6132588926

Committed 09 Sep 2023 06:38PM UTC coverage: 14.013% (-44.7%) from 58.701%

Build # 6132588926

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FatalError42O

Commit Message

fixed Busted support (hopefully)

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0.44

/modules/quat.lua

--- A quaternion and associated utilities.
-- @module quat

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


--- Convert a quaternion to an Euler angle
-- @tparam quat a Quaternion to convert
-- @treturn vec3 euler angle in radians
function quat.to_euler()
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)

1	--- A quaternion and associated utilities.
2	-- @module quat
3
4	local constants = require(modules .. "constants")	3✔
5	local vec3 = require(modules .. "vec3")	×
6	local precond = require(modules .. "_private_precond")	×
7	local private = require(modules .. "_private_utils")	×
8	local DOT_THRESHOLD = constants.DOT_THRESHOLD	×
9	local DBL_EPSILON = constants.DBL_EPSILON	×
10	local acos = math.acos	×
11	local cos = math.cos	×
12	local sin = math.sin	×
13	local min = math.min	×
14	local max = math.max	×
15	local sqrt = math.sqrt	×
16	local quat = {}	×
17	local quat_mt = {}	×
18
19	-- Private constructor.
20	local function new(x, y, z, w)
21	return setmetatable({	×
22	x = x or 0,
23	y = y or 0,
24	z = z or 0,
25	w = w or 1	×
26	}, quat_mt)	×
27	end
28
29	-- Do the check to see if JIT is enabled. If so use the optimized FFI structs.
30	local status, ffi
31	if type(jit) == "table" and jit.status() then	×
32	status, ffi = pcall(require, "ffi")	×
33	if status then	×
34	ffi.cdef "typedef struct { double x, y, z, w;} cpml_quat;"	×
35	new = ffi.typeof("cpml_quat")	×
36	end
37	end
38
39	-- Statically allocate a temporary variable used in some of our functions.
40	local tmp = new()	×
41	local qv, uv, uuv = vec3(), vec3(), vec3()	×
42
43	--- Constants
44	-- @table quat
45	-- @field unit Unit quaternion
46	-- @field zero Empty quaternion
47	quat.unit = new(0, 0, 0, 1)	×
48	quat.zero = new(0, 0, 0, 0)	×
49
50	--- The public constructor.
51	-- @param x Can be of two types: </br>
52	-- number x X component
53	-- table {x, y, z, w} or {x=x, y=y, z=z, w=w}
54	-- @tparam number y Y component
55	-- @tparam number z Z component
56	-- @tparam number w W component
57	-- @treturn quat out
58	function quat.new(x, y, z, w)	×
59	-- number, number, number, number
60	if x and y and z and w then	×
61	precond.typeof(x, "number", "new: Wrong argument type for x")	×
62	precond.typeof(y, "number", "new: Wrong argument type for y")	×
63	precond.typeof(z, "number", "new: Wrong argument type for z")	×
64	precond.typeof(w, "number", "new: Wrong argument type for w")	×
65
66	return new(x, y, z, w)	×
67
68	-- {x, y, z, w} or {x=x, y=y, z=z, w=w}
69	elseif type(x) == "table" then	×
70	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]	×
71	precond.typeof(xx, "number", "new: Wrong argument type for x")	×
72	precond.typeof(yy, "number", "new: Wrong argument type for y")	×
73	precond.typeof(zz, "number", "new: Wrong argument type for z")	×
74	precond.typeof(ww, "number", "new: Wrong argument type for w")	×
75
76	return new(xx, yy, zz, ww)	×
77	end
78
79	return new(0, 0, 0, 1)	×
80	end
81
82	--- Create a quaternion from an angle/axis pair.
83	-- @tparam number angle Angle (in radians)
84	-- @param axis/x -- Can be of two types, a vec3 axis, or the x component of that axis
85	-- @param y axis -- y component of axis (optional, only if x component param used)
86	-- @param z axis -- z component of axis (optional, only if x component param used)
87	-- @treturn quat out
88	function quat.from_angle_axis(angle, axis, a3, a4)	×
89	if axis and a3 and a4 then	×
90	local x, y, z = axis, a3, a4	×
91	local s = sin(angle * 0.5)	×
92	local c = cos(angle * 0.5)	×
93	return new(x * s, y * s, z * s, c)	×
94	else
95	return quat.from_angle_axis(angle, axis.x, axis.y, axis.z)	×
96	end
97	end
98
99	--- Create a quaternion from a normal/up vector pair.
