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Copyright (c) 2010-2013 Matthias Richter
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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Except as contained in this notice, the name(s) of the above copyright holders
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shall not be used in advertising or otherwise to promote the sale, use or
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other dealings in this Software without prior written authorization.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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local sqrt, cos, sin = math.sqrt, math.cos, math.sin
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vector.__index = vector
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local function new(x,y)
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return setmetatable({x = x or 0, y = y or 0}, vector)
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local function isvector(v)
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return getmetatable(v) == vector
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function vector:clone()
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return new(self.x, self.y)
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function vector:unpack()
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function vector:__tostring()
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return "("..tonumber(self.x)..","..tonumber(self.y)..")"
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function vector.__unm(a)
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return new(-a.x, -a.y)
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function vector.__add(a,b)
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assert(isvector(a) and isvector(b), "Add: wrong argument types (<vector> expected)")
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return new(a.x+b.x, a.y+b.y)
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function vector.__sub(a,b)
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assert(isvector(a) and isvector(b), "Sub: wrong argument types (<vector> expected)")
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return new(a.x-b.x, a.y-b.y)
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function vector.__mul(a,b)
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if type(a) == "number" then
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return new(a*b.x, a*b.y)
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elseif type(b) == "number" then
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return new(b*a.x, b*a.y)
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assert(isvector(a) and isvector(b), "Mul: wrong argument types (<vector> or <number> expected)")
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return a.x*b.x + a.y*b.y
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function vector.__div(a,b)
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assert(isvector(a) and type(b) == "number", "wrong argument types (expected <vector> / <number>)")
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return new(a.x / b, a.y / b)
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function vector.__eq(a,b)
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return a.x == b.x and a.y == b.y
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function vector.__lt(a,b)
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return a.x < b.x or (a.x == b.x and a.y < b.y)
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function vector.__le(a,b)
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return a.x <= b.x and a.y <= b.y
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function vector.permul(a,b)
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assert(isvector(a) and isvector(b), "permul: wrong argument types (<vector> expected)")
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return new(a.x*b.x, a.y*b.y)
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function vector:len2()
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return self.x * self.x + self.y * self.y
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function vector:len()
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return sqrt(self.x * self.x + self.y * self.y)
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function vector.dist(a, b)
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assert(isvector(a) and isvector(b), "dist: wrong argument types (<vector> expected)")
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return sqrt(dx * dx + dy * dy)
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function vector:normalize_inplace()
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self.x, self.y = self.x / l, self.y / l
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function vector:normalized()
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return self:clone():normalize_inplace()
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function vector:rotate_inplace(phi)
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local c, s = cos(phi), sin(phi)
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self.x, self.y = c * self.x - s * self.y, s * self.x + c * self.y
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function vector:rotated(phi)
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local c, s = cos(phi), sin(phi)
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return new(c * self.x - s * self.y, s * self.x + c * self.y)
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function vector:perpendicular()
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return new(-self.y, self.x)
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function vector:projectOn(v)
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assert(isvector(v), "invalid argument: cannot project vector on " .. type(v))
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-- (self * v) * v / v:len2()
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local s = (self.x * v.x + self.y * v.y) / (v.x * v.x + v.y * v.y)
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return new(s * v.x, s * v.y)
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function vector:mirrorOn(v)
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assert(isvector(v), "invalid argument: cannot mirror vector on " .. type(v))
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-- 2 * self:projectOn(v) - self
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local s = 2 * (self.x * v.x + self.y * v.y) / (v.x * v.x + v.y * v.y)
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return new(s * v.x - self.x, s * v.y - self.y)
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function vector:cross(v)
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assert(isvector(v), "cross: wrong argument types (<vector> expected)")
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return self.x * v.y - self.y * v.x
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function vector:trim_inplace(maxLen)
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local s = maxLen * maxLen / self:len2()
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s = s < 1 and 1 or math.sqrt(s)
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self.x, self.y = self.x * s, self.y * s
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function vector:trimmed(maxLen)
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return self:clone():trim_inplace(maxLen)
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return setmetatable({new = new, isvector = isvector},
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{__call = function(_, ...) return new(...) end})
added
removed
vector.lua
