--[[ Copyright (c) 2010-2013 Matthias Richter Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. Except as contained in this notice, the name(s) of the above copyright holders shall not be used in advertising or otherwise to promote the sale, use or other dealings in this Software without prior written authorization. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ]]-- local assert = assert local sqrt, cos, sin = math.sqrt, math.cos, math.sin local vector = {} vector.__index = vector local function new(x,y) return setmetatable({x = x or 0, y = y or 0}, vector) end local function isvector(v) return getmetatable(v) == vector end function vector:clone() return new(self.x, self.y) end function vector:unpack() return self.x, self.y end function vector:__tostring() return "("..tonumber(self.x)..","..tonumber(self.y)..")" end function vector.__unm(a) return new(-a.x, -a.y) end function vector.__add(a,b) assert(isvector(a) and isvector(b), "Add: wrong argument types ( expected)") return new(a.x+b.x, a.y+b.y) end function vector.__sub(a,b) assert(isvector(a) and isvector(b), "Sub: wrong argument types ( expected)") return new(a.x-b.x, a.y-b.y) end function vector.__mul(a,b) if type(a) == "number" then return new(a*b.x, a*b.y) elseif type(b) == "number" then return new(b*a.x, b*a.y) else assert(isvector(a) and isvector(b), "Mul: wrong argument types ( or expected)") return a.x*b.x + a.y*b.y end end function vector.__div(a,b) assert(isvector(a) and type(b) == "number", "wrong argument types (expected / )") return new(a.x / b, a.y / b) end function vector.__eq(a,b) return a.x == b.x and a.y == b.y end function vector.__lt(a,b) return a.x < b.x or (a.x == b.x and a.y < b.y) end function vector.__le(a,b) return a.x <= b.x and a.y <= b.y end function vector.permul(a,b) assert(isvector(a) and isvector(b), "permul: wrong argument types ( expected)") return new(a.x*b.x, a.y*b.y) end function vector:len2() return self.x * self.x + self.y * self.y end function vector:len() return sqrt(self.x * self.x + self.y * self.y) end function vector.dist(a, b) assert(isvector(a) and isvector(b), "dist: wrong argument types ( expected)") local dx = a.x - b.x local dy = a.y - b.y return sqrt(dx * dx + dy * dy) end function vector:normalize_inplace() local l = self:len() if l > 0 then self.x, self.y = self.x / l, self.y / l end return self end function vector:normalized() return self:clone():normalize_inplace() end function vector:rotate_inplace(phi) local c, s = cos(phi), sin(phi) self.x, self.y = c * self.x - s * self.y, s * self.x + c * self.y return self end function vector:rotated(phi) local c, s = cos(phi), sin(phi) return new(c * self.x - s * self.y, s * self.x + c * self.y) end function vector:perpendicular() return new(-self.y, self.x) end function vector:projectOn(v) assert(isvector(v), "invalid argument: cannot project vector on " .. type(v)) -- (self * v) * v / v:len2() local s = (self.x * v.x + self.y * v.y) / (v.x * v.x + v.y * v.y) return new(s * v.x, s * v.y) end function vector:mirrorOn(v) assert(isvector(v), "invalid argument: cannot mirror vector on " .. type(v)) -- 2 * self:projectOn(v) - self local s = 2 * (self.x * v.x + self.y * v.y) / (v.x * v.x + v.y * v.y) return new(s * v.x - self.x, s * v.y - self.y) end function vector:cross(v) assert(isvector(v), "cross: wrong argument types ( expected)") return self.x * v.y - self.y * v.x end -- ref.: http://blog.signalsondisplay.com/?p=336 function vector:trim_inplace(maxLen) local s = maxLen * maxLen / self:len2() s = s < 1 and 1 or math.sqrt(s) self.x, self.y = self.x * s, self.y * s return self end function vector:trimmed(maxLen) return self:clone():trim_inplace(maxLen) end -- the module return setmetatable({new = new, isvector = isvector}, {__call = function(_, ...) return new(...) end})