(self.t, startpos, endpos)
        go.set_position(pos, "go")
    end
end

vmath.lerp

vmath.lerp(t, q1, q2)

Linearly interpolate between two quaternions. Linear interpolation of rotations are only useful for small rotations. For interpolations of arbitrary rotations, vmath.slerp yields much better results.

The function does not clamp t between 0 and 1.

Parameters

t

number interpolation parameter, 0-1

q1

quaternion quaternion to lerp from

q2

quaternion quaternion to lerp to

t

number interpolation parameter, 0-1

q1

quaternion quaternion to lerp from

q2

quaternion quaternion to lerp to

Returns

q

quaternion the lerped quaternion

q

quaternion the lerped quaternion

Examples

function init(self)
    self.t = 0
end

function update(self, dt)
    self.t = self.t + dt
    if self.t <= 1 then
        local startrot = vmath.quat_rotation_z(0)
        local endrot = vmath.quat_rotation_z(3.141592653)
        local rot = vmath.lerp(self.t, startrot, endrot)
        go.set_rotation(rot, "go")
    end
end

vmath.lerp

vmath.lerp(t, n1, n2)

Linearly interpolate between two values. Lerp is useful to describe transitions from one value to another over time.

The function does not clamp t between 0 and 1.

Parameters

t

number interpolation parameter, 0-1

n1

number number to lerp from

n2

number number to lerp to

t

number interpolation parameter, 0-1

n1

number number to lerp from

n2

number number to lerp to

Returns

n

number the lerped number

n

number the lerped number

Examples

function init(self)
    self.t = 0
end

function update(self, dt)
    self.t = self.t + dt
    if self.t <= 1 then
        local startx = 0
        local endx = 600
        local x = vmath.lerp(self.t, startx, endx)
        go.set_position(vmath.vector3(x, 100, 0), "go")
    end
end

vmath.matrix4

vmath.matrix4()

The resulting identity matrix describes a transform with no translation or rotation.

Returns

m

matrix4 identity matrix

m

matrix4 identity matrix

Examples

local mat = vmath.matrix4()
print(mat) --> vmath.matrix4(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1)
-- get column 0:
print(mat.c0) --> vmath.vector4(1, 0, 0, 0)
-- get the value in row 3 and column 2:
print(mat.m32) --> 0

vmath.matrix4

vmath.matrix4(m1)

Creates a new matrix with all components set to the corresponding values from the supplied matrix. I.e. the function creates a copy of the given matrix.

Parameters

m1

matrix4 existing matrix

m1

matrix4 existing matrix

Returns

m

matrix4 matrix which is a copy of the specified matrix

m

matrix4 matrix which is a copy of the specified matrix

Examples

local mat1 = vmath.matrix4_rotation_x(3.141592653)
local mat2 = vmath.matrix4(mat1)
if mat1 == mat2 then
    -- yes, they are equal
    print(mat2) --> vmath.matrix4(1, 0, 0, 0, 0, -1, 8.7422776573476e-08, 0, 0, -8.7422776573476e-08, -1, 0, 0, 0, 0, 1)
end

vmath.matrix4_axis_angle

vmath.matrix4_axis_angle(v, angle)

The resulting matrix describes a rotation around the axis by the specified angle.

Parameters

v

vector3 axis

angle

number angle in radians

v

vector3 axis

angle

number angle in radians

Returns

m

matrix4 matrix represented by axis and angle

m

matrix4 matrix represented by axis and angle

Examples

local vec = vmath.vector4(1, 1, 0, 0)
local axis = vmath.vector3(0, 0, 1) -- z-axis
local mat = vmath.matrix4_axis_angle(axis, 3.141592653)
print(mat * vec) --> vmath.vector4(-0.99999994039536, -1.0000001192093, 0, 0)

vmath.matrix4_from_quat

vmath.matrix4_from_quat(q)

The resulting matrix describes the same rotation as the quaternion, but does not have any translation (also like the quaternion).

Parameters

q

quaternion quaternion to create matrix from

q

quaternion quaternion to create matrix from

Returns

m

matrix4 matrix represented by quaternion

m

matrix4 matrix represented by quaternion

Examples

local vec = vmath.vector4(1, 1, 0, 0)
local quat = vmath.quat_rotation_z(3.141592653)
local mat = vmath.matrix4_from_quat(quat)
print(mat * vec) --> vmath.matrix4_frustum(-1, 1, -1, 1, 1, 1000)

vmath.matrix4_frustum

vmath.matrix4_frustum(left, right, bottom, top, near, far)

Constructs a frustum matrix from the given values. The left, right, top and bottom coordinates of the view cone are expressed as distances from the center of the near clipping plane. The near and far coordinates are expressed as distances from the tip of the view frustum cone.

