QuaternionClass
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local quaternion = {}
local quaternion_mt = {__index = quaternion};
function quaternion_mt.__unm(q)
return quaternion.new(-q.w, -q.x, -q.y, -q.z)
end
function quaternion_mt.__mul(q0, q1)
local w0, w1 = q0.w, q1.w;
local v0, v1 = Vector3.new(q0.x, q0.y, q0.z), Vector3.new(q1.x, q1.y, q1.z);
local nw = w0*w1 - v0:Dot(v1);
local nv = v0*w1 + v1*w0 + v0:Cross(v1);
return quaternion.new(nw, nv.x, nv.y, nv.z);
end
function quaternion_mt.__pow(q, t)
local axis, theta = q:toAxisAngle();
theta = theta*t*0.5;
axis = math.sin(theta)*axis;
return quaternion.new(math.cos(theta), axis.x, axis.y, axis.z);
end
function quaternion_mt.__tostring(q)
-- print as floats, be aware a more precise number is actually stored
return string.format("%f, %f, %f, %f", q.w, q.x, q.y, q.z);
end
function quaternion.new(w, x, y, z)
local self = {};
local m = 1 / math.sqrt(w*w + x*x + y*y + z*z);
self.w = w * m;
self.x = x * m;
self.y = y * m;
self.z = z * m;
return setmetatable(self, quaternion_mt);
end
function quaternion.fromCFrame(cf)
local x, y, z, m11, m12, m13, m21, m22, m23, m31, m32, m33 = cf:components();
local qw, qx, qy, qz;
if (m11 + m22 + m33 > 0) then
qw = math.sqrt(1 + m11 + m22 + m33) * 0.5;
qx = (m32-m23) / (4*qw);
qy = (m13-m31) / (4*qw);
qz = (m21-m12) / (4*qw);
elseif (m11 > m22 and m11 > m33) then
qx = math.sqrt(1 + m11 - m22 - m33) * 0.5;
qy = (m21+m12) / (4*qx);
qz = (m31+m13) / (4*qx);
qw = (m32-m23) / (4*qx);
elseif (m22 > m33) then
qy = math.sqrt(1 + m22 - m11 - m33) * 0.5;
qx = (m21+m12) / (4*qy);
qz = (m32+m23) / (4*qy);
qw = (m13-m31) / (4*qy);
else
qz = math.sqrt(1 + m33 - m11 - m22) * 0.5;
qx = (m31+m13) / (4*qz);
qy = (m32+m23) / (4*qz);
qw = (m21-m12) / (4*qz);
end
return quaternion.new(qw, qx, qy, qz);
end
function quaternion:Dot(q2)
local q1 = self;
return q1.w*q2.w + q1.x*q2.x + q1.y*q2.y + q1.z*q2.z;
end
function quaternion:inverse()
local conjugate = self:Dot(self);
return quaternion.new(self.w / conjugate, -self.x / conjugate, -self.y / conjugate, -self.z / conjugate);
end
function quaternion:toAxisAngle()
local v = Vector3.new(self.x, self.y, self.z);
local theta = math.acos(self.w)*2;
local axis = v / math.sin(theta*0.5);
return axis, theta;
end
function quaternion:toCFrame()
local w, x, y, z = self.w, self.x, self.y, self.z;
return CFrame.new(0, 0, 0,
1-2*(y*y+z*z), 2*(y*x-w*z), 2*(w*y+z*x),
2*(w*z+y*x), 1-2*(x*x+z*z), 2*(z*y-w*x),
2*(z*x-w*y), 2*(w*x+z*y), 1-2*(x*x+y*y)
);
end
function quaternion:slerp(q2, t)
local q1 = self;
if (q1:Dot(q2) < 0) then
q2 = -q2;
end
return (q2 * q1:inverse())^t * q1;
end
return quaternion;
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