HC/shapes.lua

--[[
Copyright (c) 2011 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
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]]--

local math_abs, math_floor, math_min, math_max = math.abs, math.floor, math.min, math.max
local math_sqrt, math_log, math_pi, math_huge = math.sqrt, math.log, math.pi, math.huge
local function math_absmin(a,b) return math_abs(a) < math_abs(b) and a or b end
module(..., package.seeall)
local Class   = require(_PACKAGE .. 'class')
local vector  = require(_PACKAGE .. 'vector')
local Polygon = require(_PACKAGE .. 'polygon')
_M.class = nil
_M.vector = nil
_M.polygon = nil

local function test_axes(axes, shape_one, shape_two, sep, min_overlap)
	for _,axis in ipairs(axes) do
		local l1,r1 = shape_one:projectOn(axis)
		local l2,r2 = shape_two:projectOn(axis)
		-- do the intervals overlap?
		if r1 < l2 or r2 < l1 then return false end

		-- get the smallest absolute overlap
		local overlap = math_absmin(l2-r1, r2-l1)
		if math_abs(overlap) < min_overlap then
			sep, min_overlap = overlap * axis, math_abs(overlap)
		end
	end
	return true, sep, min_overlap
end

local function SAT(shape_one, axes_one, shape_two, axes_two)
	local collide, sep, overlap = false, vector(0,0), math_huge
	collide, sep, overlap = test_axes(axes_one, shape_one, shape_two, sep, overlap)
	if not collide then return false end
	collide, sep = test_axes(axes_two, shape_one, shape_two, sep, overlap)
	return collide, sep
end

local function outcircles_intersect(shape_one, shape_two)
	local x1,y1,r1 = shape_one:outcircle()
	local x2,y2,r2 = shape_two:outcircle()
	return (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2) <= (r1+r2)*(r1+r2)
end

--
-- base class
--
local Shape = Class{name = 'Shape', function(self, t)
	self._type = t
end}

function Shape:moveTo(x,y)
	local cx,cy = self:center()
	self:move(x - cx, y - cy)
end

-- supported shapes
Shape.POLYGON  = setmetatable({}, {__tostring = function() return 'POLYGON'  end})
Shape.COMPOUND = setmetatable({}, {__tostring = function() return 'COMPOUND' end})
Shape.CIRCLE   = setmetatable({}, {__tostring = function() return 'CIRCLE' end})

--
-- class definitions
--
local ConvexPolygonShape = Class{name = 'ConvexPolygonShape', function(self, polygon)
	Shape.construct(self, Shape.POLYGON)
	assert(polygon:isConvex(), "Polygon is not convex.")
	self._polygon = polygon
end}
ConvexPolygonShape:inherit(Shape)

local ConcavePolygonShape = Class{name = 'ConcavePolygonShape', function(self, poly)
	Shape.construct(self, Shape.COMPOUND)
	self._polygon = poly
	self._shapes = poly:splitConvex()
	for i,s in ipairs(self._shapes) do
		self._shapes[i] = ConvexPolygonShape(s)
	end
end}
ConcavePolygonShape:inherit(Shape)

function PolygonShape(polygon, ...)
	-- create from coordinates if needed
	if type(polygon) == "number" then
		polygon = Polygon(polygon, ...)
	else
		polygon = polygon:clone()
	end

	if polygon:isConvex() then
		return ConvexPolygonShape(polygon)
	end
	return ConcavePolygonShape(polygon)
end

CircleShape = Class{name = 'CircleShape', function(self, cx,cy, radius)
	Shape.construct(self, Shape.CIRCLE)
	self._center = vector(cx,cy)
	self._radius = radius
end}
CircleShape:inherit(Shape)

--
-- collision functions
--
function ConvexPolygonShape:getAxes()
	local axes = {}
	local vert = self._polygon.vertices
	for i = 1,#vert do
		axes[#axes+1] = (vert[i]-vert[(i%#vert)+1]):perpendicular():normalize_inplace()
	end
	return axes
end

function ConvexPolygonShape:projectOn(axis)
	local vertices = self._polygon.vertices
	local projection = {}
	for i = 1,#vertices do
		projection[i] = vertices[i] * axis -- same as vertices[i]:projectOn(axis) * axis
	end
	return math_min(unpack(projection)), math_max(unpack(projection))
end

function CircleShape:projectOn(axis)
	-- v:projectOn(a) * a = v * a (see ConvexPolygonShape)
	-- therefore: (c +- a*r) * a = c*a +- |a|^2 * r
	local center = self._center * axis
	local shift = self._radius * axis:len2()
	return center - shift, center + shift
end

-- collision dispatching:
-- let circle shape or compund shape handle the collision
function ConvexPolygonShape:collidesWith(other)
	if other._type ~= Shape.POLYGON then
		local collide, sep = other:collidesWith(self)
		return collide, sep and -sep
	end

