mirror of
https://github.com/SashLilac/cambridge.git
synced 2024-11-22 08:29:02 -06:00
499 lines
13 KiB
Lua
499 lines
13 KiB
Lua
--- A quaternion and associated utilities.
|
|
-- @module quat
|
|
|
|
local modules = (...):gsub('%.[^%.]+$', '') .. "."
|
|
local constants = require(modules .. "constants")
|
|
local vec3 = require(modules .. "vec3")
|
|
local precond = require(modules .. "_private_precond")
|
|
local private = require(modules .. "_private_utils")
|
|
local DOT_THRESHOLD = constants.DOT_THRESHOLD
|
|
local DBL_EPSILON = constants.DBL_EPSILON
|
|
local acos = math.acos
|
|
local cos = math.cos
|
|
local sin = math.sin
|
|
local min = math.min
|
|
local max = math.max
|
|
local sqrt = math.sqrt
|
|
local quat = {}
|
|
local quat_mt = {}
|
|
|
|
-- Private constructor.
|
|
local function new(x, y, z, w)
|
|
return setmetatable({
|
|
x = x or 0,
|
|
y = y or 0,
|
|
z = z or 0,
|
|
w = w or 1
|
|
}, quat_mt)
|
|
end
|
|
|
|
-- Do the check to see if JIT is enabled. If so use the optimized FFI structs.
|
|
local status, ffi
|
|
if type(jit) == "table" and jit.status() then
|
|
status, ffi = pcall(require, "ffi")
|
|
if status then
|
|
ffi.cdef "typedef struct { double x, y, z, w;} cpml_quat;"
|
|
new = ffi.typeof("cpml_quat")
|
|
end
|
|
end
|
|
|
|
-- Statically allocate a temporary variable used in some of our functions.
|
|
local tmp = new()
|
|
local qv, uv, uuv = vec3(), vec3(), vec3()
|
|
|
|
--- Constants
|
|
-- @table quat
|
|
-- @field unit Unit quaternion
|
|
-- @field zero Empty quaternion
|
|
quat.unit = new(0, 0, 0, 1)
|
|
quat.zero = new(0, 0, 0, 0)
|
|
|
|
--- The public constructor.
|
|
-- @param x Can be of two types: </br>
|
|
-- number x X component
|
|
-- table {x, y, z, w} or {x=x, y=y, z=z, w=w}
|
|
-- @tparam number y Y component
|
|
-- @tparam number z Z component
|
|
-- @tparam number w W component
|
|
-- @treturn quat out
|
|
function quat.new(x, y, z, w)
|
|
-- number, number, number, number
|
|
if x and y and z and w then
|
|
precond.typeof(x, "number", "new: Wrong argument type for x")
|
|
precond.typeof(y, "number", "new: Wrong argument type for y")
|
|
precond.typeof(z, "number", "new: Wrong argument type for z")
|
|
precond.typeof(w, "number", "new: Wrong argument type for w")
|
|
|
|
return new(x, y, z, w)
|
|
|
|
-- {x, y, z, w} or {x=x, y=y, z=z, w=w}
|
|
elseif type(x) == "table" then
|
|
local xx, yy, zz, ww = x.x or x[1], x.y or x[2], x.z or x[3], x.w or x[4]
|
|
precond.typeof(xx, "number", "new: Wrong argument type for x")
|
|
precond.typeof(yy, "number", "new: Wrong argument type for y")
|
|
precond.typeof(zz, "number", "new: Wrong argument type for z")
|
|
precond.typeof(ww, "number", "new: Wrong argument type for w")
|
|
|
|
return new(xx, yy, zz, ww)
|
|
end
|
|
|
|
return new(0, 0, 0, 1)
|
|
end
|
|
|
|
--- Create a quaternion from an angle/axis pair.
