Lua Arcs and Ellipses

Ellipse.lua

Ellipse = {
  --declare constants
  format='%d %d %d %d ',
  class=',Ellipse,class,'
}
function Ellipse:tostring()
  return string.format(self.format,self.x,self.y,self.width,self.height)
end --tostring
function Ellipse:new(centerX, centerY, wide, tall)
  assert(wide>=0 and tall>=0)
  local r = {x=centerX, y=centerY,
          width=wide, height=tall}
  setmetatable(r, {__tostring = Ellipse.tostring, __index = Ellipse} )
  r.tostring=Ellipse.tostring
  return r
end --new
function Ellipse:isInstance(name)
  local where=string.find(self.class, ',' .. name .. ',', 1, true)
  return where ~= nil
end --isInstance

function Ellipse:setFormat(string)
  Ellipse.format = string
end
function Ellipse:getXY()
  return self.x, self.y
end
function Ellipse:getWH()
  return self.width, self.height
end
function Ellipse:copy()
  local u = { }
  for k, v in pairs(self) do u[k] = v end
  setmetatable(u, {__tostring = Ellipse.tostring, __index = Ellipse} )
  u.tostring=Ellipse.tostring
  return u
end
function Ellipse:setXY(centerX, centerY)
  self.x=centerX  self.y=centerY
  return self
end
function Ellipse:setWH(width, height)
  assert(width>=0 and height>=0)
  self.width=width  self.height=height
  return self
end
function Ellipse:set(el)
  self.x,self.y,self.width,self.height=el.x,el.y,el.width,el.height
  return self
end
function Ellipse:isEqual(ellipse)
  if math.abs(self.x-ellipse.x)>1e-4 then return false end
  if math.abs(self.y-ellipse.y)>1e-4 then return false end
  if math.abs(self.width-ellipse.width)>1e-4 then return false end
  return math.abs(self.height-ellipse.height)<=1e-4
end
function Ellipse:area()
  return math.pi * self.width * self.height * 0.25
end
function Ellipse:circumference()  --see wikipedia ellipse/Ramanujan approximation
  local a=self.width/2
  local b=self.height/2
  return math.pi * ( (a + b)*3 - math.sqrt( (a*3+b)*(a+b*3) ) )
end
function Ellipse:isPntWithin(x, y)
  local a=self.width/2
  local b=self.height/2
  return ( (x-self.x)*(x-self.x)/(a*a) +
           (y-self.y)*(y-self.y)/(b*b) ) <= 1
end
function Ellipse:isEllipseWithin(ellipse)
  local points=ellipse:vertices(16,0,6.28)
  for i=1,#points-1,2 do
    if not self:isPntWithin(points[i], points[i+1]) then return false end
  end
  return true
end
function Ellipse:isIntersecting(ellipse)
  local points=ellipse:vertices(16,0,6.28)
  for i=1,#points-1,2 do
    if self:isPntWithin(points[i], points[i+1]) then return true end
  end
  return false
end
function Ellipse:union(ellipse) --use rectangle code
  local x1 = math.min(self.x-self.width/2, ellipse.x-ellipse.width/2)
  local y1 = math.min(self.y-self.height/2, ellipse.y-ellipse.height/2)
  local x2 = math.max(self.x+self.width/2, ellipse.x+ellipse.width/2)-x1
  local y2 = math.max(self.y+self.height/2, ellipse.y+ellipse.height/2)-y1
  self.x,self.y,self.width,self.height=x1+x2/2, y1+y2/2, x2, y2
  return self
end
function Ellipse:translate(x, y)
  self.x=self.x+x   self.y=self.y+y
  return self
end
function Ellipse:scale(x, y)
  self.width=self.width*x   self.height=self.height*y
  return self
end
function Ellipse:parse(string)
  local i=1
  for w in string.gmatch (string, "[%+%-]?%d+%.?%d*[eE]?[%+%-]?%d*") do
    if i==1 then self.x=w
    elseif i==2 then self.y=w
    elseif i==3 then self.width=w
    elseif i==4 then self.height=w
    end
    i = i+1
  end --for w
end
--[[local Vector=require('Vector')
function Ellipse:points(n,startAngle,stopAngle) --in radians, 0..pi*2
  local a=self.width/2
  local b=self.height/2
  local addin = (stopAngle-startAngle)/(n-1)
  local step=startAngle
  local poly={}
  for i=1,n do
    poly[i]=Vector:fromAngle(step):scale(a,b):translate(self.x,self.y)
    step = step + addin
  end
  return poly
end--]]
function Ellipse:vertices(n,startAngle,stopAngle) --in radians, 0..pi*2
  local a=self.width/2
  local b=self.height/2
  local addin = (stopAngle-startAngle)/(n-1)
  local step=startAngle
  local poly={}
  for i=1,n do
    poly[i*2-1] = math.cos(step)*a+self.x
    poly[i*2] = math.sin(step)*b+self.y
    step = step + addin
  end
  return poly
end
return Ellipse

main.lua

Ellipse=require('Ellipse')
local r=Ellipse:new(display.contentCenterX,display.contentCenterY-100,440,120)
print(r)
local r2=Ellipse:new(0,0,150,80)

local function draw(el)
  local rd=el:vertices(40,0,6.28)  --40 points, 0 to 2pi degrees of arc
  return display.newPolygon(el.x,el.y,rd)
end --draw

local r3,r4
local t1,t2,t3,t4,t5
local arc
local poly
local g
r4=Ellipse:new(0,0,0,0)
local t=display.newText('union',display.contentCenterX,170,system.defaultFont,32)
t:setFillColor(1,1,0)
arc=Ellipse:new(display.contentCenterX/2,display.contentHeight-100,200,150)
local function touch(event)
  r2:setXY(event.x, event.y)
  display.remove(r3)
  display.remove(t5)
  display.remove(t4)
  display.remove(t1)
  display.remove(t2)
  display.remove(t3)
  display.remove(poly)
  display.remove(g)
  r3=draw(r2)
  r3:setFillColor(0,0,1)
  t1=display.newText(string.format('(%d,%d) isPntWithin '..tostring(r:isPntWithin(event.x,event.y)),event.x,event.y),display.contentCenterX,50,system.defaultFont,32)
  t2=display.newText(string.format('isEllipseWithin '..tostring(r:isEllipseWithin(r2))),   
                     display.contentCenterX,80,system.defaultFont,32)
  t3=display.newText(string.format('isIntersecting '..tostring(r:isIntersecting(r2))),   
                     display.contentCenterX,110,system.defaultFont,32)
  r4:set(r):union(r2)
  r4:translate(0,200)
  t5=draw(r4)
  t5:setFillColor(1,1,0)
  local rd=arc:vertices(40,math.random()*3,math.random()*3.14+3.14)
  rd[#rd+1]=arc.x  rd[#rd+1]=arc.y
  poly=display.newPolygon(arc.x,arc.y,rd)
  poly.fill=nil
  poly:setStrokeColor(1,0,0)
  poly.strokeWidth=2
  poly:translate(250,0)
  g=display.newGroup()
  for i=1,#rd-4,2 do
    local l=display.newLine(rd[i],rd[i+1],rd[i+2],rd[i+3])
    l.strokeWidth=2
    l:setStrokeColor(1,0,0)
    g:insert(l)
  end
end --touch

draw(r)
Runtime:addEventListener('tap', touch)