Parameters

left

number coordinate for left clipping plane

right

number coordinate for right clipping plane

bottom

number coordinate for bottom clipping plane

top

number coordinate for top clipping plane

near

number coordinate for near clipping plane

far

number coordinate for far clipping plane

left

number coordinate for left clipping plane

right

number coordinate for right clipping plane

bottom

number coordinate for bottom clipping plane

top

number coordinate for top clipping plane

near

number coordinate for near clipping plane

far

number coordinate for far clipping plane

Returns

m

matrix4 matrix representing the frustum

m

matrix4 matrix representing the frustum

Examples

-- Construct a projection frustum with a vertical and horizontal
-- FOV of 45 degrees. Useful for rendering a square view.
local proj = vmath.matrix4_frustum(-1, 1, -1, 1, 1, 1000)
render.set_projection(proj)

vmath.matrix4_look_at

vmath.matrix4_look_at(eye, look_at, up)

The resulting matrix is created from the supplied look-at parameters. This is useful for constructing a view matrix for a camera or rendering in general.

Parameters

eye

vector3 eye position

look_at

vector3 look-at position

up

vector3 up vector

eye

vector3 eye position

look_at

vector3 look-at position

up

vector3 up vector

Returns

m

matrix4 look-at matrix

m

matrix4 look-at matrix

Examples

-- Set up a perspective camera at z 100 with 45 degrees (pi/2) FOV
-- Aspect ratio 4:3
local eye = vmath.vector3(0, 0, 100)
local look_at = vmath.vector3(0, 0, 0)
local up = vmath.vector3(0, 1, 0)
local view = vmath.matrix4_look_at(eye, look_at, up)
render.set_view(view)
local proj = vmath.matrix4_perspective(3.141592/2, 4/3, 1, 1000)
render.set_projection(proj)

vmath.matrix4_orthographic

vmath.matrix4_orthographic(left, right, bottom, top, near, far)

Creates an orthographic projection matrix. This is useful to construct a projection matrix for a camera or rendering in general.

Parameters

left

number coordinate for left clipping plane

right

number coordinate for right clipping plane

bottom

number coordinate for bottom clipping plane

top

number coordinate for top clipping plane

near

number coordinate for near clipping plane

far

number coordinate for far clipping plane

left

number coordinate for left clipping plane

right

number coordinate for right clipping plane

bottom

number coordinate for bottom clipping plane

top

number coordinate for top clipping plane

near

number coordinate for near clipping plane

far

number coordinate for far clipping plane

Returns

m

matrix4 orthographic projection matrix

m

matrix4 orthographic projection matrix

Examples

-- Set up an orthographic projection based on the width and height
-- of the game window.
local w = render.get_width()
local h = render.get_height()
local proj = vmath.matrix4_orthographic(- w / 2, w / 2, -h / 2, h / 2, -1000, 1000)
render.set_projection(proj)

vmath.matrix4_perspective

vmath.matrix4_perspective(fov, aspect, near, far)

Creates a perspective projection matrix. This is useful to construct a projection matrix for a camera or rendering in general.

Parameters

fov

number angle of the full vertical field of view in radians

aspect

number aspect ratio

near

number coordinate for near clipping plane

far

number coordinate for far clipping plane

fov

number angle of the full vertical field of view in radians

aspect

number aspect ratio

near

number coordinate for near clipping plane

far

number coordinate for far clipping plane

Returns

m

matrix4 perspective projection matrix

m

matrix4 perspective projection matrix

Examples

-- Set up a perspective camera at z 100 with 45 degrees (pi/2) FOV
-- Aspect ratio 4:3
local eye = vmath.vector3(0, 0, 100)
local look_at = vmath.vector3(0, 0, 0)
local up = vmath.vector3(0, 1, 0)
local view = vmath.matrix4_look_at(eye, look_at, up)
render.set_view(view)
local proj = vmath.matrix4_perspective(3.141592/2, 4/3, 1, 1000)
render.set_projection(proj)

vmath.matrix4_rotation_x

vmath.matrix4_rotation_x(angle)

The resulting matrix describes a rotation around the x-axis by the specified angle.

