Module:Mapa/Orthographic projection

return function(size,dp,vc)
	local rd=6370000/dp
	local u=math.pi/180
	local c={{math.cos(vc[1]*u),math.sin(vc[1]*u)},{math.cos(vc[2]*u),math.sin(vc[2]*u)}}
	local function invert(zq)
		local vp={(zq[1]-size[1]/2)/rd,-(zq[2]-size[2]/2)/rd}
		local vq=math.sqrt(1-vp[1]*vp[1]-vp[2]*vp[2])
		local y=vq*c[2][1]-vp[2]*c[2][2]
		return {math.atan2(vp[1],y)/u+vc[1],math.atan2(vq*c[2][2]+vp[2]*c[2][1],math.sqrt(vp[1]*vp[1]+y*y))/u}
	end
	local range={invert({0,0})[1],invert({size[1],0})[1],invert({0,size[2]})[2],invert({size[1]/2,0})[2]}
	local function convert(vp)
		local p={{math.cos(vp[1]*u),math.sin(vp[1]*u)},{math.cos(vp[2]*u),math.sin(vp[2]*u)}}
		return {
			p[2][1]*(p[1][2]*c[1][1]-p[1][1]*c[1][2])*rd+size[1]/2,
			(p[2][1]*(p[1][1]*c[1][1]+p[1][2]*c[1][2])*c[2][2]-p[2][2]*c[2][1])*rd+size[2]/2
		}
	end
	local function clip(inner,ps)
		local result=ps
		for k=0,1 do
			for j=0,1 do
				local v=(j==0 and 0-2) or size[k+1]+2
				local ps=result
				local list={}
				for i=1,#ps do
					local p={ps[i],ps[i%#ps+1]}
					if (p[1][k+1]>=v)==(j==0) then
						table.insert(list,p[1])
					end
					if not (inner and i==#ps) then
						if (p[1][k+1]>=v)~=(p[2][k+1]>=v) then
							local r={}
							r[k%2+1]=v
							r[(k+1)%2+1]=p[1][(k+1)%2+1]+(v-p[1][k%2+1])*(p[2][(k+1)%2+1]-p[1][(k+1)%2+1])/(p[2][k%2+1]-p[1][k%2+1]) 
							table.insert(list,r)
						end
					end
				end
				result=list
			end
		end
		return result
	end
	return {
		convert=convert,
		convertMulti=function(inner,ps)
			local t={}
			for _,p in ipairs(ps) do
				table.insert(t,convert(p))
			end
			return clip(inner,t)
		end,
		contains=function(rect)
			return rect[1]<range[2] and range[1]<rect[2] and rect[3]<range[4] and range[3]<rect[4]
		end,
		getSize=function()
			return size
		end,
		getDp=function()
			return dp
		end
	}
end