Add light vector module

vector-light.lua

@@ -0,0 +1,144 @@
+--[[
+Copyright (c) 2012 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 sqrt, cos, sin = math.sqrt, math.cos, math.sin
+
+local function str(x,y)
+	return "("..tonumber(x)..","..tonumber(y)..")"
+end
+
+local function neg(x,y)
+	return -x, -y
+end
+
+local function add(x1,y1, x2,y2)
+	return x1+x2, y1+y2
+end
+
+local function sub(x1,y1, x2,y2)
+	return x1-x2, y1-y2
+end
+
+
+local function mul(x,y, s)
+	return s*x, s*y
+end
+
+local function div(x,y, s)
+	return x/s, y/s
+end
+
+local function permul(x1,y1, x2,y2)
+	return x1*x2, y1*y2
+end
+
+local function dot(x1,y1, x2,y2)
+	return x1*x2 + y1*y2
+end
+
+local function det(x1,y1, x2,y2)
+	return x1 * y2 - y1 * x2
+end
+
+local function eq(x1,y1, x2,y2)
+	return x1 == x2 and y1 == y2
+end
+
+local function lt(x1,y1, x2,y2)
+	return x1 < x2 or (x1 == x2 and y1 < y2)
+end
+
+local function le(x1,y1, x2,y2)
+	return x1 <= x2 and y1 <= y2
+end
+
+local function len2(x,y)
+	return x*x + y*y
+end
+
+local function len(x,y)
+	return sqrt(x*x + y*y)
+end
+
+local function dist(x1,y1, x2,y2)
+	return len(x1-x2, y1-y2)
+end
+
+local function normalize(x,y)
+	local l = len(x,y)
+	return x/l, y/l
+end
+
+local function rotate(x,y, phi)
+	local c, s = cos(phi), sin(phi)
+	return c*x - s*y, s*x + c*y
+end
+
+local function perpendicular(x,y)
+	return -y, x
+end
+
+local function project(x,y, u,v)
+	local s = (x*u + y*v) / (u*u + v*v)
+	return s*u, s*v
+end
+
+local function mirror(x,y, u,v)
+	local s = 2 * (x*u + y*v) / (u*u + v*v)
+	return s*u - x, s*v - y
+end
+
+
+-- the module
+return {
+	str = str,
+
+	-- arithmetic
+	neg    = neg,
+	add    = add,
+	sub    = sub,
+	mul    = mul,
+	div    = div,
+	permul = permul,
+	dot    = dot,
+	det    = det,
+	cross  = det,
+
+	-- relation
+	eq = eq,
+	lt = lt,
+	le = le,
+
+	-- misc operations
+	len2          = len2,
+	len           = len,
+	dist          = dist,
+	normalize     = normalize,
+	rotate        = rotate,
+	perpendicular = perpendicular,
+	project       = project,
+	mirror        = mirror,
+}