75 lines
1.9 KiB
Lua
75 lines
1.9 KiB
Lua
--[[
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Copied over from https://rosettacode.org/wiki/Quaternion_type#Lua
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--]]
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--////////////////--
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--// quaternion //--
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--////////////////--
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local Quaternion = {}
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function Quaternion.new( a, b, c, d )
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local q = { a = a or 1, b = b or 0, c = c or 0, d = d or 0 }
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local metatab = {}
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setmetatable( q, metatab )
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metatab.__add = Quaternion.add
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metatab.__sub = Quaternion.sub
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metatab.__unm = Quaternion.unm
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metatab.__mul = Quaternion.mul
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return q
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end
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function Quaternion.add( p, q )
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if type( p ) == "number" then
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return Quaternion.new( p+q.a, q.b, q.c, q.d )
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elseif type( q ) == "number" then
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return Quaternion.new( p.a+q, p.b, p.c, p.d )
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else
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return Quaternion.new( p.a+q.a, p.b+q.b, p.c+q.c, p.d+q.d )
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end
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end
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function Quaternion.sub( p, q )
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if type( p ) == "number" then
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return Quaternion.new( p-q.a, q.b, q.c, q.d )
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elseif type( q ) == "number" then
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return Quaternion.new( p.a-q, p.b, p.c, p.d )
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else
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return Quaternion.new( p.a-q.a, p.b-q.b, p.c-q.c, p.d-q.d )
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end
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end
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function Quaternion.unm( p )
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return Quaternion.new( -p.a, -p.b, -p.c, -p.d )
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end
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function Quaternion.mul( p, q )
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if type( p ) == "number" then
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return Quaternion.new( p*q.a, p*q.b, p*q.c, p*q.d )
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elseif type( q ) == "number" then
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return Quaternion.new( p.a*q, p.b*q, p.c*q, p.d*q )
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else
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return Quaternion.new( p.a*q.a - p.b*q.b - p.c*q.c - p.d*q.d,
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p.a*q.b + p.b*q.a + p.c*q.d - p.d*q.c,
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p.a*q.c - p.b*q.d + p.c*q.a + p.d*q.b,
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p.a*q.d + p.b*q.c - p.c*q.b + p.d*q.a )
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end
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end
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function Quaternion.conj( p )
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return Quaternion.new( p.a, -p.b, -p.c, -p.d )
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end
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function Quaternion.norm( p )
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return math.sqrt( p.a^2 + p.b^2 + p.c^2 + p.d^2 )
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end
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function Quaternion.print( p )
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print( string.format( "%f + %fi + %fj + %fk\n", p.a, p.b, p.c, p.d ) )
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end
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return Quaternion |