excessive / cpml / 1

Committed 21 Apr 2022 05:46PM UTC coverage: 54.321% (+0.7%) from 53.574%

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Merge pull request #76 from xiejiangzhi/xjz

Add Vec3.angle_to

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/modules/quat.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 quat 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)

1	--- A quaternion and associated utilities.
2	-- @module quat
3
4	local modules = (...):gsub('%.[^%.]+$', '') .. "."	28✔
5	local constants = require(modules .. "constants")	28✔
6	local vec3 = require(modules .. "vec3")	28✔
7	local precond = require(modules .. "_private_precond")	28✔
8	local private = require(modules .. "_private_utils")	28✔
9	local DOT_THRESHOLD = constants.DOT_THRESHOLD	28✔
10	local DBL_EPSILON = constants.DBL_EPSILON	28✔
11	local acos = math.acos	28✔
12	local cos = math.cos	28✔
13	local sin = math.sin	28✔
14	local min = math.min	28✔
15	local max = math.max	28✔
16	local sqrt = math.sqrt	28✔
17	local quat = {}	28✔
18	local quat_mt = {}	28✔
19
20	-- Private constructor.
21	local function new(x, y, z, w)
22	return setmetatable({	1,540✔
23	x = x or 0,	770✔
24	y = y or 0,	770✔
25	z = z or 0,	770✔
26	w = w or 1	770✔
27	}, quat_mt)	1,540✔
28	end
29
30	-- Do the check to see if JIT is enabled. If so use the optimized FFI structs.
31	local status, ffi
32	if type(jit) == "table" and jit.status() then	28✔
33	status, ffi = pcall(require, "ffi")	×
34	if status then	×
UNCOV 35	ffi.cdef "typedef struct { double x, y, z, w;} cpml_quat;"	×
UNCOV 36	new = ffi.typeof("cpml_quat")	×
37	end
38	end
39
40	-- Statically allocate a temporary variable used in some of our functions.
41	local tmp = new()	28✔
42	local qv, uv, uuv = vec3(), vec3(), vec3()	28✔
43
44	--- Constants
45	-- @table quat
46	-- @field unit Unit quaternion
47	-- @field zero Empty quaternion
48	quat.unit = new(0, 0, 0, 1)	28✔
49	quat.zero = new(0, 0, 0, 0)	28✔
50
51	--- The public constructor.
52	-- @param x Can be of two types: </br>
53	-- number x X component
54	-- table {x, y, z, w} or {x=x, y=y, z=z, w=w}
55	-- @tparam number y Y component
56	-- @tparam number z Z component
57	-- @tparam number w W component
58	-- @treturn quat out
59	function quat.new(x, y, z, w)	28✔
60	-- number, number, number, number
61	if x and y and z and w then	308✔
62	precond.typeof(x, "number", "new: Wrong argument type for x")	259✔
63	precond.typeof(y, "number", "new: Wrong argument type for y")	259✔
64	precond.typeof(z, "number", "new: Wrong argument type for z")	259✔
65	precond.typeof(w, "number", "new: Wrong argument type for w")	259✔
66
67	return new(x, y, z, w)	259✔
68
69	-- {x, y, z, w} or {x=x, y=y, z=z, w=w}
70	elseif type(x) == "table" then	49✔
71	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]	14✔
72	precond.typeof(xx, "number", "new: Wrong argument type for x")	14✔
73	precond.typeof(yy, "number", "new: Wrong argument type for y")	14✔
74	precond.typeof(zz, "number", "new: Wrong argument type for z")	14✔
75	precond.typeof(ww, "number", "new: Wrong argument type for w")	14✔
76
77	return new(xx, yy, zz, ww)	14✔
78	end
79
80	return new(0, 0, 0, 1)	35✔
81	end
82
83	--- Create a quaternion from an angle/axis pair.