100	-- @tparam vec3 normal
101	-- @tparam vec3 up (optional)
102	-- @treturn quat out
103	function quat.from_direction(normal, up)	×
104	local u = up or vec3.unit_z	×
105	local n = normal:normalize()	×
106	local a = u:cross(n)	×
107	local d = u:dot(n)	×
108	return new(a.x, a.y, a.z, d + 1)	×
109	end
110
111	--- Clone a quaternion.
112	-- @tparam quat a Quaternion to clone
113	-- @treturn quat out
114	function quat.clone(a)	×
115	return new(a.x, a.y, a.z, a.w)	×
116	end
117
118	--- Add two quaternions.
119	-- @tparam quat a Left hand operand
120	-- @tparam quat b Right hand operand
121	-- @treturn quat out
122	function quat.add(a, b)	×
123	return new(	×
124	a.x + b.x,	×
125	a.y + b.y,	×
126	a.z + b.z,	×
127	a.w + b.w	×
128	)
129	end
130
131	--- Subtract a quaternion from another.
132	-- @tparam quat a Left hand operand
133	-- @tparam quat b Right hand operand
134	-- @treturn quat out
135	function quat.sub(a, b)	×
136	return new(	×
137	a.x - b.x,	×
138	a.y - b.y,	×
139	a.z - b.z,	×
140	a.w - b.w	×
141	)
142	end
143
144	--- Multiply two quaternions.
145	-- @tparam quat a Left hand operand
146	-- @tparam quat b Right hand operand
147	-- @treturn quat quaternion equivalent to "apply b, then a"
148	function quat.mul(a, b)	×
149	return new(	×
150	a.x * b.w + a.w * b.x + a.y * b.z - a.z * b.y,	×
151	a.y * b.w + a.w * b.y + a.z * b.x - a.x * b.z,	×
152	a.z * b.w + a.w * b.z + a.x * b.y - a.y * b.x,	×
153	a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z	×
154	)
155	end
156
157	--- Multiply a quaternion and a vec3.
158	-- @tparam quat a Left hand operand
159	-- @tparam vec3 b Right hand operand
160	-- @treturn vec3 out
161	function quat.mul_vec3(a, b)	×
162	qv.x = a.x	×
163	qv.y = a.y	×
164	qv.z = a.z	×
165	uv = qv:cross(b)	×
166	uuv = qv:cross(uv)	×
167	return b + ((uv * a.w) + uuv) * 2	×
168	end
169
170	--- Raise a normalized quaternion to a scalar power.
171	-- @tparam quat a Left hand operand (should be a unit quaternion)
172	-- @tparam number s Right hand operand
173	-- @treturn quat out
174	function quat.pow(a, s)	×
175	-- Do it as a slerp between identity and a (code borrowed from slerp)
176	if a.w < 0 then	×
177	a = -a	×
178	end
179	local dot = a.w	×
180
181	dot = min(max(dot, -1), 1)	×
182
183	local theta = acos(dot) * s	×
184	local c = new(a.x, a.y, a.z, 0):normalize() * sin(theta)	×
185	c.w = cos(theta)	×
186	return c	×
187	end
188
189	--- Normalize a quaternion.
190	-- @tparam quat a Quaternion to normalize
191	-- @treturn quat out
192	function quat.normalize(a)	×
193	if a:is_zero() then	×
194	return new(0, 0, 0, 0)	×
195	end
196	return a:scale(1 / a:len())	×
197	end
198
199	--- Get the dot product of two quaternions.
200	-- @tparam quat a Left hand operand
201	-- @tparam quat b Right hand operand
202	-- @treturn number dot
203	function quat.dot(a, b)	×
204	return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w	×
205	end
206
207	--- Return the length of a quaternion.
208	-- @tparam quat a Quaternion to get length of
209	-- @treturn number len
210	function quat.len(a)	×
211	return sqrt(a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w)	×
212	end
213
214	--- Return the squared length of a quaternion.
215	-- @tparam quat a Quaternion to get length of
216	-- @treturn number len
217	function quat.len2(a)	×
218	return a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w	×
219	end
220
221	--- Multiply a quaternion by a scalar.
222	-- @tparam quat a Left hand operand
223	-- @tparam number s Right hand operand
224	-- @treturn quat out
225	function quat.scale(a, s)	×
226	return new(	×
227	a.x * s,	×
228	a.y * s,	×
229	a.z * s,	×
230	a.w * s	×
231	)
232	end
233
234	--- Alias of from_angle_axis.
235	-- @tparam number angle Angle (in radians)
236	-- @param axis/x -- Can be of two types, a vec3 axis, or the x component of that axis
237	-- @param y axis -- y component of axis (optional, only if x component param used)
238	-- @param z axis -- z component of axis (optional, only if x component param used)
