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
in the Software without restriction, including without limitation the rights
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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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
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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 _PACKAGE = (...):match("^(.+)%.[^%.]+")
if not common and common.class then
	class_commons = true
	require(_PACKAGE .. '.class')
end
local vector  = require(_PACKAGE .. '.vector-light')
local Polygon = require(_PACKAGE .. '.polygon')

local function math_absmin(a,b) return math_abs(a) < math_abs(b) and a or b end
local function test_axes(axes, shape_one, shape_two, sx,sy, 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
			sx,sy = vector.mul(overlap, axis.x, axis.y)
			min_overlap = math_abs(overlap)
		end
	end
	return true, sx,sy, min_overlap
end

local function SAT(shape_one, axes_one, shape_two, axes_two)
	local collide, sx,sy, overlap = false, 0,0, math_huge
	collide, sx,sy, overlap = test_axes(axes_one, shape_one, shape_two, sx,sy, overlap)
	print('1', collide, sx,sy, overlap)
	if not collide then return false end
	collide, sx,sy, overlap = test_axes(axes_two, shape_one, shape_two, sx,sy, overlap)
	print('2', collide, sx,sy, overlap)
	return collide, sx,sy
end

local function outcircles_intersect(shape_one, shape_two)
	local x1,y1,r1 = shape_one:outcircle()
	local x2,y2,r2 = shape_two:outcircle()
	return vector.len2(x1-x2, y1-y2) <= (r1+r2)*(r1+r2)
end

--
-- base class
--
local Shape = {}
function Shape:init(t)
	self._type = t
	self._rotation = 0
end

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

function Shape:rotation()
	return self._rotation
end

function Shape:rotate(angle)
	self._rotation = self._rotation + angle
end

function Shape:setRotation(angle, x,y)
	return self:rotate(angle - self._rotation, x,y)
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})
Shape.POINT    = setmetatable({}, {__tostring = function() return 'POINT' end})

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

local ConcavePolygonShape = {}
function ConcavePolygonShape:init(poly)
	Shape.init(self, Shape.COMPOUND)
	self._polygon = poly
	self._shapes = poly:splitConvex()
	for i,s in ipairs(self._shapes) do
		self._shapes[i] = common.instance(ConvexPolygonShape, s)
	end
end

local CircleShape = {}
function CircleShape:init(cx,cy, radius)
	Shape.init(self, Shape.CIRCLE)
	self._center = {x = cx, y = cy}
	self._radius = radius
end

local PointShape = {}
function PointShape:init(x,y)
	Shape.init(self, Shape.POINT)
	self._pos = {x = x, y = y}
end

--
-- collision functions
--
function ConvexPolygonShape:getAxes()
	local axes = {}
	local vert = self._polygon.vertices
	local p,q = vert[#vert], vert[#vert]
	for i = 1,#vert do
		p,q = q, vert[i]
		local x,y = vector.normalize(vector.perpendicular(p.x-q.x, p.y-q.y))
		axes[#axes+1] = {x = x, y = y}
	end
	return axes
end

function ConvexPolygonShape:projectOn(axis)
	local v = self._polygon.vertices
	local min,max = math_huge,-math_huge
	for i = 1,#v do
		local p = vector.dot(v[i].x,v[i].y, axis.x,axis.y) -- = v[i]:projectOn(axis) * axis
		min = math_min(p, min)
		max = math_max(p, max)
	end
	return min, max
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 = vector.dot(self._center.x,self._center.y, axis.x,axis.y)
	local shift  = self._radius * vector.len2(axis.x, axis.y)
	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, sx,sy = other:collidesWith(self)
		return collide, sx and -sx, sy and -sy
	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 other._type == Shape.POINT then
		return other:collidesWith(self)
	end

	if not outcircles_intersect(self, other) then return false end

	-- TODO: better way of doing this. report all the separations?
	local collide,dx,dy,count = false,0,0,0
	for _,s in ipairs(self._shapes) do
		local status, sx,sy = s:collidesWith(other)
		collide = collide or status
		if status then
			dx,dy = dx+sx, dy+sy
			count = count + 1
		end
	end
	return collide, dx/count, dy/count
end

function CircleShape:collidesWith(other)
	if other._type == Shape.CIRCLE then
		local px,py = self._center.x-other._center.x, self._center.y-other._center.y
		local d = vector.len2(px,py)
		local radii = self._radius + other._radius
		if d < radii*radii then
			-- if circles overlap, push it out upwards
			if d == 0 then return true, 0,radii end
			-- otherwise push out in best direction
			return true, vector.mul(radii - math_sqrt(d), vector.normalize(px,py))
		end
		return false
	elseif other._type == Shape.COMPOUND then
		local collide, sep = other:collidesWith(self)
		return collide, sep and -sep
	elseif other._type == Shape.POINT then
		return other:collidesWith(self)
	end

