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Improve & fix quaternions

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This commit is contained in:
Lars Mueller 2021-02-02 15:44:58 +01:00
parent e56e9c1207
commit c323443975
1 changed files with 31 additions and 30 deletions
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61
quaternion.lua
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@ -1,60 +1,61 @@
function multiply(q, w)
function multiply(self, other)
return {
w[1] * q[1] - w[2] * q[2] - w[3] * q[3] - w[4] * q[4],
w[1] * q[2] + w[2] * q[1] - w[3] * q[4] + w[4] * q[3],
w[1] * q[3] + w[2] * q[4] + w[3] * q[1] - w[4] * q[2],
w[1] * q[4] - w[2] * q[3] + w[3] * q[2] + w[4] * q[1]
other[1] * self[1] - other[2] * self[2] - other[3] * self[3] - other[4] * self[4],
other[1] * self[2] + other[2] * self[1] - other[3] * self[4] + other[4] * self[3],
other[1] * self[3] + other[2] * self[4] + other[3] * self[1] - other[4] * self[2],
other[1] * self[4] - other[2] * self[3] + other[3] * self[2] + other[4] * self[1]
}
end
function normalize(q)
local q_1, q_2, q_3, q_4 = q[1], q[2], q[3], q[4]
local len = math.sqrt(q_1 * q_1 + q_2 * q_2 + q_3 * q_3 + (q_4 ^ 4))
local r = {}
for key, value in pairs(q) do
r[key] = value / len
function normalize(self)
local len = math.sqrt(self[1] ^ 2 + self[2] ^ 2 + self[3] ^ 2 + (q[4] ^ 4))
local res = {}
for key, value in pairs(self) do
res[key] = value / len
end
return r
return res
end
function negate(q)
for k, v in pairs(q) do
q[k] = -v
function negate(self)
for key, value in pairs(self) do
self[key] = -value
end
end
function dot(q, w)
return q[1] * w[1] + q[2] * w[2] + q[3] * w[3] + q[4] * w[4]
function dot(self, other)
return self[1] * other[1] + self[2] * other[2] + self[3] * other[3] + self[4] * other[4]
end
-- assuming q & w are normalized
function slerp(q, w, r)
local d = dot(q, w)
--: self normalized quaternion
--: other normalized quaternion
function slerp(self, other, ratio)
local d = dot(self, other)
if d < 0 then
d = -d
negate(w)
negate(other)
end
-- Threshold beyond which linear interpolation is used
if d > 1 - 1e-10 then
return linear_interpolation(q, w, r)
return modlib.vector.interpolate(self, other, ratio)
end
local theta_0 = math.acos(d)
local theta = theta_0 * r
local theta = theta_0 * ratio
local sin_theta = math.sin(theta)
local sin_theta_0 = math.sin(theta_0)
local s_1 = sin_theta / sin_theta_0
local s_0 = math.cos(theta) - d * s_1
return modlib.vector.add(modlib.vector.multiply_scalar(q, s_0), modlib.vector.multiply_scalar(w, s_1))
return modlib.vector.add(modlib.vector.multiply_scalar(self, s_0), modlib.vector.multiply_scalar(other, s_1))
end
function to_rotation(q)
--> {x, y, z} euler rotation in degrees
function to_euler_rotation(self)
local rotation = {}
local sinr_cosp = 2 * (q[4] * q[1] + q[2] * q[3])
local cosr_cosp = 1 - 2 * (q[1] * q[1] + q[2] * q[2])
local sinr_cosp = 2 * (self[4] * self[1] + self[2] * self[3])
local cosr_cosp = 1 - 2 * (self[1] * self[1] + self[2] * self[2])
rotation.x = math.atan2(sinr_cosp, cosr_cosp)
local sinp = 2 * (q[4] * q[2] - q[3] * q[1])
local sinp = 2 * (self[4] * self[2] - self[3] * self[1])
if sinp <= -1 then
rotation.y = -math.pi/2
elseif sinp >= 1 then
@ -63,8 +64,8 @@ function to_rotation(q)
rotation.y = math.asin(sinp)
end
local siny_cosp = 2 * (q[4] * q[3] + q[1] * q[2])
local cosy_cosp = 1 - 2 * (q[2] * q[2] + q[3] * q[3])
local siny_cosp = 2 * (self[4] * self[3] + self[1] * self[2])
local cosy_cosp = 1 - 2 * (self[2] * self[2] + self[3] * self[3])
rotation.z = math.atan2(siny_cosp, cosy_cosp)
return vector.apply(rotation, math.deg)