Parameters

angle

number angle in radians around x-axis

angle

number angle in radians around x-axis

Returns

m

matrix4 matrix from rotation around x-axis

m

matrix4 matrix from rotation around x-axis

Examples

local vec = vmath.vector4(1, 1, 0, 0)
local mat = vmath.matrix4_rotation_x(3.141592653)
print(mat * vec) --> vmath.vector4(1, -1, -8.7422776573476e-08, 0)

vmath.matrix4_rotation_y

vmath.matrix4_rotation_y(angle)

The resulting matrix describes a rotation around the y-axis by the specified angle.

Parameters

angle

number angle in radians around y-axis

angle

number angle in radians around y-axis

Returns

m

matrix4 matrix from rotation around y-axis

m

matrix4 matrix from rotation around y-axis

Examples

local vec = vmath.vector4(1, 1, 0, 0)
local mat = vmath.matrix4_rotation_y(3.141592653)
print(mat * vec) --> vmath.vector4(-1, 1, 8.7422776573476e-08, 0)

vmath.matrix4_rotation_z

vmath.matrix4_rotation_z(angle)

The resulting matrix describes a rotation around the z-axis by the specified angle.

Parameters

angle

number angle in radians around z-axis

angle

number angle in radians around z-axis

Returns

m

matrix4 matrix from rotation around z-axis

m

matrix4 matrix from rotation around z-axis

Examples

local vec = vmath.vector4(1, 1, 0, 0)
local mat = vmath.matrix4_rotation_z(3.141592653)
print(mat * vec) --> vmath.vector4(-0.99999994039536, -1.0000001192093, 0, 0)

vmath.mul_per_elem

vmath.mul_per_elem(v1, v2)

Performs an element wise multiplication between two vectors of the same type The returned value is a vector defined as (e.g. for a vector3):

v = vmath.mul_per_elem(a, b) = vmath.vector3(a.x * b.x, a.y * b.y, a.z * b.z)

Parameters

v1

vector3 | vector4 first vector

v2

vector3 | vector4 second vector

v1

vector3 | vector4 first vector

v2

vector3 | vector4 second vector

Returns

v

vector3 | vector4 multiplied vector

v

vector3 | vector4 multiplied vector

Examples

local blend_color = vmath.mul_per_elem(color1, color2)

vmath.normalize

vmath.normalize(v1)

Normalizes a vector, i.e. returns a new vector with the same direction as the input vector, but with length 1.

The length of the vector must be above 0, otherwise a division-by-zero will occur.

Parameters

v1

vector3 | vector4 | quat vector to normalize

v1

vector3 | vector4 | quat vector to normalize

Returns

v

vector3 | vector4 | quat new normalized vector

v

vector3 | vector4 | quat new normalized vector

Examples

local vec = vmath.vector3(1, 2, 3)
local norm_vec = vmath.normalize(vec)
print(norm_vec) --> vmath.vector3(0.26726123690605, 0.5345224738121, 0.80178368091583)
print(vmath.length(norm_vec)) --> 0.99999994039536

vmath.ortho_inv

vmath.ortho_inv(m1)

The resulting matrix is the inverse of the supplied matrix. The supplied matrix has to be an ortho-normal matrix, e.g. describe a regular object transformation.

For matrices that are not ortho-normal use the general inverse vmath.inv() instead.

Parameters

m1

matrix4 ortho-normalized matrix to invert

m1

matrix4 ortho-normalized matrix to invert

Returns

m

matrix4 inverse of the supplied matrix

m

matrix4 inverse of the supplied matrix

Examples

local mat1 = vmath.matrix4_rotation_z(3.141592653)
local mat2 = vmath.ortho_inv(mat1)
-- M * inv(M) = identity matrix
print(mat1 * mat2) --> vmath.matrix4(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1)

vmath.project

vmath.project(v1, v2)

Calculates the extent the projection of the first vector onto the second. The returned value is a scalar p defined as:

p = |P| cos θ / |Q|

where θ is the angle between the vectors P and Q.