	-- else: type is POLYGON, use the SAT
	if not outcircles_intersect(self, other) then return false end
	return SAT(self, self:getAxes(), other, other:getAxes())
end

function ConcavePolygonShape:collidesWith(other)
	if not outcircles_intersect(self, other) then return false end

	local sep, collide, collisions = vector(0,0), false, 0
	for _,s in ipairs(self._shapes) do
		local status, separating_vector = s:collidesWith(other)
		collide = collide or status
		if status then
			sep, collisions = sep + separating_vector, collisions + 1
		end
	end
	return collide, sep / collisions
end

function CircleShape:collidesWith(other)
	if other._type == Shape.CIRCLE then
		local d = self._center:dist(other._center)
		local radii = self._radius + other._radius
		if d < radii then
			-- if circles overlap, push it out upwards
			if d == 0 then return true, radii * vector(0,1) end
			-- otherwise push out in best direction
			return true, (radii - d) * (self._center - other._center):normalize_inplace()
		end
		return false
	elseif other._type == Shape.COMPOUND then
		local collide, sep = other:collidesWith(self)
		return collide, sep and -sep
	end

	-- else: other._type == POLYGON
	if not outcircles_intersect(self, other) then return false end
	-- retrieve closest edge to center
	local points = other._polygon.vertices
	local closest, dist = points[1], (self._center - points[1]):len2()
	for i = 2,#points do
		local d = (self._center - points[i]):len2()
		if d < dist then
			closest, dist = points[i], d
		end
	end
	local axis = vector(0,1)
	if dist ~= 0 then axis = (closest - self._center):normalize_inplace() end
	return SAT(self, {axis}, other, other:getAxes())
end

--
-- point location/ray intersection
--
function ConvexPolygonShape:contains(x,y)
	return self._polygon:contains(x,y)
end

function ConcavePolygonShape:contains(x,y)
	return self._polygon:contains(x,y)
end

function CircleShape:contains(x,y)
	return (vector(x,y) - self._center):len2() < self._radius * self._radius
end


function ConcavePolygonShape:intersectsRay(x,y, dx,dy)
	return self._polygon:intersectsRay(x,y, dx,dy)
end

function ConvexPolygonShape:intersectsRay(x,y, dx,dy)
	return self._polygon:intersectsRay(x,y, dx,dy)
end

-- circle intersection if distance of ray/center is smaller
-- than radius
function CircleShape:intersectsRay(x,y, dx,dy)
	local pc = vector(x,y) - self._center
	local d = vector(dx,dy)

	local a = d * d
	local b = 4 * d * pc
	local c = pc * pc - self._radius * self._radius
	local discriminant = b*b - 4*a*c
	if discriminant < 0 then return false end

	discriminant = math_sqrt(discriminant)
	return true, math_min(-b + discriminant, -b - discriminant) / (2*a)
end

--
-- auxiliary
--
function ConvexPolygonShape:center()
	return self._polygon.centroid:unpack()
end

function ConcavePolygonShape:center()
	return self._polygon.centroid:unpack()
end

function CircleShape:center()
	return self._center:unpack()
end


function ConvexPolygonShape:outcircle()
	local cx,cy = self:center()
	return cx,cy, self._polygon._radius
end

function ConcavePolygonShape:outcircle()
	local cx,cy = self:center()
	return cx,cy, self._polygon._radius
end

function CircleShape:outcircle()
	local cx,cy = self:center()
	return cx,cy, self._radius
end


function ConvexPolygonShape:move(x,y)
	self._polygon:move(x,y)
end

function ConcavePolygonShape:move(x,y)
	self._polygon:move(x,y)
	for _,p in ipairs(self._shapes) do
		p:move(x,y)
	end
end

function CircleShape:move(x,y)
	self._center = self._center + vector(x,y)
end


function ConcavePolygonShape:rotate(angle,cx,cy)
	self._polygon:rotate(angle,cx)
	for _,p in ipairs(self._shapes) do
		p:rotate(angle, cx and vector(cx,cy) or self._polygon.centroid)
	end
end

function ConvexPolygonShape:rotate(angle, cx,cy)
	self._polygon:rotate(angle, cx, cy)
end

function CircleShape:rotate(angle, cx,cy)
	if not cx then return end
	local c = vector(cx,cy)
	self._center = (self._center - c):rotate_inplace(angle) + c
end


function ConvexPolygonShape:draw(mode)
	local mode = mode or 'line'
	love.graphics.polygon(mode, self._polygon:unpack())
end

function ConcavePolygonShape:draw(mode)
	local mode = mode or 'line'
	if mode == 'line' then
		love.graphics.polygon('line', self._polygon:unpack())
	else
		for _,p in ipairs(self._shapes) do
			love.graphics.polygon(mode, p._polygon:unpack())
		end
	end
end

function CircleShape:draw(mode, segments)
	local segments = segments or math_max(3, math_floor(math_pi * math_log(self._radius)))
	love.graphics.circle(mode, self._center.x, self._center.y, self._radius, segments)
end