HC/shape.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
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
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Except as contained in this notice, the name(s) of the above copyright holders
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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 _PATH = (...):gsub("shape$", "")
local Class = require(_PATH .. 'class')
local vector = require(_PATH .. 'vector')
Class = Class.new
vector = vector.new

local function combine_axes(a, b)
	local in_a = {}
	for i = 1,#a do in_a[ tostring(a[i]) ] = true end
	for i = 1,#b do
		if not in_a[ tostring(b[i]) ] then
			a[#a+1] = b[i]
		end
	end
	return a
end

local function SAT(axis_table, shape_one, shape_two)
	local sep,min_overlap = vector(0,0),math.huge
	for _,axis in ipairs(axis_table) do
		local l1,r1 = shape_one:projectOn(axis)
		local l2,r2 = shape_two:projectOn(axis)

		local a,b = math.max(l1,l2), math.min(r1,r2)
		if b < a then
			return false
		end

		local overlap = b-a
		if overlap < min_overlap then
			sep, min_overlap = axis * -overlap, overlap
		end
	end
	return true, sep
end

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

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

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

function PolygonShape:projectOn(axis)
	local vertices = self._polygon.vertices
	local left, right = math.huge, -math.huge
	for i = 1,#vertices do
		local projection = vertices[i] * axis -- same as vertices[i]:projectOn(axis) * axis
		if projection < left then
			left = projection
		end
		if projection > right then
			right = projection
		end
	end
	return left, right
end

function PolygonShape:collidesWith(other)
	if other._type ~= Shape.POLYGON then
		return other:collidesWith(self)
	end

	-- else: type is POLYGON, use the SAT
	return SAT(combine_axes(self:getAxes(), other:getAxes()), self, other)
end

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

function PolygonShape:centroid()
	return self._polygon.centroid:unpack()
end

function PolygonShape:move(x,y)
	-- y not given => x is a vector
	if y then x = vector(x,y) end
	self._polygon:move(x)
end

function PolygonShape:rotate(angle, center)
	self._polygon:rotate(angle, center)
end


---------------------------------
-- Concave (but simple) polygon
--
CompoundShape = Class{name = 'CompoundShape', 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] = PolygonShape(s)
	end
end}
CompoundShape:inherit(Shape)

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

function CompoundShape: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 CompoundShape:centroid()
	return self._polygon.centroid:unpack()
end

function CompoundShape:move(x,y)
	-- y not give => x is a vector
	if y then x = vector(x,y) end
	self._polygon:move(x)
	for _,p in ipairs(self._shapes) do
		p:move(x)
	end
end

function CompoundShape:rotate(angle)
	self._polygon:rotate(angle)
	for _,p in ipairs(self._shapes) do
		p:rotate(angle, self._polygon.centroid)
	end
end

-------------------
-- Perfect circle
--
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)

function CircleShape:collidesWith(other)
	if other._type == Shape.CIRCLE then
		return SAT({(other._center - self._center):normalize_inplace()}, self, other)
	elseif other._type == Shape.COMPOUND then
		return other:collidesWith(self)
	end
	-- else: other._type == POLYGON
	-- retrieve closest edge to center
	local function getClosest(center, points, distOld, k, i, inc)
		local distNew = (points[i] - center):len2()
		if distOld < distNew then return points[k],distOld end
		k, i = i, i + inc
		if i > #points then i = 1 end
		if i < 1 then i = #points end
		return getClosest(center, points, distNew, k, i, inc)
	end

	local closestLeft,dl = getClosest(self._center, other._polygon.vertices, math.huge, 1,2, 1)
	local closestRight,dr = getClosest(self._center, other._polygon.vertices, math.huge, 2,1, -1)
	local closest = dl < dr and closestLeft or closestRight
	return SAT(combine_axes(other:getAxes(), {(closest - self._center):normalize_inplace()}), self, other)
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

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

function CircleShape:move(x,y)
	-- y not given => x is a vector
	if y then x = vector(x,y) end
	self._center = self._center + x
end

function CircleShape:rotate(angle)
	-- yeah, right
end

function CircleShape:projectOn(axis)
	-- v:projectOn(a) * a = v * a (see PolygonShape)
	-- 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

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