LÖVE

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local rectangleX = 200
local rectangleY = 200
local width = 100
-- X, Y pairs for the 4 clockwise points of a square.
local polygonPoints = {
    rectangleX, rectangleY,
    rectangleX+width, rectangleY,
    rectangleX+width, rectangleY+width,
    rectangleX, rectangleY+width,
}

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-- push-rectangle.lua
-- cc0, darkfrei 2023

local pr = {}

function pr.newPolygon (polygon)
	if #polygon % 2 ~= 0 then
    error('Polygon coordinates are missing a value')
	end
	local minX, minY = polygon[1], polygon[2]
	local maxX, maxY = polygon[1], polygon[2]
	for i = 3, #polygon-1, 2 do
		minX = math.min (minX, polygon[i])
		minY = math.min (minY, polygon[i+1])
		maxX = math.max (maxX, polygon[i])
		maxY = math.max (maxY, polygon[i+1])
	end
	for i = 1, #polygon-1, 2 do
		polygon[i] = polygon[i] - minX
		polygon[i+1] = polygon[i+1] - minY
	end
	polygon.x = minX
	polygon.y = minY
	polygon.w = maxX-minX
	polygon.h = maxY-minY
	return polygon
end


function pr.newline (line)
	if #line % 2 ~= 0 then
    error('line coordinates are missing a value')
	end
	local minX, minY = line[1], line[2]
	local maxX, maxY = line[1], line[2]
	for i = 3, #line-1, 2 do
		minX = math.min (minX, line[i])
		maxX = math.max (maxX, line[i])
		minY = math.min (minY, line[i+1])
		maxY = math.max (maxY, line[i+1])
	end
	line.x, line.y = minX, minY
	line.w, line.h = maxX-minX, maxY-minY
	return line
end

local function getDot (poly, line)
	local px, py = poly.x, poly.y
	local x1, y1 = line[1], line[2]
	local x2, y2 = line[3], line[4]
	local dx = x2 - x1
	local dy = y2 - y1
	local positiveBiggestDot = 0.0
	local negativeBiggestDot = 0.0
	local indexPositiveBiggest = nil
	local indexNegativeBiggest = nil
	for index = 1, #poly-1, 2 do
			local vertexVectorX = px+poly[index] - x1
			local vertexVectorY = py+poly[index+1] - y1
			local dot = -dy*vertexVectorX + dx*vertexVectorY
			if dot > 0.0 then
					if dot > positiveBiggestDot then
							positiveBiggestDot = dot
							indexPositiveBiggest = index
					end
			else
					if dot < negativeBiggestDot then
							negativeBiggestDot = dot
							indexNegativeBiggest = index
					end
			end
	end
	if positiveBiggestDot > -negativeBiggestDot then		
		return negativeBiggestDot, indexPositiveBiggest and indexNegativeBiggest
	else
		return positiveBiggestDot, indexNegativeBiggest and indexPositiveBiggest
	end
end

function pr.collision(poly, line)
	local bigdot, index = getDot (poly, line)
	if not index then
		-- All polygon points are on the same side of the line line, so
		-- the line can't possibly cross the polygon.
		poly.force = nil
		return
	end
	poly.index = index
	
	local px, py = poly.x+poly[index], poly.y+poly[index+1]
	local x1, y1 = line[1], line[2]
	local x2, y2 = line[3], line[4]
	local dx = x2 - x1
	local dy = y2 - y1
	
	local vertexVectorX = px-x1
	local vertexVectorY = py - y1
	local dot = dx*vertexVectorX + dy*vertexVectorY
	local vectorScale = dot / (dx * dx + dy * dy)
	local collisionX = x1+dx*vectorScale
	local collisionY = y1+dy*vectorScale
	
	poly.force = {
		px-poly.x, py-poly.y,
			collisionX-poly.x, collisionY-poly.y}
	return collisionX-(px), collisionY-(py)
end



function pr.push (poly, line, tx, ty)
	if poly.x > line.x+line.w or line.x > poly.x+poly.w 
	or poly.y > line.y+line.h or line.y > poly.y+poly.h then
		-- no collision
		poly.collision = false
		poly.force = false
		return tx, ty
	end
	
	local pushX, pushY = pr.collision(poly, line)
	if pushX then
		tx = poly.x+pushX
		ty = poly.y+pushY
	end
	poly.collision = true
	return tx, ty
end

return pr

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local vectorScale = dot / (dx * dx + dy * dy)

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vectorScale = vectorScale > 1.0 and 1.0 or (vectorScale < 0.0 and 0.0 or vectorScale)