|
|
-- @tparam number angle Angle (in radians)
|
|
-- @param axis/x -- Can be of two types, a vec3 axis, or the x component of that axis
|
|
-- @param y axis -- y component of axis (optional, only if x component param used)
|
|
-- @param z axis -- z component of axis (optional, only if x component param used)
|
|
-- @treturn quat out
|
|
function quat.from_angle_axis(angle, axis, a3, a4)
|
|
if axis and a3 and a4 then
|
|
local x, y, z = axis, a3, a4
|
|
local s = sin(angle * 0.5)
|
|
local c = cos(angle * 0.5)
|
|
return new(x * s, y * s, z * s, c)
|
|
else
|
|
return quat.from_angle_axis(angle, axis.x, axis.y, axis.z)
|
|
end
|
|
end
|
|
|
|
--- Create a quaternion from a normal/up vector pair.
|
|
-- @tparam vec3 normal
|
|
-- @tparam vec3 up (optional)
|
|
-- @treturn quat out
|
|
function quat.from_direction(normal, up)
|
|
local u = up or vec3.unit_z
|
|
local n = normal:normalize()
|
|
local a = u:cross(n)
|
|
local d = u:dot(n)
|
|
return new(a.x, a.y, a.z, d + 1)
|
|
end
|
|
|
|
--- Clone a quaternion.
|
|
-- @tparam quat a Quaternion to clone
|
|
-- @treturn quat out
|
|
function quat.clone(a)
|
|
return new(a.x, a.y, a.z, a.w)
|
|
end
|
|
|
|
--- Add two quaternions.
|
|
-- @tparam quat a Left hand operand
|
|
-- @tparam quat b Right hand operand
|
|
-- @treturn quat out
|
|
function quat.add(a, b)
|
|
return new(
|
|
a.x + b.x,
|
|
a.y + b.y,
|
|
a.z + b.z,
|
|
a.w + b.w
|
|
)
|
|
end
|
|
|
|
--- Subtract a quaternion from another.
|
|
-- @tparam quat a Left hand operand
|
|
-- @tparam quat b Right hand operand
|
|
-- @treturn quat out
|
|
function quat.sub(a, b)
|
|
return new(
|
|
a.x - b.x,
|
|
a.y - b.y,
|
|
a.z - b.z,
|
|
a.w - b.w
|
|
)
|
|
end
|
|
|
|
--- Multiply two quaternions.
|
|
-- @tparam quat a Left hand operand
|
|
-- @tparam quat b Right hand operand
|
|
-- @treturn quat quaternion equivalent to "apply b, then a"
|
|
function quat.mul(a, b)
|
|
return new(
|
|
a.x * b.w + a.w * b.x + a.y * b.z - a.z * b.y,
|
|
a.y * b.w + a.w * b.y + a.z * b.x - a.x * b.z,
|
|
a.z * b.w + a.w * b.z + a.x * b.y - a.y * b.x,
|
|
a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z
|
|
)
|
|
end
|
|
|
|
--- Multiply a quaternion and a vec3.
|
|
-- @tparam quat a Left hand operand
|
|
-- @tparam vec3 b Right hand operand
|
|
-- @treturn vec3 out
|
|
function quat.mul_vec3(a, b)
|
|
qv.x = a.x
|
|
qv.y = a.y
|
|
qv.z = a.z
|
|
uv = qv:cross(b)
|
|
uuv = qv:cross(uv)
|
|
return b + ((uv * a.w) + uuv) * 2
|
|
end
|
|
|
|
--- Raise a normalized quaternion to a scalar power.
|
|
-- @tparam quat a Left hand operand (should be a unit quaternion)
|
|
-- @tparam number s Right hand operand
|
|
-- @treturn quat out
|
|
function quat.pow(a, s)
|
|
-- Do it as a slerp between identity and a (code borrowed from slerp)
|
|
if a.w < 0 then
|
|
a = -a
|
|
end
|
|
local dot = a.w
|
|
|
|
dot = min(max(dot, -1), 1)
|
|
|
|
local theta = acos(dot) * s
|
|
local c = new(a.x, a.y, a.z, 0):normalize() * sin(theta)
|
|
c.w = cos(theta)
|
|
return c
|
|
end
|
|
|
|
--- Normalize a quaternion.