Parameters

v1

vector3 vector to be projected on the second

v2

vector3 vector onto which the first will be projected, must not have zero length

v1

vector3 vector to be projected on the second

v2

vector3 vector onto which the first will be projected, must not have zero length

Returns

n

number the projected extent of the first vector onto the second

n

number the projected extent of the first vector onto the second

Examples

local v1 = vmath.vector3(1, 1, 0)
local v2 = vmath.vector3(2, 0, 0)
print(vmath.project(v1, v2)) --> 0.5

vmath.quat

vmath.quat()

Creates a new identity quaternion. The identity quaternion is equal to:

vmath.quat(0, 0, 0, 1)

Returns

q

quaternion new identity quaternion

q

quaternion new identity quaternion

Examples

local quat = vmath.quat()
print(quat) --> vmath.quat(0, 0, 0, 1)
print(quat.w) --> 1

vmath.quat

vmath.quat(q1)

Creates a new quaternion with all components set to the corresponding values from the supplied quaternion. I.e. This function creates a copy of the given quaternion.

Parameters

q1

quaternion existing quaternion

q1

quaternion existing quaternion

Returns

q

quaternion new quaternion

q

quaternion new quaternion

Examples

local quat1 = vmath.quat(1, 2, 3, 4)
local quat2 = vmath.quat(quat1)
if quat1 == quat2 then
    -- yes, they are equal
    print(quat2) --> vmath.quat(1, 2, 3, 4)
end

vmath.quat

vmath.quat(x, y, z, w)

Creates a new quaternion with the components set according to the supplied parameter values.

Parameters

x

number x coordinate

y

number y coordinate

z

number z coordinate

w

number w coordinate

x

number x coordinate

y

number y coordinate

z

number z coordinate

w

number w coordinate

Returns

q

quaternion new quaternion

q

quaternion new quaternion

Examples

local quat = vmath.quat(1, 2, 3, 4)
print(quat) --> vmath.quat(1, 2, 3, 4)

vmath.quat_axis_angle

vmath.quat_axis_angle(v, angle)

The resulting quaternion describes a rotation of angle radians around the axis described by the unit vector v.

Parameters

v

vector3 axis

angle

number angle

v

vector3 axis

angle

number angle

Returns

q

quaternion quaternion representing the axis-angle rotation

q

quaternion quaternion representing the axis-angle rotation

Examples

local axis = vmath.vector3(1, 0, 0)
local rot = vmath.quat_axis_angle(axis, 3.141592653)
local vec = vmath.vector3(1, 1, 0)
print(vmath.rotate(rot, vec)) --> vmath.vector3(1, -1, -8.7422776573476e-08)

vmath.quat_basis

vmath.quat_basis(x, y, z)

The resulting quaternion describes the rotation from the identity quaternion (no rotation) to the coordinate system as described by the given x, y and z base unit vectors.

Parameters

x

vector3 x base vector

y

vector3 y base vector

z

vector3 z base vector

x

vector3 x base vector

y

vector3 y base vector

z

vector3 z base vector

Returns

q

quaternion quaternion representing the rotation of the specified base vectors

q

quaternion quaternion representing the rotation of the specified base vectors

Examples

-- Axis rotated 90 degrees around z.
local rot_x = vmath.vector3(0, -1, 0)
local rot_y = vmath.vector3(1, 0, 0)
local z = vmath.vector3(0, 0, 1)
local rot1 = vmath.quat_basis(rot_x, rot_y, z)
local rot2 = vmath.quat_from_to(vmath.vector3(0, 1, 0), vmath.vector3(1, 0, 0))
if rot1 == rot2 then
    -- These quaternions are equal!
    print(rot2) --> vmath.quat(0, 0, -0.70710676908493, 0.70710676908493)
end

vmath.quat_from_to

vmath.quat_from_to(v1, v2)

The resulting quaternion describes the rotation that, if applied to the first vector, would rotate the first vector to the second. The two vectors must be unit vectors (of length 1).

The result is undefined if the two vectors point in opposite directions

Parameters

v1

vector3 first unit vector, before rotation

v2

vector3 second unit vector, after rotation

v1

vector3 first unit vector, before rotation

v2

vector3 second unit vector, after rotation

Returns

q

quaternion quaternion representing the rotation from first to second vector

q

quaternion quaternion representing the rotation from first to second vector

Examples

local v1 = vmath.vector3(1, 0, 0)
local v2 = vmath.vector3(0, 1, 0)
local rot = vmath.quat_from_to(v1, v2)
print(vmath.rotate(rot, v1)) --> vmath.vector3(0, 0.99999994039536, 0)

vmath.quat_rotation_x

vmath.quat_rotation_x(angle)

The resulting quaternion describes a rotation of angle radians around the x-axis.

