#!/usr/bin/lua

module('gluon.pointwithinshape', package.seeall)

-- Begin https://love2d.org/wiki/PointWithinShape
function PointWithinShape(shape, tx, ty)
	if #shape == 0 then
		return false
	elseif #shape == 1 then
		return shape[1].x == tx and shape[1].y == ty
	elseif #shape == 2 then
		return PointWithinLine(shape, tx, ty)
	else
		return CrossingsMultiplyTest(shape, tx, ty)
	end
end

function BoundingBox(box, tx, ty)
	return	(box[2].x >= tx and box[2].y >= ty)
		and (box[1].x <= tx and box[1].y <= ty)
		or  (box[1].x >= tx and box[2].y >= ty)
		and (box[2].x <= tx and box[1].y <= ty)
end

function colinear(line, x, y, e)
	e = e or 0.1
	m = (line[2].y - line[1].y) / (line[2].x - line[1].x)
	local function f(x) return line[1].y + m*(x - line[1].x) end
	return math.abs(y - f(x)) <= e
end

function PointWithinLine(line, tx, ty, e)
	e = e or 0.66
	if BoundingBox(line, tx, ty) then
		return colinear(line, tx, ty, e)
	else
		return false
	end
end

-------------------------------------------------------------------------
-- The following function is based off code from
-- [ http://erich.realtimerendering.com/ptinpoly/ ]
--
--[[
 ======= Crossings Multiply algorithm ===================================
 * This version is usually somewhat faster than the original published in
 * Graphics Gems IV; by turning the division for testing the X axis crossing
 * into a tricky multiplication test this part of the test became faster,
 * which had the additional effect of making the test for "both to left or
 * both to right" a bit slower for triangles than simply computing the
 * intersection each time.  The main increase is in triangle testing speed,
 * which was about 15% faster; all other polygon complexities were pretty much
 * the same as before.  On machines where division is very expensive (not the
 * case on the HP 9000 series on which I tested) this test should be much
 * faster overall than the old code.  Your mileage may (in fact, will) vary,
 * depending on the machine and the test data, but in general I believe this
 * code is both shorter and faster.  This test was inspired by unpublished
 * Graphics Gems submitted by Joseph Samosky and Mark Haigh-Hutchinson.
 * Related work by Samosky is in:
 *
 * Samosky, Joseph, "SectionView: A system for interactively specifying and
 * visualizing sections through three-dimensional medical image data",
 * M.S. Thesis, Department of Electrical Engineering and Computer Science,
 * Massachusetts Institute of Technology, 1993.
 *
 --]]

--[[ Shoot a test ray along +X axis.  The strategy is to compare vertex Y values
 * to the testing point's Y and quickly discard edges which are entirely to one
 * side of the test ray.  Note that CONVEX and WINDING code can be added as
 * for the CrossingsTest() code; it is left out here for clarity.
 *
 * Input 2D polygon _pgon_ with _numverts_ number of vertices and test point
 * _point_, returns 1 if inside, 0 if outside.
 --]]
function CrossingsMultiplyTest(pgon, tx, ty)
	local i, yflag0, yflag1, inside_flag
	local vtx0, vtx1

	local numverts = #pgon

	vtx0 = pgon[numverts]
	vtx1 = pgon[1]

	-- get test bit for above/below X axis
	yflag0 = ( vtx0.y >= ty )
	inside_flag = false

	for i=2,numverts+1 do
		yflag1 = ( vtx1.y >= ty )

		--[[ Check if endpoints straddle (are on opposite sides) of X axis
		 * (i.e. the Y's differ); if so, +X ray could intersect this edge.
		 * The old test also checked whether the endpoints are both to the
		 * right or to the left of the test point.  However, given the faster
		 * intersection point computation used below, this test was found to
		 * be a break-even proposition for most polygons and a loser for
		 * triangles (where 50% or more of the edges which survive this test
		 * will cross quadrants and so have to have the X intersection computed
		 * anyway).  I credit Joseph Samosky with inspiring me to try dropping
		 * the "both left or both right" part of my code.
		 --]]
		if ( yflag0 ~= yflag1 ) then
			--[[ Check intersection of pgon segment with +X ray.
			 * Note if >= point's X; if so, the ray hits it.
			 * The division operation is avoided for the ">=" test by checking
			 * the sign of the first vertex wrto the test point; idea inspired
			 * by Joseph Samosky's and Mark Haigh-Hutchinson's different
			 * polygon inclusion tests.
			 --]]
			if ( ((vtx1.y - ty) * (vtx0.x - vtx1.x) >= (vtx1.x - tx) * (vtx0.y - vtx1.y)) == yflag1 ) then
				inside_flag =  not inside_flag
			end
		end

		-- Move to the next pair of vertices, retaining info as possible.
		yflag0  = yflag1
		vtx0    = vtx1
		vtx1    = pgon[i]
	end

	return  inside_flag
end
-- End https://love2d.org/wiki/PointWithinShape