463 lines
11 KiB
Lua
463 lines
11 KiB
Lua
--- A quaternion and associated utilities.
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-- @module quat
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local modules = (...):gsub('%.[^%.]+$', '') .. "."
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local constants = require(modules .. "constants")
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local vec3 = require(modules .. "vec3")
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local DOT_THRESHOLD = constants.DOT_THRESHOLD
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local DBL_EPSILON = constants.DBL_EPSILON
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local abs = math.abs
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local acos = math.acos
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local asin = math.asin
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local atan2 = math.atan2
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local cos = math.cos
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local sin = math.sin
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local min = math.min
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local max = math.max
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local sqrt = math.sqrt
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local pi = math.pi
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local quat = {}
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-- Private constructor.
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local function new(x, y, z, w)
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local q = {}
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q.x, q.y, q.z, q.w = x, y, z, w
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return setmetatable(q, quat_mt)
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end
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quat.unit = new(0, 0, 0, 1)
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quat.zero = new(0, 0, 0, 0)
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-- Do the check to see if JIT is enabled. If so use the optimized FFI structs.
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local status, ffi
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if type(jit) == "table" and jit.status() then
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status, ffi = pcall(require, "ffi")
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if status then
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ffi.cdef "typedef struct { double x, y, z, w;} cpml_quat;"
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new = ffi.typeof("cpml_quat")
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end
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end
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--- The public constructor.
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-- @param x Can be of two types: </br>
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-- number x component
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-- table {x, y, z, w} or {x = x, y = y, z = z, w = w}
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-- @tparam number y y component
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-- @tparam number z z component
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-- @tparam number w w component
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function quat.new(x, y, z, w)
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-- number, number, number, number
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if x and y and z and w then
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assert(type(x) == "number", "new: Wrong argument type for x (<number> expected)")
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assert(type(y) == "number", "new: Wrong argument type for y (<number> expected)")
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assert(type(z) == "number", "new: Wrong argument type for z (<number> expected)")
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assert(type(w) == "number", "new: Wrong argument type for w (<number> expected)")
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return new(x, y, z, w)
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-- {x=x, y=y, z=z, w=w} or {x, y, z, w}
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elseif type(x) == "table" then
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local x, y, z, w = x.x or x[1], x.y or x[2], x.z or x[3], x.w or x[4]
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assert(type(x) == "number", "new: Wrong argument type for x (<number> expected)")
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assert(type(y) == "number", "new: Wrong argument type for y (<number> expected)")
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assert(type(z) == "number", "new: Wrong argument type for z (<number> expected)")
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assert(type(w) == "number", "new: Wrong argument type for w (<number> expected)")
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return new(x, y, z, w)
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else
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return new(0, 0, 0, 1)
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end
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end
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--- Create a quaternion from an axis, angle pair.
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-- @tparam number angle
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-- @tparam vec3 axis
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-- @treturn quat
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function quat.from_angle_axis(angle, axis)
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local len = vec3.len(axis)
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local s = sin(angle * 0.5)
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local c = cos(angle * 0.5)
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return new(axis.x * s, axis.y * s, axis.z * s, c)
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end
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--- Create a quaternion from a normalized, up vector pair.
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-- @tparam vec3 normal
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-- @tparam vec3 up
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-- @treturn quat
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function quat.from_direction(normal, up)
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local a = vec3.cross(vec3(), up, normal)
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local d = vec3.dot(up, normal)
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return new(a.x, a.y, a.z, d + 1)
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end
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--- Clone a quaternion.
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-- @tparam quat a
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-- @treturn quat clone
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function quat.clone(a)
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return new(a.x, a.y, a.z, a.w)
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end
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--- Component-wise add a quaternion.
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-- @tparam quat out
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-- @tparam quat a
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-- @tparam quat b
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-- @treturn quat out
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function quat.add(out, a, b)
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out.x = a.x + b.x
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out.y = a.y + b.y
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out.z = a.z + b.z
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out.w = a.w + b.w
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return out
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end
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--- Component-wise subtract a quaternion.
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-- @tparam quat out
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-- @tparam quat a
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-- @tparam quat b
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-- @treturn quat out
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function quat.sub(out, a, b)
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out.x = a.x - b.x
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out.y = a.y - b.y
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out.z = a.z - b.z
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out.w = a.w - b.w
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return out
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end
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--- Perform a quaternion multiplication.
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-- @tparam quat out
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-- @tparam quat a
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-- @tparam quat b
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-- @treturn quat out
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function quat.mul(out, a, b)
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out.x = a.x * b.w + a.w * b.x + a.y * b.z - a.z * b.y
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out.y = a.y * b.w + a.w * b.y + a.z * b.x - a.x * b.z
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out.z = a.z * b.w + a.w * b.z + a.x * b.y - a.y * b.x
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out.w = a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z
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return out
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end
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--- Perform a quaternion and vec3 multiplication.
