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
THE SOFTWARE.
]]--

local math_min, math_sqrt, math_huge = math.min, math.sqrt, math.huge

local _PACKAGE, common_local = (...):match("^(.+)%.[^%.]+"), common
if not (type(common) == 'table' and common.class and common.instance) then
	assert(common_class ~= false, 'No class commons specification available.')
	require(_PACKAGE .. '.class')
end
local vector  = require(_PACKAGE .. '.vector-light')
local Polygon = require(_PACKAGE .. '.polygon')
local GJK     = require(_PACKAGE .. '.gjk') -- actual collision detection

-- reset global table `common' (required by class commons)
if common_local ~= common then
	common_local, common = common, common_local
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

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

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

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

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

--
-- collision functions
--
function ConvexPolygonShape:support(dx,dy)
	local v = self._polygon.vertices
	local max, vmax = -math_huge
	for i = 1,#v do
		local d = vector.dot(v[i].x,v[i].y, dx,dy)
		if d > max then
			max, vmax = d, v[i]
		end
	end
	return vmax.x, vmax.y
end

function CircleShape:support(dx,dy)
	return vector.add(self._center.x, self._center.y,
		vector.mul(self._radius, vector.normalize(dx,dy)))
end

-- collision dispatching:
-- let circle shape or compund shape handle the collision
function ConvexPolygonShape:collidesWith(other)
	if self == other then return false end
	if other._type ~= 'polygon' then
		local collide, sx,sy = other:collidesWith(self)
		return collide, sx and -sx, sy and -sy
	end

	-- else: type is POLYGON
	return GJK(self, other)
end

function ConcavePolygonShape:collidesWith(other)
	if self == other then return false end
	if other._type == 'point' then
		return other:collidesWith(self)
	end

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

function CircleShape:collidesWith(other)
	if self == other then return false end
	if other._type == '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 == 'polygon' then
		return GJK(self, other)
	end

	-- else: let the other shape decide
	local collide, sx,sy = other:collidesWith(self)
	return collide, sx and -sx, sy and -sy
end

function PointShape:collidesWith(other)
	if self == other then return false end
	if other._type == '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

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

function ConvexPolygonShape:intersectionsWithRay(x,y, dx,dy)
	return self._polygon:intersectionsWithRay(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:intersectionsWithRay(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 {} end

	discr = math_sqrt(discr)
	local ts, t1, t2 = {}, discr-b, -discr-b
	if t1 >= 0 then ts[#ts+1] = t1/(2*a) end
	if t2 >= 0 then ts[#ts+1] = t2/(2*a) end
	return ts
end

function CircleShape:intersectsRay(x,y, dx,dy)
	local tmin = math_huge
	for _, t in ipairs(self:intersectionsWithRay(x,y,dx,dy)) do
		tmin = math_min(t, tmin)
	end
	return tmin ~= math_huge, tmin
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 = px/dx
	-- see (px,py) and (dx,dy) point in same direction
	return (t == py/dy), t
end

function PointShape:intersectionsWithRay(x,y, dx,dy)
	local intersects, t = self:intersectsRay(x,y, dx,dy)
	return intersects and {t} or {}
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:bbox()
end

function ConcavePolygonShape:bbox()
	return self._polygon:bbox()
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 ConcavePolygonShape:scale(s)
	assert(type(s) == "number" and s > 0, "Invalid argument. Scale must be greater than 0")
	local cx,cy = self:center()
	self._polygon:scale(s, cx,cy)
	for _, p in ipairs(self._shapes) do
		local dx,dy = vector.sub(cx,cy, p:center())
		p:scale(s)
		p:moveTo(cx-dx*s, cy-dy*s)
	end
end

function ConvexPolygonShape:scale(s)
	assert(type(s) == "number" and s > 0, "Invalid argument. Scale must be greater than 0")
	self._polygon:scale(s, self:center())
end

function CircleShape:scale(s)
	assert(type(s) == "number" and s > 0, "Invalid argument. Scale must be greater than 0")
	self._radius = self._radius * s
end

function PointShape:scale()
	-- nothing
end


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

function ConcavePolygonShape:draw(mode, wireframe)
	local mode = mode or 'line'
	if mode == 'line' then
		love.graphics.polygon('line', self._polygon:unpack())
		if not wireframe then return end
	end
	for _,p in ipairs(self._shapes) do
		love.graphics.polygon(mode, p._polygon:unpack())
	end
end

function CircleShape:draw(mode, segments)
	local x, y, r = self:outcircle()
	love.graphics.circle(mode or 'line', x, y, r, segments)
end

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


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

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

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

	return common_local.instance(ConcavePolygonShape, polygon)
end

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

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

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