84	-- @tparam number angle Angle (in radians)
85	-- @param axis/x -- Can be of two types, a vec3 axis, or the x component of that axis
86	-- @param y axis -- y component of axis (optional, only if x component param used)
87	-- @param z axis -- z component of axis (optional, only if x component param used)
88	-- @treturn quat out
89	function quat.from_angle_axis(angle, axis, a3, a4)	28✔
90	if axis and a3 and a4 then	35✔
91	local x, y, z = axis, a3, a4	21✔
92	local s = sin(angle * 0.5)	21✔
93	local c = cos(angle * 0.5)	21✔
94	return new(x * s, y * s, z * s, c)	21✔
95	else
96	return quat.from_angle_axis(angle, axis.x, axis.y, axis.z)	14✔
97	end
98	end
99
100	--- Create a quaternion from a normal/up vector pair.
101	-- @tparam vec3 normal
102	-- @tparam vec3 up (optional)
103	-- @treturn quat out
104	function quat.from_direction(normal, up)	28✔
105	local u = up or vec3.unit_z	7✔
106	local n = normal:normalize()	7✔
107	local a = u:cross(n)	7✔
108	local d = u:dot(n)	7✔
109	return new(a.x, a.y, a.z, d + 1)	7✔
110	end
111
112	--- Clone a quaternion.
113	-- @tparam quat a Quaternion to clone
114	-- @treturn quat out
115	function quat.clone(a)	28✔
116	return new(a.x, a.y, a.z, a.w)	7✔
117	end
118
119	--- Add two quaternions.
120	-- @tparam quat a Left hand operand
121	-- @tparam quat b Right hand operand
122	-- @treturn quat out
123	function quat.add(a, b)	28✔
124	return new(	56✔
125	a.x + b.x,	28✔
126	a.y + b.y,	28✔
127	a.z + b.z,	28✔
128	a.w + b.w	28✔
129	)
130	end
131
132	--- Subtract a quaternion from another.
133	-- @tparam quat a Left hand operand
134	-- @tparam quat b Right hand operand
135	-- @treturn quat out
136	function quat.sub(a, b)	28✔
137	return new(	56✔
138	a.x - b.x,	28✔
139	a.y - b.y,	28✔
140	a.z - b.z,	28✔
141	a.w - b.w	28✔
142	)
143	end
144
145	--- Multiply two quaternions.
146	-- @tparam quat a Left hand operand
147	-- @tparam quat b Right hand operand
148	-- @treturn quat quaternion equivalent to "apply b, then a"
149	function quat.mul(a, b)	28✔
150	return new(	42✔
151	a.x * b.w + a.w * b.x + a.y * b.z - a.z * b.y,	21✔
152	a.y * b.w + a.w * b.y + a.z * b.x - a.x * b.z,	21✔
153	a.z * b.w + a.w * b.z + a.x * b.y - a.y * b.x,	21✔
154	a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z	21✔
155	)
156	end
157
158	--- Multiply a quaternion and a vec3.
159	-- @tparam quat a Left hand operand
160	-- @tparam vec3 b Right hand operand
161	-- @treturn quat out
162	function quat.mul_vec3(a, b)	28✔
163	qv.x = a.x	35✔
164	qv.y = a.y	35✔
165	qv.z = a.z	35✔
166	uv = qv:cross(b)	35✔
167	uuv = qv:cross(uv)	35✔
168	return b + ((uv * a.w) + uuv) * 2	35✔
169	end
170
171	--- Raise a normalized quaternion to a scalar power.
172	-- @tparam quat a Left hand operand (should be a unit quaternion)
173	-- @tparam number s Right hand operand
174	-- @treturn quat out
175	function quat.pow(a, s)	28✔
176	-- Do it as a slerp between identity and a (code borrowed from slerp)
177	if a.w < 0 then	42✔
UNCOV 178	a = -a	×
179	end
180	local dot = a.w	42✔
181
182	dot = min(max(dot, -1), 1)	42✔
183
184	local theta = acos(dot) * s	42✔
185	local c = new(a.x, a.y, a.z, 0):normalize() * sin(theta)	42✔
186	c.w = cos(theta)	42✔
187	return c	42✔
188	end
189
190	--- Normalize a quaternion.