|
|
-- @tparam quat a Quaternion to normalize
|
|
-- @treturn quat out
|
|
function quat.normalize(a)
|
|
if a:is_zero() then
|
|
return new(0, 0, 0, 0)
|
|
end
|
|
return a:scale(1 / a:len())
|
|
end
|
|
|
|
--- Get the dot product of two quaternions.
|
|
-- @tparam quat a Left hand operand
|
|
-- @tparam quat b Right hand operand
|
|
-- @treturn number dot
|
|
function quat.dot(a, b)
|
|
return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w
|
|
end
|
|
|
|
--- Return the length of a quaternion.
|
|
-- @tparam quat a Quaternion to get length of
|
|
-- @treturn number len
|
|
function quat.len(a)
|
|
return sqrt(a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w)
|
|
end
|
|
|
|
--- Return the squared length of a quaternion.
|
|
-- @tparam quat a Quaternion to get length of
|
|
-- @treturn number len
|
|
function quat.len2(a)
|
|
return a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w
|
|
end
|
|
|
|
--- Multiply a quaternion by a scalar.
|
|
-- @tparam quat a Left hand operand
|
|
-- @tparam number s Right hand operand
|
|
-- @treturn quat out
|
|
function quat.scale(a, s)
|
|
return new(
|
|
a.x * s,
|
|
a.y * s,
|
|
a.z * s,
|
|
a.w * s
|
|
)
|
|
end
|
|
|
|
--- Alias of from_angle_axis.
|
|
-- @tparam number angle Angle (in radians)
|
|
-- @param axis/x -- Can be of two types, a vec3 axis, or the x component of that axis
|
|
-- @param y axis -- y component of axis (optional, only if x component param used)
|
|
-- @param z axis -- z component of axis (optional, only if x component param used)
|
|
-- @treturn quat out
|
|
function quat.rotate(angle, axis, a3, a4)
|
|
return quat.from_angle_axis(angle, axis, a3, a4)
|
|
end
|
|
|
|
--- Return the conjugate of a quaternion.
|
|
-- @tparam quat a Quaternion to conjugate
|
|
-- @treturn quat out
|
|
function quat.conjugate(a)
|
|
return new(-a.x, -a.y, -a.z, a.w)
|
|
end
|
|
|
|
--- Return the inverse of a quaternion.
|
|
-- @tparam quat a Quaternion to invert
|
|
-- @treturn quat out
|
|
function quat.inverse(a)
|
|
tmp.x = -a.x
|
|
tmp.y = -a.y
|
|
tmp.z = -a.z
|
|
tmp.w = a.w
|
|
return tmp:normalize()
|
|
end
|
|
|
|
--- Return the reciprocal of a quaternion.
|
|
-- @tparam quat a Quaternion to reciprocate
|
|
-- @treturn quat out
|
|
function quat.reciprocal(a)
|
|
if a:is_zero() then
|
|
error("Cannot reciprocate a zero quaternion")
|
|
return false
|
|
end
|
|
|
|
tmp.x = -a.x
|
|
tmp.y = -a.y
|
|
tmp.z = -a.z
|
|
tmp.w = a.w
|
|
|
|
return tmp:scale(1 / a:len2())
|
|
end
|
|
|
|
--- Lerp between two quaternions.
|
|
-- @tparam quat a Left hand operand
|
|
-- @tparam quat b Right hand operand
|
|
-- @tparam number s Step value
|
|
-- @treturn quat out
|
|
function quat.lerp(a, b, s)
|
|
return (a + (b - a) * s):normalize()
|
|
end
|
|
|
|
--- Slerp between two quaternions.