Parameters

angle

number angle in radians around x-axis

angle

number angle in radians around x-axis

Returns

q

quaternion quaternion representing the rotation around the x-axis

q

quaternion quaternion representing the rotation around the x-axis

Examples

local rot = vmath.quat_rotation_x(3.141592653)
local vec = vmath.vector3(1, 1, 0)
print(vmath.rotate(rot, vec)) --> vmath.vector3(1, -1, -8.7422776573476e-08)

vmath.quat_rotation_y

vmath.quat_rotation_y(angle)

The resulting quaternion describes a rotation of angle radians around the y-axis.

Parameters

angle

number angle in radians around y-axis

angle

number angle in radians around y-axis

Returns

q

quaternion quaternion representing the rotation around the y-axis

q

quaternion quaternion representing the rotation around the y-axis

Examples

local rot = vmath.quat_rotation_y(3.141592653)
local vec = vmath.vector3(1, 1, 0)
print(vmath.rotate(rot, vec)) --> vmath.vector3(-1, 1, 8.7422776573476e-08)

vmath.quat_rotation_z

vmath.quat_rotation_z(angle)

The resulting quaternion describes a rotation of angle radians around the z-axis.

Parameters

angle

number angle in radians around z-axis

angle

number angle in radians around z-axis

Returns

q

quaternion quaternion representing the rotation around the z-axis

q

quaternion quaternion representing the rotation around the z-axis

Examples

local rot = vmath.quat_rotation_z(3.141592653)
local vec = vmath.vector3(1, 1, 0)
print(vmath.rotate(rot, vec)) --> vmath.vector3(-0.99999988079071, -1, 0)

vmath.rotate

vmath.rotate(q, v1)

Returns a new vector from the supplied vector that is rotated by the rotation described by the supplied quaternion.

Parameters

q

quatertion quaternion

v1

vector3 vector to rotate

q

quatertion quaternion

v1

vector3 vector to rotate

Returns

v

vector3 the rotated vector

v

vector3 the rotated vector

Examples

local vec = vmath.vector3(1, 1, 0)
local rot = vmath.quat_rotation_z(3.141592563)
print(vmath.rotate(rot, vec)) --> vmath.vector3(-1.0000002384186, -0.99999988079071, 0)

vmath.slerp

vmath.slerp(t, v1, v2)

Spherically interpolates between two vectors. The difference to lerp is that slerp treats the vectors as directions instead of positions in space.

The direction of the returned vector is interpolated by the angle and the magnitude is interpolated between the magnitudes of the from and to vectors.

Slerp is computationally more expensive than lerp. The function does not clamp t between 0 and 1.

Parameters

t

number interpolation parameter, 0-1

v1

vector3 | vector4 vector to slerp from

v2

vector3 | vector4 vector to slerp to

t

number interpolation parameter, 0-1

v1

vector3 | vector4 vector to slerp from

v2

vector3 | vector4 vector to slerp to

Returns

v

vector3 | vector4 the slerped vector

v

vector3 | vector4 the slerped vector

Examples

function init(self)
    self.t = 0
end

function update(self, dt)
    self.t = self.t + dt
    if self.t <= 1 then
        local startpos = vmath.vector3(0, 600, 0)
        local endpos = vmath.vector3(600, 0, 0)
        local pos = vmath.slerp(self.t, startpos, endpos)
        go.set_position(pos, "go")
    end
end

vmath.slerp

vmath.slerp(t, q1, q2)

Slerp travels the torque-minimal path maintaining constant velocity, which means it travels along the straightest path along the rounded surface of a sphere. Slerp is useful for interpolation of rotations.

Slerp travels the torque-minimal path, which means it travels along the straightest path the rounded surface of a sphere.

The function does not clamp t between 0 and 1.

Parameters

t

number interpolation parameter, 0-1

q1

quaternion quaternion to slerp from

q2

quaternion quaternion to slerp to

t

number interpolation parameter, 0-1

q1

quaternion quaternion to slerp from

q2

quaternion quaternion to slerp to

Returns

q

quaternion the slerped quaternion

q

quaternion the slerped quaternion

Examples

function init(self)
    self.t = 0
end

function update(self, dt)
    self.t = self.t + dt
    if self.t <= 1 then
        local startrot = vmath.quat_rotation_z(0)
        local endrot = vmath.quat_rotation_z(3.141592653)
        local rot = vmath.slerp(self.t, startrot, endrot)
        go.set_rotation(rot, "go")
    end
end

vmath.vector

vmath.vector(t)

Creates a vector of arbitrary size. The vector is initialized with numeric values from a table.

The table values are converted to floating point values. If a value cannot be converted, a 0 is stored in that value position in the vector.