191	-- @tparam quat a Quaternion to normalize
192	-- @treturn quat out
193	function quat.normalize(a)	28✔
194	if a:is_zero() then	126✔
UNCOV 195	return new(0, 0, 0, 0)	×
196	end
197	return a:scale(1 / a:len())	126✔
198	end
199
200	--- Get the dot product of two quaternions.
201	-- @tparam quat a Left hand operand
202	-- @tparam quat b Right hand operand
203	-- @treturn number dot
204	function quat.dot(a, b)	28✔
205	return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w	28✔
206	end
207
208	--- Return the length of a quaternion.
209	-- @tparam quat a Quaternion to get length of
210	-- @treturn number len
211	function quat.len(a)	28✔
212	return sqrt(a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w)	133✔
213	end
214
215	--- Return the squared length of a quaternion.
216	-- @tparam quat a Quaternion to get length of
217	-- @treturn number len
218	function quat.len2(a)	28✔
219	return a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w	21✔
220	end
221
222	--- Multiply a quaternion by a scalar.
223	-- @tparam quat a Left hand operand
224	-- @tparam number s Right hand operand
225	-- @treturn quat out
226	function quat.scale(a, s)	28✔
227	return new(	434✔
228	a.x * s,	217✔
229	a.y * s,	217✔
230	a.z * s,	217✔
231	a.w * s	217✔
232	)
233	end
234
235	--- Alias of from_angle_axis.
236	-- @tparam number angle Angle (in radians)
237	-- @param axis/x -- Can be of two types, a vec3 axis, or the x component of that axis
238	-- @param y axis -- y component of axis (optional, only if x component param used)
239	-- @param z axis -- z component of axis (optional, only if x component param used)
240	-- @treturn quat out
241	function quat.rotate(angle, axis, a3, a4)	28✔
UNCOV 242	return quat.from_angle_axis(angle, axis, a3, a4)	×
243	end
244
245	--- Return the conjugate of a quaternion.
246	-- @tparam quat a Quaternion to conjugate
247	-- @treturn quat out
248	function quat.conjugate(a)	28✔
249	return new(-a.x, -a.y, -a.z, a.w)	7✔
250	end
251
252	--- Return the inverse of a quaternion.
253	-- @tparam quat a Quaternion to invert
254	-- @treturn quat out
255	function quat.inverse(a)	28✔
256	tmp.x = -a.x	7✔
257	tmp.y = -a.y	7✔
258	tmp.z = -a.z	7✔
259	tmp.w = a.w	7✔
260	return tmp:normalize()	7✔
261	end
262
263	--- Return the reciprocal of a quaternion.
264	-- @tparam quat a Quaternion to reciprocate
265	-- @treturn quat out
266	function quat.reciprocal(a)	28✔
267	if a:is_zero() then	14✔
UNCOV 268	error("Cannot reciprocate a zero quaternion")	×
UNCOV 269	return false	×
270	end
271
272	tmp.x = -a.x	14✔
273	tmp.y = -a.y	14✔
274	tmp.z = -a.z	14✔
275	tmp.w = a.w	14✔
276
277	return tmp:scale(1 / a:len2())	14✔
278	end
279
280	--- Lerp between two quaternions.
281	-- @tparam quat a Left hand operand
282	-- @tparam quat b Right hand operand
283	-- @tparam number s Step value
284	-- @treturn quat out
285	function quat.lerp(a, b, s)	28✔
286	return (a + (b - a) * s):normalize()	14✔
287	end
288
289	--- Slerp between two quaternions.