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-- @tparam quat out
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-- @tparam quat a
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-- @tparam vec3 b
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-- @treturn vec3 out
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local uv, uuv = vec3(), vec3()
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function quat.mul_vec3(out, a, b)
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vec3.cross(uv, a, b)
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vec3.cross(uuv, a, uv)
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vec3.mul(out, uv, a.w)
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vec3.add(out, out, uuv)
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vec3.mul(out, out, 2)
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vec3.add(out, b, out)
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return out
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end
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--- Pow a quaternion by an exponent
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-- @tparam quat out
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-- @tparam quat a
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-- @tparam number n
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-- @treturn quat out
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function quat.pow(out, a, n)
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if n == 0 then
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out.x = 0
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out.y = 0
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out.z = 0
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out.w = 1
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elseif n > 0 then
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out.x = a.x^(n-1)
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out.y = a.y^(n-1)
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out.z = a.z^(n-1)
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out.w = a.w^(n-1)
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quat.mul(out, a, out)
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elseif n < 0 then
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quat.reciprocal(out, a)
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out.x = out.x^(-n)
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out.y = out.y^(-n)
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out.z = out.z^(-n)
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out.w = out.w^(-n)
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end
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return out
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end
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--- Normalize a quaternion.
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-- @tparam quat out
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-- @tparam quat a
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-- @treturn quat out
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function quat.normalize(out, a)
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local l = 1 / quat.len(a)
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quat.scale(out, a, l)
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return out
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end
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--- Return the inner angle between two quaternions.
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-- @tparam quat a
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-- @tparam quat b
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-- @treturn number angle
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function quat.dot(a, b)
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return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w
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end
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--- Return the length of a quaternion.
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-- @tparam quat a
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-- @treturn number len
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function quat.len(a)
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return sqrt(a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w)
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end
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--- Return the squared length of a quaternion.
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-- @tparam quat a
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-- @treturn number len
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function quat.len2(a)
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return a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w
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end
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--- Component-wise scale a quaternion by a scalar.
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-- @tparam quat out
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-- @tparam quat a
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-- @tparam number s
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-- @treturn quat out
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function quat.scale(out, a, s)
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out.x = a.x * s
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out.y = a.y * s
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out.z = a.z * s
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out.w = a.w * s
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return out
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end
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--- Return the conjugate of a quaternion.
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-- @tparam quat out
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-- @tparam quat a
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-- @treturn quat out
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function quat.conjugate(out, a)
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out.x = -a.x
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out.y = -a.y
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out.z = -a.z
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out.w = a.w
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return out
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end
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--- Return the inverse of a quaternion.
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-- @tparam quat out
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-- @tparam quat a
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-- @treturn quat out
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function quat.inverse(out, a)
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quat.conjugate(out, a)
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quat.normalize(out, out)
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return out
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end
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--- Return the reciprocal of a quaternion.
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-- @tparam quat out
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-- @tparam quat a
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-- @treturn quat out
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function quat.reciprocal(out, a)
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assert(not quat.is_zer(a), "Cannot reciprocate a zero quaternion")
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local l = quat.len2(a)
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quat.conjugate(out, a)
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quat.scale(out, out, 1 / l)
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return out
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end
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--- Linearly interpolate from one quaternion to the next.
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-- @tparam quat out
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-- @tparam quat a
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-- @tparam quat b
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-- @tparam number s 0-1 range number; 0 = a 1 = b
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-- @treturn quat out
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function quat.lerp(out, a, b, s)
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quat.sub(out, b, a)
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quat.mul(out, out, s)
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quat.add(out, a, out)
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quat.normalize(out, out)
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return out
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end
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--- Slerp from one quaternion to the next.
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-- @tparam quat out
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-- @tparam quat a
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-- @tparam quat b
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-- @tparam number s 0-1 range number; 0 = a 1 = b
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-- @treturn quat out
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function quat.slerp(out, a, b, s)
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local dot = quat.dot(a, b)
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if dot < 0 then
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quat.scale(a, a, -1)
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dot = -dot
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end
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if dot > DOT_THRESHOLD then
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quat.lerp(out, a, b, s)
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return
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end
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dot = min(max(dot, -1), 1)
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local temp = quat.new()
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local theta = acos(dot) * s
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quat.scale(out, a, dot)
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quat.sub(out, b, out)
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quat.normalize(out, out)
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quat.scale(out, out, sin(theta))
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quat.scale(temp, a, cos(theta))
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quat.add(out, temp, out)
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return out
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end
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--- Return the imaginary part of the quaternion as a vec3.
