Vector math

Namespace: vmath Language: Lua Type: Defold Lua File: script_vmath.cpp Source: engine/script/src/script_vmath.cpp

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 (scaled) or divided by numbers.
• 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]

API

vmath.clamp

Type: FUNCTION Clamp input value to be in range of [min, max]. In case if input value has vector3|vector4 type return new vector3|vector4 with clamped value at every vector’s element. Min/max arguments can be vector3|vector4. In that case clamp excuted per every vector’s element

Parameters

• value (number

  vector3

  vector4) - Input value or vector of values

• min (number

  vector3

  vector4) - Min value(s) border

• max (number

  vector3

  vector4) - Max value(s) border

Returns

• clamped_value (number

  vector3

  vector4) - Clamped value or vector

Examples

local value1 = 56
print(vmath.clamp(value1, 89, 134)) -> 89
local v2 = vmath.vector3(190, 190, -10)
print(vmath.clamp(v2, -50, 150)) -> vmath.vector3(150, 150, -10)
local v3 = vmath.vector4(30, -30, 45, 1)
print(vmath.clamp(v3, 0, 20)) -> vmath.vector4(20, 0, 20, 1)

local min_v = vmath.vector4(0, -10, -10, 1)
print(vmath.clamp(v3, min_v, 20)) -> vmath.vector4(20, -10, 20, 1)

vmath.conj

Type: FUNCTION 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 (quaternion) - quaternion of which to calculate the conjugate

Returns

• q (quaternion) - the conjugate

Examples

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

vmath.cross

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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.euler_to_quat

Type: FUNCTION Converts euler angles (x, y, z) in degrees into a quaternion The error is guaranteed to be less than 0.001. If the first argument is vector3, its values are used as x, y, z angles.

Parameters

• x (number

  vector3) - rotation around x-axis in degrees or vector3 with euler angles in degrees

• y (number) - rotation around y-axis in degrees
• z (number) - rotation around z-axis in degrees

Returns

• q (quaternion) - quaternion describing an equivalent rotation (231 (YZX) rotation sequence)

Examples

local q = vmath.euler_to_quat(0, 45, 90)
print(q) --> vmath.quat(0.27059805393219, 0.27059805393219, 0.65328145027161, 0.65328145027161)

local v = vmath.vector3(0, 0, 90)
print(vmath.euler_to_quat(v)) --> vmath.quat(0, 0, 0.70710676908493, 0.70710676908493)

vmath.inv

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

  quaternion) - value of which to calculate the length

Returns

• 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

Type: FUNCTION Returns the squared length of the supplied vector or quaternion.

Parameters

• v (vector3

  vector4

  quaternion) - value of which to calculate the squared length

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

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

Parameters

• v (vector3) - axis
• angle (number) - angle in radians

Returns

• 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_compose

Type: FUNCTION Creates a new matrix constructed from separate translation vector, roation quaternion and scale vector

Parameters

• translation (vector3

  vector4) - translation

• rotation (quaternion) - rotation
• scale (vector3) - scale

Returns

• matrix (matrix4) - new matrix4

Examples

local translation = vmath.vector3(103, -95, 14)
local quat = vmath.quat(1, 2, 3, 4)
local scale = vmath.vector3(1, 0.5, 0.5)
local result = vmath.matrix4_compose(translation, quat, scale)
print(result) --> vmath.matrix4(-25, -10, 11, 103, 28, -9.5, 2, -95, -10, 10, -4.5, 14, 0, 0, 0, 1)

vmath.matrix4_frustum

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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_quat

Type: FUNCTION 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

Returns

• 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_quat(quat)
print(mat * vec) --> vmath.matrix4_frustum(-1, 1, -1, 1, 1, 1000)

vmath.matrix4_rotation_x

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

Parameters

• angle (number) - angle in radians around x-axis

Returns

• 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

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

Parameters

• angle (number) - angle in radians around y-axis

Returns

• 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

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

Parameters

• angle (number) - angle in radians around z-axis

Returns

• 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.matrix4_scale

Type: FUNCTION Creates a new matrix constructed from scale vector

Parameters

• scale (vector3) - scale

Returns

• matrix (matrix4) - new matrix4

Examples

local scale = vmath.vector3(1, 0.5, 0.5)
local result = vmath.matrix4_scale(scale)
print(result) --> vmath.matrix4(1, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 1)

vmath.matrix4_scale

Type: FUNCTION creates a new matrix4 from uniform scale

Parameters

• scale (number) - scale

Returns

• matrix (matrix4) - new matrix4

Examples

local result = vmath.matrix4_scale(0.5)
print(result) --> vmath.matrix4(0.5, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 1)

vmath.matrix4_scale

Type: FUNCTION Creates a new matrix4 from three scale components

Parameters

• scale_x (number) - scale along X axis
• scale_y (number) - sclae along Y axis
• scale_z (number) - scale along Z asis

Returns

• matrix (matrix4) - new matrix4

Examples

local result = vmath.matrix4_scale(1, 0.5, 0.5)
print(result) --> vmath.matrix4(1, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 1)

vmath.matrix4_translation

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

Parameters

• position (vector3

  vector4) - position vector to create matrix from

Returns

• m (matrix4) - matrix from the supplied position vector

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

Type: FUNCTION 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

Returns

• v (vector3

  vector4) - multiplied vector

Examples

local blend_color = vmath.mul_per_elem(color1, color2)

vmath.normalize

Type: FUNCTION 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

  quaternion) - vector to normalize

Returns

• v (vector3

  vector4

  quaternion) - 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION Creates a new identity quaternion. The identity quaternion is equal to: vmath.quat(0, 0, 0, 1)

Returns

• q (quaternion) - new identity quaternion

Examples

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

vmath.quat

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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_matrix4

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

Parameters

• matrix (matrix4) - source matrix4

Returns

• q (quaternion) - new quaternion

vmath.quat_rotation_x

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

Parameters

• angle (number) - angle in radians around x-axis

Returns

• 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

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

Parameters

• angle (number) - angle in radians around y-axis

Returns

• 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

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

Parameters

• angle (number) - angle in radians around z-axis

Returns

• 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.quat_to_euler

Type: FUNCTION Converts a quaternion into euler angles (r0, r1, r2), based on YZX rotation order. To handle gimbal lock (singularity at r1 ~ +/- 90 degrees), the cut off is at r0 = +/- 88.85 degrees, which snaps to +/- 90. The provided quaternion is expected to be normalized. The error is guaranteed to be less than +/- 0.02 degrees

Parameters

• q (quaternion) - source quaternion

Returns

• x (number) - euler angle x in degrees
• y (number) - euler angle y in degrees
• z (number) - euler angle z in degrees

Examples

local q = vmath.quat_rotation_z(math.rad(90))
print(vmath.quat_to_euler(q)) --> 0 0 90

local q2 = vmath.quat_rotation_y(math.rad(45)) * vmath.quat_rotation_z(math.rad(90))
local v = vmath.vector3(vmath.quat_to_euler(q2))
print(v) --> vmath.vector3(0, 45, 90)

vmath.rotate

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

Parameters

• q (quaternion) - quaternion
• v1 (vector3) - vector to rotate

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

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

Returns

• v (vector3) - new zero vector

Examples

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

vmath.vector3

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

Parameters

• n (number) - scalar value to splat

Returns

• v (vector3) - new vector

Examples

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

vmath.vector3

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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

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

Returns

• v (vector4) - new zero vector

Examples

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

vmath.vector4

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

Parameters

• n (number) - scalar value to splat

Returns

• 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

Type: FUNCTION 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

Returns

• 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

Type: FUNCTION 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

Returns

• 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)