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90 lines
No EOL
2.6 KiB
Lua
90 lines
No EOL
2.6 KiB
Lua
--- Quaternion
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local qt
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local sin, cos = math.sin, math.cos
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local m4 = require((...):match("^(.*)qt$").."m4")
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-- qt methods
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-- Unless specified otherwise, all operations are done in place and do not create a new quaternion.
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local qt_mt = {
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-- Clone the quaternion. Returns a new quaternion.
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clone = function(self)
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return qt(self[1], self[2], self[3], self[4])
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end,
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-- Set quaternion
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set = function(self, other)
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self[1], self[2], self[3], self[4] = other[1], other[2], other[3], other[4]
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return self
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end,
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-- Retrieve coordinates
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unpack = function(self)
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return self[1], self[2], self[3], self[4]
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end,
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-- Convert to m4 rotation matrix. Returns a new 4x4 matrix.
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toM4 = function(self)
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local x, y, z, w = self[1], self[2], self[3], self[4]
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local xx, yy, zz = x*x, y*y, z*z
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local xw, xy, xz = x*w, x*y, x*z
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local yw, yz = y*w, y*z
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local zw = z*w
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return m4{
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1-2*(yy+zz), 2*(xy-zw), 2*(xz+yw), 0,
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2*(xy+zw), 1-2*(xx+zz), 2*(yz-xw), 0,
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2*(xz-yw), 2*(yz+xw), 1-2*(xx+yy), 0,
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0, 0, 0, 1
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}
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end,
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-- Common operations. Returns a new quaternion.
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__sub = function(self, other)
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return qt(self[1] - other[1], self[2] - other[2], self[3] - other[3], self[4] - other[4])
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end,
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__add = function(self, other)
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return qt(self[1] + other[1], self[2] + other[2], self[3] + other[3], self[4] - other[4])
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end,
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__unm = function(self)
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return qt(-self[1], -self[2], -self[3], -self[4])
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end,
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__mul = function(self, other)
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local sx, sy, sz, sw = self[1], self[2], self[3], self[4]
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local ox, oy, oz, ow = other[1], other[2], other[3], other[4]
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return qt(sw * ow - sx * ox - sy * oy - sz * oz, sx * ow + sw * ox + sy * oz - sz * oy, sy * ow + sw * oy + sz * ox - sx * oz, sz * ow + sw * oz + sx * oy - sy * ox)
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end,
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__eq = function(self, other)
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return self[1] == other[1] and self[2] == other[2] and self[3] == other[3] and self[4] == other[4]
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end,
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__tostring = function(self)
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return ("qt(%s,%s,%s,%s)"):format(self[1], self[2], self[3], self[4])
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end
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}
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qt_mt.__index = qt_mt
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qt = setmetatable({
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--- Create a new identity quaternion
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identity = function()
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return qt(0, 0, 0, 1)
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end,
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--- Create a new quaternion from a rotation
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fromAngleAxis = function(angle, axis)
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local halfAngle = angle / 2
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local s = sin(halfAngle)
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return qt(axis[1] * s, axis[2] * s, axis[3] * s, cos(halfAngle))
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end,
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}, {
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-- If x is a table, will reuse it without copying.
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__call = function(self, x, y, z, w)
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if type(x) == "number" then
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return setmetatable({ x, y, z, w }, qt_mt)
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else
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return setmetatable(x, qt_mt)
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end
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end
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})
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return qt |