290	-- @tparam quat a Left hand operand
291	-- @tparam quat b Right hand operand
292	-- @tparam number s Step value
293	-- @treturn quat out
294	function quat.slerp(a, b, s)	28✔
295	local dot = a:dot(b)	7✔
296
297	if dot < 0 then	7✔
UNCOV 298	a = -a	×
UNCOV 299	dot = -dot	×
300	end
301
302	if dot > DOT_THRESHOLD then	7✔
303	return a:lerp(b, s)	7✔
304	end
305
306	dot = min(max(dot, -1), 1)	×
307
308	local theta = acos(dot) * s	×
UNCOV 309	local c = (b - a * dot):normalize()	×
UNCOV 310	return a * cos(theta) + c * sin(theta)	×
311	end
312
313	--- Unpack a quaternion into individual components.
314	-- @tparam quat a Quaternion to unpack
315	-- @treturn number x
316	-- @treturn number y
317	-- @treturn number z
318	-- @treturn number w
319	function quat.unpack(a)	28✔
320	return a.x, a.y, a.z, a.w	7✔
321	end
322
323	--- Return a boolean showing if a table is or is not a quat.
324	-- @tparam quat a Quaternion to be tested
325	-- @treturn boolean is_quat
326	function quat.is_quat(a)	28✔
327	if type(a) == "cdata" then	525✔
UNCOV 328	return ffi.istype("cpml_quat", a)	×
329	end
330
UNCOV 331	return	×
332	type(a) == "table" and	525✔
333	type(a.x) == "number" and	399✔
334	type(a.y) == "number" and	399✔
335	type(a.z) == "number" and	399✔
336	type(a.w) == "number"	525✔
337	end
338
339	--- Return a boolean showing if a table is or is not a zero quat.
340	-- @tparam quat a Quaternion to be tested
341	-- @treturn boolean is_zero
342	function quat.is_zero(a)	28✔
UNCOV 343	return	×
344	a.x == 0 and	147✔
345	a.y == 0 and	7✔
346	a.z == 0 and	7✔
347	a.w == 0	147✔
348	end
349
350	--- Return a boolean showing if a table is or is not a real quat.
351	-- @tparam quat a Quaternion to be tested
352	-- @treturn boolean is_real
353	function quat.is_real(a)	28✔
UNCOV 354	return	×
355	a.x == 0 and	7✔
356	a.y == 0 and	7✔
357	a.z == 0	7✔
358	end
359
360	--- Return a boolean showing if a table is or is not an imaginary quat.
361	-- @tparam quat a Quaternion to be tested
362	-- @treturn boolean is_imaginary
363	function quat.is_imaginary(a)	28✔
364	return a.w == 0	7✔
365	end
366
367	--- Return whether any component is NaN
368	-- @tparam quat a Quaternion to be tested
369	-- @treturn boolean if x,y,z, or w is NaN
370	function quat.has_nan(a)	28✔
UNCOV 371	return private.is_nan(a.x) or	×
UNCOV 372	private.is_nan(a.y) or	×
UNCOV 373	private.is_nan(a.z) or	×
UNCOV 374	private.is_nan(a.w)	×
375	end
376
377	--- Convert a quaternion into an angle plus axis components.
378	-- @tparam quat a Quaternion to convert
379	-- @tparam identityAxis vec3 of axis to use on identity/degenerate quaternions (optional, default returns 0,0,0,1)
380	-- @treturn number angle
381	-- @treturn x axis-x
382	-- @treturn y axis-y
383	-- @treturn z axis-z
384	function quat.to_angle_axis_unpack(a, identityAxis)	28✔
385	if a.w > 1 or a.w < -1 then	49✔
386	a = a:normalize()	14✔
387	end
388
389	-- If length of xyz components is less than DBL_EPSILON, this is zero or close enough (an identity quaternion)
390	-- Normally an identity quat would return a nonsense answer, so we return an arbitrary zero rotation early.
391	-- FIXME: Is it safe to assume there are no valid quaternions with nonzero degenerate lengths?