239	-- @treturn quat out
240	function quat.rotate(angle, axis, a3, a4)	×
241	return quat.from_angle_axis(angle, axis, a3, a4)	×
242	end
243
244	--- Return the conjugate of a quaternion.
245	-- @tparam quat a Quaternion to conjugate
246	-- @treturn quat out
247	function quat.conjugate(a)	×
248	return new(-a.x, -a.y, -a.z, a.w)	×
249	end
250
251	--- Return the inverse of a quaternion.
252	-- @tparam quat a Quaternion to invert
253	-- @treturn quat out
254	function quat.inverse(a)	×
255	tmp.x = -a.x	×
256	tmp.y = -a.y	×
257	tmp.z = -a.z	×
258	tmp.w = a.w	×
259	return tmp:normalize()	×
260	end
261
262	--- Return the reciprocal of a quaternion.
263	-- @tparam quat a Quaternion to reciprocate
264	-- @treturn quat out
265	function quat.reciprocal(a)	×
266	if a:is_zero() then	×
267	error("Cannot reciprocate a zero quaternion")	×
268	return false	×
269	end
270
271	tmp.x = -a.x	×
272	tmp.y = -a.y	×
273	tmp.z = -a.z	×
274	tmp.w = a.w	×
275
276	return tmp:scale(1 / a:len2())	×
277	end
278
279	--- Lerp between two quaternions.
280	-- @tparam quat a Left hand operand
281	-- @tparam quat b Right hand operand
282	-- @tparam number s Step value
283	-- @treturn quat out
284	function quat.lerp(a, b, s)	×
285	return (a + (b - a) * s):normalize()	×
286	end
287
288	--- Slerp between two quaternions.
289	-- @tparam quat a Left hand operand
290	-- @tparam quat b Right hand operand
291	-- @tparam number s Step value
292	-- @treturn quat out
293	function quat.slerp(a, b, s)	×
294	local dot = a:dot(b)	×
295
296	if dot < 0 then	×
297	a = -a	×
298	dot = -dot	×
299	end
300
301	if dot > DOT_THRESHOLD then	×
302	return a:lerp(b, s)	×
303	end
304
305	dot = min(max(dot, -1), 1)	×
306
307	local theta = acos(dot) * s	×
308	local c = (b - a * dot):normalize()	×
309	return a * cos(theta) + c * sin(theta)	×
310	end
311
312	--- Unpack a quaternion into individual components.
313	-- @tparam quat a Quaternion to unpack
314	-- @treturn number x
315	-- @treturn number y
316	-- @treturn number z
317	-- @treturn number w
318	function quat.unpack(a)	×
319	return a.x, a.y, a.z, a.w	×
320	end
321
322	--- Return a boolean showing if a table is or is not a quat.
323	-- @tparam quat a Quaternion to be tested
324	-- @treturn boolean is_quat
325	function quat.is_quat(a)	×
326	if type(a) == "cdata" then	×
327	return ffi.istype("cpml_quat", a)	×
328	end
329
330	return	×
331	type(a) == "table" and	×
332	type(a.x) == "number" and	×
333	type(a.y) == "number" and	×
334	type(a.z) == "number" and	×
335	type(a.w) == "number"	×
336	end
337
338	--- Return a boolean showing if a table is or is not a zero quat.
339	-- @tparam quat a Quaternion to be tested
340	-- @treturn boolean is_zero
341	function quat.is_zero(a)	×
342	return	×
343	a.x == 0 and	×
344	a.y == 0 and	×
345	a.z == 0 and	×
346	a.w == 0	×
347	end
348
349	--- Return a boolean showing if a table is or is not a real quat.
350	-- @tparam quat a Quaternion to be tested
351	-- @treturn boolean is_real
352	function quat.is_real(a)	×
353	return	×
354	a.x == 0 and	×
355	a.y == 0 and	×
356	a.z == 0	×
357	end
358
359	--- Return a boolean showing if a table is or is not an imaginary quat.
360	-- @tparam quat a Quaternion to be tested
361	-- @treturn boolean is_imaginary
362	function quat.is_imaginary(a)	×
363	return a.w == 0	×
364	end
365
366	--- Return whether any component is NaN
367	-- @tparam quat a Quaternion to be tested
368	-- @treturn boolean if x,y,z, or w is NaN
369	function quat.has_nan(a)	×
370	return private.is_nan(a.x) or	×
371	private.is_nan(a.y) or	×
372	private.is_nan(a.z) or	×
373	private.is_nan(a.w)	×
374	end
375
376	--- Convert a quaternion into an angle plus axis components.
377	-- @tparam quat a Quaternion to convert
378	-- @tparam identityAxis vec3 of axis to use on identity/degenerate quaternions (optional, default returns 0,0,0,1)
379	-- @treturn number angle
380	-- @treturn x axis-x
381	-- @treturn y axis-y
382	-- @treturn z axis-z