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-- @tparam vec3 out
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-- @tparam quat a
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-- @treturn vec3 out
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function quat.imaginary(out, a)
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out.x = a.x
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out.y = a.y
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out.z = a.z
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return out
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end
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--- Return the real part of a quaternion.
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-- @tparam quat a
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-- @treturn number real
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function quat.real(a)
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return a.w
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end
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--- Unpack a quaternion into form x,y,z,w.
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-- @tparam quat a
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-- @treturn number x
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-- @treturn number y
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-- @treturn number z
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-- @treturn number w
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function quat.unpack(a)
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return a.x, a.y, a.z, a.w
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end
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function quat.to_angle_axis(a)
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if a.w > 1 or a.w < -1 then
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a = quat.normalize(a, a)
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end
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local angle = 2 * acos(a.w)
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local s = sqrt(1 - a.w * a.w)
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local x, y, z
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if s < constants.DBL_EPSILON then
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x = a.x
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y = a.y
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z = a.z
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else
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x = a.x / s -- normalize axis
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y = a.y / s
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z = a.z / s
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end
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return angle, vec3(x, y, z)
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end
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function quat.to_vec3(out, a)
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out.x = a.x
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out.y = a.y
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out.z = a.z
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return out
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end
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--- Return a string formatted "{x, y, z, w}"
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-- @tparam quat a
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-- @treturn string
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function quat.to_string(a)
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return string.format("(%+0.3f,%+0.3f,%+0.3f,%+0.3f)", a.x, a.y, a.z, a.w)
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end
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--- Return a boolean showing if a table is or is not a quat
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-- @param q object to be tested
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-- @treturn boolean
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function quat.is_quat(q)
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return
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(
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type(v) == "table" or
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type(v) == "cdata"
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) and
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type(v.x) == "number" and
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type(v.y) == "number" and
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type(v.z) == "number" and
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type(v.w) == "number"
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end
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function quat.is_zero(a)
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return
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a.x == 0 and
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a.y == 0 and
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a.z == 0 and
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a.w == 0
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end
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function quat.is_real(a)
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return
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a.x == 0 and
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a.y == 0 and
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a.z == 0
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end
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function quat.is_imaginary(a)
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return a.w == 0
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end
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local quat_mt = {}
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quat_mt.__index = quat
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quat_mt.__tostring = quat.to_string
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function quat_mt.__call(self, x, y, z, w)
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return new(x, y, z, w)
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end
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function quat_mt.__unm(a)
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return quat.scale(new(), a, -1)
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end
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function quat_mt.__eq(a,b)
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assert(quat.is_quat(a), "__eq: Wrong argument type for left hand operant. (<cpml.quat> expected)")
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assert(quat.is_quat(b), "__eq: Wrong argument type for right hand operant. (<cpml.quat> expected)")
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return a.x == b.x and a.y == b.y and a.z == b.z and a.w == b.w
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end
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function quat_mt.__add(a, b)
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assert(quat.is_quat(a), "__add: Wrong argument type for left hand operant. (<cpml.quat> expected)")
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assert(quat.is_quat(b), "__add: Wrong argument type for right hand operant. (<cpml.quat> expected)")
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return quat.add(new(), a, b)
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end
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function quat_mt.__sub(a, b)
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assert(quat.is_quat(a), "__sub: Wrong argument type for left hand operant. (<cpml.quat> expected)")
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assert(quat.is_quat(b), "__sub: Wrong argument type for right hand operant. (<cpml.quat> expected)")
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return quat.sub(new(), a, b)
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end
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function quat_mt.__mul(a, b)
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assert(quat.is_quat(a), "__mul: Wrong argument type for left hand operant. (<cpml.quat> expected)")
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assert(quat.is_quat(b) or vec3.is_vec3(b) or type(b) = "number", "__mul: Wrong argument type for right hand operant. (<cpml.quat> or <cpml.vec3> expected)")
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if quat.is_quat(b) then
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return quat.mul(new(), a, b)
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end
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if type(b) == "number" then
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return quat.scale(new(), a, b)
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end
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return quat.mul_vec3(vec3(), a, b)
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end
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function quat_mt.__pow(a, n)
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assert(quat.is_quat(a), "__pow: Wrong argument type for left hand operant. (<cpml.quat> expected)")
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assert(type(b) == "number", "__pow: Wrong argument type for right hand operant. (<number> expected)")
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return quat.pow(new(), a, n)
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end
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if status then
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ffi.metatype(new, quat_mt)
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end
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return setmetatable({}, quat_mt)
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