|
|
-- @tparam quat a Left hand operand
|
|
-- @tparam quat b Right hand operand
|
|
-- @tparam number s Step value
|
|
-- @treturn quat out
|
|
function quat.slerp(a, b, s)
|
|
local dot = a:dot(b)
|
|
|
|
if dot < 0 then
|
|
a = -a
|
|
dot = -dot
|
|
end
|
|
|
|
if dot > DOT_THRESHOLD then
|
|
return a:lerp(b, s)
|
|
end
|
|
|
|
dot = min(max(dot, -1), 1)
|
|
|
|
local theta = acos(dot) * s
|
|
local c = (b - a * dot):normalize()
|
|
return a * cos(theta) + c * sin(theta)
|
|
end
|
|
|
|
--- Unpack a quaternion into individual components.
|
|
-- @tparam quat a Quaternion to unpack
|
|
-- @treturn number x
|
|
-- @treturn number y
|
|
-- @treturn number z
|
|
-- @treturn number w
|
|
function quat.unpack(a)
|
|
return a.x, a.y, a.z, a.w
|
|
end
|
|
|
|
--- Return a boolean showing if a table is or is not a quat.
|
|
-- @tparam quat a Quaternion to be tested
|
|
-- @treturn boolean is_quat
|
|
function quat.is_quat(a)
|
|
if type(a) == "cdata" then
|
|
return ffi.istype("cpml_quat", a)
|
|
end
|
|
|
|
return
|
|
type(a) == "table" and
|
|
type(a.x) == "number" and
|
|
type(a.y) == "number" and
|
|
type(a.z) == "number" and
|
|
type(a.w) == "number"
|
|
end
|
|
|
|
--- Return a boolean showing if a table is or is not a zero quat.
|
|
-- @tparam quat a Quaternion to be tested
|
|
-- @treturn boolean is_zero
|
|
function quat.is_zero(a)
|
|
return
|
|
a.x == 0 and
|
|
a.y == 0 and
|
|
a.z == 0 and
|
|
a.w == 0
|
|
end
|
|
|
|
--- Return a boolean showing if a table is or is not a real quat.
|
|
-- @tparam quat a Quaternion to be tested
|
|
-- @treturn boolean is_real
|
|
function quat.is_real(a)
|
|
return
|
|
a.x == 0 and
|
|
a.y == 0 and
|
|
a.z == 0
|
|
end
|
|
|
|
--- Return a boolean showing if a table is or is not an imaginary quat.
|
|
-- @tparam quat a Quaternion to be tested
|
|
-- @treturn boolean is_imaginary
|
|
function quat.is_imaginary(a)
|
|
return a.w == 0
|
|
end
|
|
|
|
--- Return whether any component is NaN
|
|
-- @tparam quat a Quaternion to be tested
|
|
-- @treturn boolean if x,y,z, or w is NaN
|
|
function quat.has_nan(a)
|
|
return private.is_nan(a.x) or
|
|
private.is_nan(a.y) or
|
|
private.is_nan(a.z) or
|
|
private.is_nan(a.w)
|
|
end
|
|
|
|
--- Convert a quaternion into an angle plus axis components.
|
|
-- @tparam quat a Quaternion to convert
|
|
-- @tparam identityAxis vec3 of axis to use on identity/degenerate quaternions (optional, default returns 0,0,0,1)
|
|
-- @treturn number angle
|
|
-- @treturn x axis-x
|
|
-- @treturn y axis-y
|
|
-- @treturn z axis-z
|
|
function quat.to_angle_axis_unpack(a, identityAxis)
|
|
if a.w > 1 or a.w < -1 then
|
|
a = a:normalize()
|
|
end
|
|
|
|
-- If length of xyz components is less than DBL_EPSILON, this is zero or close enough (an identity quaternion)
|
|
-- Normally an identity quat would return a nonsense answer, so we return an arbitrary zero rotation early.
|
|
-- FIXME: Is it safe to assume there are *no* valid quaternions with nonzero degenerate lengths?
