Lightweight Ray Object

line.lua

--[[
Copyright (c) 2014 Tanner Rogalsky

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 Line = {}
Line.__index = Line
local Vector = require("vector")

function Line.new(x1, y1, x2, y2)
  local self = setmetatable({}, Line)

  self.origin = Vector(x1, y1)
  self.destination = Vector(x2, y2)
  self.delta = self.destination - self.origin

  return self
end

function Line.is_line(line)
  return getmetatable(line) == Line
end

function Line.__lt(a,b)
  return a.delta:len() < b.delta:len()
end

function Line:rotate(phi)
  local x1, y1 = self.origin:unpack()
  local x2, y2 = (self.delta:rotated(phi) + self.origin):unpack()
  return Line.new(x1, y1, x2, y2)
end

function Line:intersects(other)
  assert(Line.is_line(other), "Can only check against other Lines.")

  local px, py = self.origin:unpack()
  local dx, dy = self.delta:unpack()

  local o_px, o_py = other.origin:unpack()
  local o_dx, o_dy = other.delta:unpack()

  local mag = self.delta:len()
  local o_mag = other.delta:len()
  if dx / mag == o_dx / o_mag and dy / mag == o_dy / o_mag then
    -- Directions are the same.
    return nil
  end

  -- SOLVE FOR T1 & T2
  -- http://ncase.github.io/sight-and-light/
  local T2 = (dx * (o_py - py) + dy * (px - o_px)) / (o_dx * dy - o_dy * dx)
  local T1 = (o_px + o_dx * T2 - px) / dx

  if T1 < 0 then return nil end
  if T2 < 0 or T2 > 1 then return nil end

  -- Return the intersection ray
  return Line.new(px, py, px + dx * T1, py + dy * T1)
end

function Line:unpack()
  local x1, y1 = self.origin:unpack()
  local x2, y2 = self.destination:unpack()
  return x1, y1, x2, y2
end

return Line

vector.lua

--[[
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, atan2 = math.sqrt, math.cos, math.sin, math.atan2

local vector = {}
vector.__index = vector

local function new(x,y)
  return setmetatable({x = x or 0, y = y or 0}, vector)
end
local zero = new(0,0)

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 (<vector> 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 (<vector> 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 (<vector> or <number> 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 <vector> / <number>)")
  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 (<vector> 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 (<vector> expected)")
  local dx = a.x - b.x
  local dy = a.y - b.y
  return sqrt(dx * dx + dy * dy)
end

function vector.dist2(a, b)
  assert(isvector(a) and isvector(b), "dist: wrong argument types (<vector> expected)")
  local dx = a.x - b.x
  local dy = a.y - b.y
  return (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 (<vector> 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:angleTo(other)
  if other then
    return atan2(self.y, self.x) - atan2(other.y, other.x)
  end
  return atan2(self.y, self.x)
end

function vector:trimmed(maxLen)
  return self:clone():trim_inplace(maxLen)
end


-- the module
return setmetatable({new = new, isvector = isvector, zero = zero},
{__call = function(_, ...) return new(...) end})