392	if a.xa.x + a.ya.y + a.za.z < constants.DBL_EPSILONconstants.DBL_EPSILON then	49✔
393	if identityAxis then	14✔
394	return 0,identityAxis:unpack()	7✔
395	else
396	return 0,0,0,1	7✔
397	end
398	end
399
400	local x, y, z
401	local angle = 2 * acos(a.w)	35✔
402	local s = sqrt(1 - a.w * a.w)	35✔
403
404	if s < DBL_EPSILON then	35✔
405	x = a.x	7✔
406	y = a.y	7✔
407	z = a.z	7✔
408	else
409	x = a.x / s	28✔
410	y = a.y / s	28✔
411	z = a.z / s	28✔
412	end
413
414	return angle, x, y, z	35✔
415	end
416
417	--- Convert a quaternion into an angle/axis pair.
418	-- @tparam quat a Quaternion to convert
419	-- @tparam identityAxis vec3 of axis to use on identity/degenerate quaternions (optional, default returns 0,vec3(0,0,1))
420	-- @treturn number angle
421	-- @treturn vec3 axis
422	function quat.to_angle_axis(a, identityAxis)	28✔
423	local angle, x, y, z = a:to_angle_axis_unpack(identityAxis)	35✔
424	return angle, vec3(x, y, z)	35✔
425	end
426
427	--- Convert a quaternion into a vec3.
428	-- @tparam quat a Quaternion to convert
429	-- @treturn vec3 out
430	function quat.to_vec3(a)	28✔
431	return vec3(a.x, a.y, a.z)	7✔
432	end
433
434	--- Return a formatted string.
435	-- @tparam quat a Quaternion to be turned into a string
436	-- @treturn string formatted
437	function quat.to_string(a)	28✔
438	return string.format("(%+0.3f,%+0.3f,%+0.3f,%+0.3f)", a.x, a.y, a.z, a.w)	7✔
439	end
440
441	quat_mt.__index = quat	28✔
442	quat_mt.__tostring = quat.to_string	28✔
443
444	function quat_mt.__call(_, x, y, z, w)	28✔
445	return quat.new(x, y, z, w)	301✔
446	end
447
448	function quat_mt.__unm(a)	28✔
449	return a:scale(-1)	7✔
450	end
451
452	function quat_mt.__eq(a,b)	28✔
453	if not quat.is_quat(a) or not quat.is_quat(b) then	49✔
UNCOV 454	return false	×
455	end
456	return a.x == b.x and a.y == b.y and a.z == b.z and a.w == b.w	49✔
457	end
458
459	function quat_mt.__add(a, b)	28✔
460	precond.assert(quat.is_quat(a), "__add: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))	21✔
461	precond.assert(quat.is_quat(b), "__add: Wrong argument type '%s' for right hand operand. (<cpml.quat> expected)", type(b))	21✔
462	return a:add(b)	21✔
463	end
464
465	function quat_mt.__sub(a, b)	28✔
466	precond.assert(quat.is_quat(a), "__sub: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))	21✔
467	precond.assert(quat.is_quat(b), "__sub: Wrong argument type '%s' for right hand operand. (<cpml.quat> expected)", type(b))	21✔
468	return a:sub(b)	21✔
469	end
470
471	function quat_mt.__mul(a, b)	28✔
472	precond.assert(quat.is_quat(a), "__mul: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))	105✔
473	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)")	105✔
474
475	if quat.is_quat(b) then	105✔
476	return a:mul(b)	14✔
477	end
478
479	if type(b) == "number" then	91✔
480	return a:scale(b)	63✔
481	end
482
483	return a:mul_vec3(b)	28✔
484	end
485
486	function quat_mt.__pow(a, n)	28✔
487	precond.assert(quat.is_quat(a), "__pow: Wrong argument type '%s' for left hand operand. (<cpml.quat> expected)", type(a))	21✔
488	precond.typeof(n, "number", "__pow: Wrong argument type for right hand operand.")	21✔
489	return a:pow(n)	21✔
490	end
491
492	if status then	28✔
UNCOV 493	xpcall(function() -- Allow this to silently fail; assume failure means someone messed with package.loaded	×
UNCOV 494	ffi.metatype(new, quat_mt)	×
UNCOV 495	end, function() end)	×
496	end
497
498	return setmetatable({}, quat_mt)	28✔

excessive / cpml / 1

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