luanti-extended-engine-features/leef-math-cd2025
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Merge pull request #29 from mcclure/quat-component

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Quaternions: Add "unpacked" versions of to_angle_axis and from_angle
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Colby Klein 2018-02-22 04:07:06 -08:00 committed by GitHub
commit ef46425cfe
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2 changed files with 46 additions and 11 deletions
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42
modules/quat.lua
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@ -80,12 +80,19 @@ end
--- Create a quaternion from an angle/axis pair.
-- @tparam number angle Angle (in radians)
-- @tparam vec3 axis
-- @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)
local s = sin(angle * 0.5)
local c = cos(angle * 0.5)
return new(axis.x * s, axis.y * s, axis.z * s, c)
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.
@ -229,10 +236,12 @@ end
--- Alias of from_angle_axis.
-- @tparam number angle Angle (in radians)
-- @tparam vec3 axis
-- @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)
return quat.from_angle_axis(angle, axis)
function quat.rotate(angle, axis, a3, a4)
return quat.from_angle_axis(angle, axis, a3, a4)
end
--- Return the conjugate of a quaternion.
@ -357,11 +366,13 @@ function quat.is_imaginary(a)
return a.w == 0
end
--- Convert a quaternion into an angle/axis pair.
--- Convert a quaternion into an angle plus axis components.
-- @tparam quat a Quaternion to convert
-- @treturn number angle
-- @treturn vec3 axis
function quat.to_angle_axis(a)
-- @treturn x axis-x
-- @treturn y axis-y
-- @treturn z axis-z
function quat.to_angle_axis_unpack(a)
if a.w > 1 or a.w < -1 then
a = a:normalize()
end
@ -380,6 +391,15 @@ function quat.to_angle_axis(a)
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
-- @treturn number angle
-- @treturn vec3 axis
function quat.to_angle_axis(a)
local angle, x, y, z = a:to_angle_axis_unpack()
return angle, vec3(x, y, z)
end

15
spec/quat_spec.lua
View File

@ -279,6 +279,13 @@ describe("quat:", function()
assert.is.equal(vec3.unit_z, axis)
end)
it("converts between a quaternion and angle/axis (specify by component)", function()
local a = quat.from_angle_axis(math.pi, vec3.unit_z.x, vec3.unit_z.y, vec3.unit_z.z)
local angle, axis = a:to_angle_axis()
assert.is.equal(math.pi, angle)
assert.is.equal(vec3.unit_z, axis)
end)
it("converts between a quaternion and angle/axis (w=2)", function()
local angle, axis = quat(1, 1, 1, 2):to_angle_axis()
assert.is_true(utils.tolerance(1.427-angle, 0.001))
@ -287,6 +294,14 @@ describe("quat:", function()
assert.is_true(utils.tolerance(0.577-axis.z, 0.001))
end)
it("converts between a quaternion and angle/axis (w=2) (by component)", function()
local angle, x,y,z = quat(1, 1, 1, 2):to_angle_axis_unpack()
assert.is_true(utils.tolerance(1.427-angle, 0.001))
assert.is_true(utils.tolerance(0.577-x, 0.001))
assert.is_true(utils.tolerance(0.577-y, 0.001))
assert.is_true(utils.tolerance(0.577-z, 0.001))
end)
it("converts between a quaternion and angle/axis (w=1)", function()
local angle, axis = quat(1, 2, 3, 1):to_angle_axis()
assert.is.equal(0, angle)