Vector math API documentation

Version: beta

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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.

PARAMETERS

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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.matrix4_translation()

vmath.matrix4_translation(position)

The resulting matrix describes a translation of a point in euclidean space.

PARAMETERS

RETURNS

EXAMPLES

-- Set camera view from custom view and translation matrices
local mat_trans = vmath.matrix4_translation(vmath.vector3(0, 10, 100))
local mat_view  = vmath.matrix4_rotation_y(-3.141592/4)
render.set_view(mat_view * mat_trans)

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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)

PARAMETERS

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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.

PARAMETERS

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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.

PARAMETERS

RETURNS

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

RETURNS

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

RETURNS

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

RETURNS

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)