Parameters

t

table table of numbers

t

table table of numbers

Returns

v

vector new vector

v

vector new vector

Examples

How to create a vector with custom data to be used for animation easing:

local values = { 0, 0.5, 0 }
local vec = vmath.vector(values)
print(vec) --> vmath.vector (size: 3)
print(vec[2]) --> 0.5

vmath.vector3

vmath.vector3()

Creates a new zero vector with all components set to 0.

Returns

v

vector3 new zero vector

v

vector3 new zero vector

Examples

local vec = vmath.vector3()
pprint(vec) --> vmath.vector3(0, 0, 0)
print(vec.x) --> 0

vmath.vector3

vmath.vector3(n)

Creates a new vector with all components set to the supplied scalar value.

Parameters

n

number scalar value to splat

n

number scalar value to splat

Returns

v

vector3 new vector

v

vector3 new vector

Examples

local vec = vmath.vector3(1.0)
print(vec) --> vmath.vector3(1, 1, 1)
print(vec.x) --> 1

vmath.vector3

vmath.vector3(v1)

Creates a new vector with all components set to the corresponding values from the supplied vector. I.e. This function creates a copy of the given vector.

Parameters

v1

vector3 existing vector

v1

vector3 existing vector

Returns

v

vector3 new vector

v

vector3 new vector

Examples

local vec1 = vmath.vector3(1.0)
local vec2 = vmath.vector3(vec1)
if vec1 == vec2 then
    -- yes, they are equal
    print(vec2) --> vmath.vector3(1, 1, 1)
end

vmath.vector3

vmath.vector3(x, y, z)

Creates a new vector with the components set to the supplied values.

Parameters

x

number x coordinate

y

number y coordinate

z

number z coordinate

x

number x coordinate

y

number y coordinate

z

number z coordinate

Returns

v

vector3 new vector

v

vector3 new vector

Examples

local vec = vmath.vector3(1.0, 2.0, 3.0)
print(vec) --> vmath.vector3(1, 2, 3)
print(-vec) --> vmath.vector3(-1, -2, -3)
print(vec * 2) --> vmath.vector3(2, 4, 6)
print(vec + vmath.vector3(2.0)) --> vmath.vector3(3, 4, 5)
print(vec - vmath.vector3(2.0)) --> vmath.vector3(-1, 0, 1)

vmath.vector4

vmath.vector4()

Creates a new zero vector with all components set to 0.

Returns

v

vector4 new zero vector

v

vector4 new zero vector

Examples

local vec = vmath.vector4()
print(vec) --> vmath.vector4(0, 0, 0, 0)
print(vec.w) --> 0

vmath.vector4

vmath.vector4(n)

Creates a new vector with all components set to the supplied scalar value.

Parameters

n

number scalar value to splat

n

number scalar value to splat

Returns

v

vector4 new vector

v

vector4 new vector

Examples

local vec = vmath.vector4(1.0)
print(vec) --> vmath.vector4(1, 1, 1, 1)
print(vec.w) --> 1

vmath.vector4

vmath.vector4(v1)

Creates a new vector with all components set to the corresponding values from the supplied vector. I.e. This function creates a copy of the given vector.

Parameters

v1

vector4 existing vector

v1

vector4 existing vector

Returns

v

vector4 new vector

v

vector4 new vector

Examples

local vect1 = vmath.vector4(1.0)
local vect2 = vmath.vector4(vec1)
if vec1 == vec2 then
    -- yes, they are equal
    print(vec2) --> vmath.vector4(1, 1, 1, 1)
end

vmath.vector4

vmath.vector4(x, y, z, w)

Creates a new vector with the components set to the supplied values.

Parameters

x

number x coordinate

y

number y coordinate

z

number z coordinate

w

number w coordinate

x

number x coordinate

y

number y coordinate

z

number z coordinate

w

number w coordinate

Returns

v

vector4 new vector

v

vector4 new vector

Examples

local vec = vmath.vector4(1.0, 2.0, 3.0, 4.0)
print(vec) --> vmath.vector4(1, 2, 3, 4)
print(-vec) --> vmath.vector4(-1, -2, -3, -4)
print(vec * 2) --> vmath.vector4(2, 4, 6, 8)
print(vec + vmath.vector4(2.0)) --> vmath.vector4(3, 4, 5, 6)
print(vec - vmath.vector4(2.0)) --> vmath.vector4(-1, 0, 1, 2)