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

function PointShape:collidesWith(other)
	if other._type == Shape.POINT then
		return (self._pos == other._pos), 0,0
	end
	return other:contains(self._pos.x, self._pos.y), 0,0
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.len2(x-self._center.x, y-self._center.y) < self._radius * self._radius
end

function PointShape:contains(x,y)
	return x == self._pos.x and y == self._pos.y
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.
-- with r(s) = p + d*s = (x,y) + (dx,dy) * s defining the ray and
-- (x - cx)^2 + (y - cy)^2 = r^2, this problem is eqivalent to
-- solving [with c = (cx,cy)]:
--
--     d*d s^2 + 2 d*(p-c) s + (p-c)*(p-c)-r^2 = 0
function CircleShape:intersectsRay(x,y, dx,dy)
	local pcx,pcy = x-self._center.x, y-self._center.y

	local a = vector.len2(dx,dy)
	local b = 2 * vector.dot(dx,dy, pcx,pcy)
	local c = vector.len2(pcx,pcy) - self._radius * self._radius
	local discr = b*b - 4*a*c
	if discr < 0 then return false end

	discr = math_sqrt(discr)
	local s1,s2 = discr-b, -discr-b
	if s1 < 0 then -- first solution is off the ray
		return s2 >= 0, s2/(2*a)
	elseif s2 < 0 then -- second solution is off the ray
		return s1 >= 0, s1/(2*a)
	end
	-- both solutions on the ray
	return true, math_min(s1,s2)/(2*a)
end

-- point shape intersects ray if it lies on the ray
function PointShape:intersectsRay(x,y,dx,dy)
	local px,py = self._pos.x-x, self._pos.y-y
	local t = vector.dot(px,py, dx,dy) / vector.len2(dx,dy)
	return t >= 0, t
end

--
-- auxiliary
--
function ConvexPolygonShape:center()
	return self._polygon.centroid.x, self._polygon.centroid.y
end

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

function CircleShape:center()
	return self._center.x, self._center.y
end

function PointShape:center()
	return self._pos.x, self._pos.y
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 PointShape:outcircle()
	return self._pos.x, self._pos.y, 0
end

function ConvexPolygonShape:bbox()
	return self._polygon:getBBox()
end

function ConcavePolygonShape:bbox()
	return self._polygon:getBBox()
end

function CircleShape:bbox()
	local cx,cy = self:center()
	local r = self._radius
	return cx-r,cy-r, cx+r,cy+r
end

function PointShape:bbox()
	local x,y = self:center()
	return x,y,x,y
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.x = self._center.x + x
	self._center.y = self._center.y + y
end

function PointShape:move(x,y)
	self._pos.x = self._pos.x + x
	self._pos.y = self._pos.y + y
end


function ConcavePolygonShape:rotate(angle,cx,cy)
	Shape.rotate(self, angle)
	if not (cx and cy) then
		cx,cy = self:center()
	end
	self._polygon:rotate(angle,cx,cy)
	for _,p in ipairs(self._shapes) do
		p:rotate(angle, cx,cy)
	end
end

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

function CircleShape:rotate(angle, cx,cy)
	Shape.rotate(self, angle)
	if not (cx and cy) then return end
	self._center.x,self._center.y = vector.add(cx,cy, vector.rotate(angle, self._center.x-cx, self._center.y-cy))
end

function PointShape:rotate(angle, cx,cy)
	Shape.rotate(self, angle)
	if not (cx and cy) then return end
	self._pos.x,self._pos.y = vector.add(cx,cy, vector.rotate(angle, self._pos.x-cx, self._pos.y-cy))
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)
	love.graphics.circle(mode or 'line', self:outcircle())
end

function PointShape:draw()
	love.graphics.point(self:center())
end


Shape = common.class('Shape', Shape)
ConvexPolygonShape  = common.class('ConvexPolygonShape',  ConvexPolygonShape,  Shape)
ConcavePolygonShape = common.class('ConcavePolygonShape', ConcavePolygonShape, Shape)
CircleShape         = common.class('CircleShape',         CircleShape,         Shape)
PointShape          = common.class('PointShape',          PointShape,          Shape)

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

	if polygon:isConvex() then
		return common.instance(ConvexPolygonShape, polygon)
	end
	return common.instance(ConcavePolygonShape, polygon)
end

local function newCircleShape(...)
	return common.instance(CircleShape, ...)
end

local function newPointShape(...)
	return common.instance(PointShape, ...)
end

return {
	ConcavePolygonShape = ConcavePolygonShape,
	ConvexPolygonShape  = ConvexPolygonShape,
	CircleShape         = CircleShape,
	PointShape          = PointShape,
	newPolygonShape     = newPolygonShape,
	newCircleShape      = newCircleShape,
	newPointShape       = newPointShape,
}