383	function quat.to_angle_axis_unpack(a, identityAxis)	×
384	if a.w > 1 or a.w < -1 then	×
385	a = a:normalize()	×
386	end
387
388	-- If length of xyz components is less than DBL_EPSILON, this is zero or close enough (an identity quaternion)
389	-- Normally an identity quat would return a nonsense answer, so we return an arbitrary zero rotation early.
390	-- FIXME: Is it safe to assume there are no valid quaternions with nonzero degenerate lengths?
391	if a.xa.x + a.ya.y + a.za.z < constants.DBL_EPSILONconstants.DBL_EPSILON then	×
392	if identityAxis then	×
393	return 0,identityAxis:unpack()	×
394	else
395	return 0,0,0,1	×
396	end
397	end
398
399	local x, y, z
400	local angle = 2 * acos(a.w)	×
401	local s = sqrt(1 - a.w * a.w)	×
402
403	if s < DBL_EPSILON then	×
404	x = a.x	×
405	y = a.y	×
406	z = a.z	×
407	else
408	x = a.x / s	×
409	y = a.y / s	×
410	z = a.z / s	×
411	end
412
413	return angle, x, y, z	×
414	end
415
416	--- Convert a quaternion into an angle/axis pair.
417	-- @tparam quat a Quaternion to convert
418	-- @tparam identityAxis vec3 of axis to use on identity/degenerate quaternions (optional, default returns 0,vec3(0,0,1))
419	-- @treturn number angle
420	-- @treturn vec3 axis
421	function quat.to_angle_axis(a, identityAxis)	×
422	local angle, x, y, z = a:to_angle_axis_unpack(identityAxis)	×
423	return angle, vec3(x, y, z)	×
424	end
425
426	--- Convert a quaternion into a vec3.
427	-- @tparam quat a Quaternion to convert
428	-- @treturn vec3 out
429	function quat.to_vec3(a)	×
430	return vec3(a.x, a.y, a.z)	×
431	end
432
433	--- Return a formatted string.
434	-- @tparam quat a Quaternion to be turned into a string
435	-- @treturn string formatted
436	function quat.to_string(a)	×
437	return string.format("(%+0.3f,%+0.3f,%+0.3f,%+0.3f)", a.x, a.y, a.z, a.w)	×
438	end
439
440
441	--- Convert a quaternion to an Euler angle
442	-- @tparam quat a Quaternion to convert
443	-- @treturn vec3 euler angle in radians
444	function quat.to_euler()	×
445	end
446
447	quat_mt.__index = quat	×
448	quat_mt.__tostring = quat.to_string	×
449
450	function quat_mt.__call(_, x, y, z, w)	×
451	return quat.new(x, y, z, w)	×
452	end
453
454	function quat_mt.__unm(a)	×
455	return a:scale(-1)	×
456	end
457
458	function quat_mt.__eq(a,b)	×
459	if not quat.is_quat(a) or not quat.is_quat(b) then	×
460	return false	×
461	end
462	return a.x == b.x and a.y == b.y and a.z == b.z and a.w == b.w	×
463	end
464
465	function quat_mt.__add(a, b)	×
466	precond.assert(quat.is_quat(a), "__add: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))	×
467	precond.assert(quat.is_quat(b), "__add: Wrong argument type '%s' for right hand operand. (<cpml.quat> expected)", type(b))	×
468	return a:add(b)	×
469	end
470
471	function quat_mt.__sub(a, b)	×
472	precond.assert(quat.is_quat(a), "__sub: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))	×
473	precond.assert(quat.is_quat(b), "__sub: Wrong argument type '%s' for right hand operand. (<cpml.quat> expected)", type(b))	×
474	return a:sub(b)	×
475	end
476
477	function quat_mt.__mul(a, b)	×
478	precond.assert(quat.is_quat(a), "__mul: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))	×
479	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)")	×
480
481	if quat.is_quat(b) then	×
482	return a:mul(b)	×
483	end
484
485	if type(b) == "number" then	×
486	return a:scale(b)	×
487	end
488
489	return a:mul_vec3(b)	×
490	end
491
492	function quat_mt.__pow(a, n)	×
493	precond.assert(quat.is_quat(a), "__pow: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))	×
494	precond.typeof(n, "number", "__pow: Wrong argument type for right hand operand.")	×
495	return a:pow(n)	×
496	end
497
498	if status then	×
499	xpcall(function() -- Allow this to silently fail; assume failure means someone messed with package.loaded	×
500	ffi.metatype(new, quat_mt)	×
501	end, function() end)	×
502	end
503
504	return setmetatable({}, quat_mt)	×

excessive / cpml / 6132588926

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