|
|
if a.x*a.x + a.y*a.y + a.z*a.z < constants.DBL_EPSILON*constants.DBL_EPSILON then
|
|
if identityAxis then
|
|
return 0,identityAxis:unpack()
|
|
else
|
|
return 0,0,0,1
|
|
end
|
|
end
|
|
|
|
local x, y, z
|
|
local angle = 2 * acos(a.w)
|
|
local s = sqrt(1 - a.w * a.w)
|
|
|
|
if s < DBL_EPSILON then
|
|
x = a.x
|
|
y = a.y
|
|
z = a.z
|
|
else
|
|
x = a.x / s
|
|
y = a.y / s
|
|
z = a.z / s
|
|
end
|
|
|
|
return angle, x, y, z
|
|
end
|
|
|
|
--- Convert a quaternion into an angle/axis pair.
|
|
-- @tparam quat a Quaternion to convert
|
|
-- @tparam identityAxis vec3 of axis to use on identity/degenerate quaternions (optional, default returns 0,vec3(0,0,1))
|
|
-- @treturn number angle
|
|
-- @treturn vec3 axis
|
|
function quat.to_angle_axis(a, identityAxis)
|
|
local angle, x, y, z = a:to_angle_axis_unpack(identityAxis)
|
|
return angle, vec3(x, y, z)
|
|
end
|
|
|
|
--- Convert a quaternion into a vec3.
|
|
-- @tparam quat a Quaternion to convert
|
|
-- @treturn vec3 out
|
|
function quat.to_vec3(a)
|
|
return vec3(a.x, a.y, a.z)
|
|
end
|
|
|
|
--- Return a formatted string.
|
|
-- @tparam quat a Quaternion to be turned into a string
|
|
-- @treturn string formatted
|
|
function quat.to_string(a)
|
|
return string.format("(%+0.3f,%+0.3f,%+0.3f,%+0.3f)", a.x, a.y, a.z, a.w)
|
|
end
|
|
|
|
quat_mt.__index = quat
|
|
quat_mt.__tostring = quat.to_string
|
|
|
|
function quat_mt.__call(_, x, y, z, w)
|
|
return quat.new(x, y, z, w)
|
|
end
|
|
|
|
function quat_mt.__unm(a)
|
|
return a:scale(-1)
|
|
end
|
|
|
|
function quat_mt.__eq(a,b)
|
|
if not quat.is_quat(a) or not quat.is_quat(b) then
|
|
return false
|
|
end
|
|
return a.x == b.x and a.y == b.y and a.z == b.z and a.w == b.w
|
|
end
|
|
|
|
function quat_mt.__add(a, b)
|
|
precond.assert(quat.is_quat(a), "__add: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))
|
|
precond.assert(quat.is_quat(b), "__add: Wrong argument type '%s' for right hand operand. (<cpml.quat> expected)", type(b))
|
|
return a:add(b)
|
|
end
|
|
|
|
function quat_mt.__sub(a, b)
|
|
precond.assert(quat.is_quat(a), "__sub: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))
|
|
precond.assert(quat.is_quat(b), "__sub: Wrong argument type '%s' for right hand operand. (<cpml.quat> expected)", type(b))
|
|
return a:sub(b)
|
|
end
|
|
|
|
function quat_mt.__mul(a, b)
|
|
precond.assert(quat.is_quat(a), "__mul: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))
|
|
assert(quat.is_quat(b) or vec3.is_vec3(b) or type(b) == "number", "__mul: Wrong argument type for right hand operand. (<cpml.quat> or <cpml.vec3> or <number> expected)")
|
|
|
|
if quat.is_quat(b) then
|
|
return a:mul(b)
|
|
end
|
|
|
|
if type(b) == "number" then
|
|
return a:scale(b)
|
|
end
|
|
|
|
return a:mul_vec3(b)
|
|
end
|
|
|
|
function quat_mt.__pow(a, n)
|
|
precond.assert(quat.is_quat(a), "__pow: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))
|
|
precond.typeof(n, "number", "__pow: Wrong argument type for right hand operand.")
|
|
return a:pow(n)
|
|
end
|
|
|
|
if status then
|
|
xpcall(function() -- Allow this to silently fail; assume failure means someone messed with package.loaded
|
|
ffi.metatype(new, quat_mt)
|
|
end, function() end)
|
|
end
|
|
|
|
return setmetatable({}, quat_mt)
|