mirror of
https://github.com/luau-lang/luau.git
synced 2024-12-13 05:20:38 +00:00
d01addc625
Co-authored-by: Rodactor <rodactor@roblox.com>
334 lines
7.4 KiB
Lua
334 lines
7.4 KiB
Lua
--[[
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MIT License
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Copyright (c) 2017 Gabriel de Quadros Ligneul
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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]]
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-- Julia sets via interval cell-mapping (quadtree version)
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local bench = script and require(script.Parent.bench_support) or require("bench_support")
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function test()
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--require"julia" local f=f
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local io=io
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local root,exterior
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local cx,cy
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local Rxmin,Rxmax,Rymin,Rymax=-2.0,2.0,-2.0,2.0
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local white=1.0
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local black=0.0
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local gray=0.5
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local N=0
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local nE=0
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local E={}
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local write=print
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local function output(a1,a2,a3,a4,a5,a6)
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--[[write(
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a1 or ""," ",
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a2 or ""," ",
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a3 or ""," ",
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a4 or ""," ",
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a5 or ""," ",
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a6 or ""," \n")]]
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end
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local function imul(xmin,xmax,ymin,ymax)
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local mm=xmin*ymin
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local mM=xmin*ymax
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local Mm=xmax*ymin
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local MM=xmax*ymax
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local m,M=mm,mm
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if m>mM then m=mM elseif M<mM then M=mM end
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if m>Mm then m=Mm elseif M<Mm then M=Mm end
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if m>MM then m=MM elseif M<MM then M=MM end
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return m,M
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end
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local function isqr(xmin,xmax)
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local u=xmin*xmin
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local v=xmax*xmax
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if xmin<=0.0 and 0.0<=xmax then
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if u<v then return 0.0,v else return 0.0,u end
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else
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if u<v then return u,v else return v,u end
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end
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end
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local function f(xmin,xmax,ymin,ymax)
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local x2min,x2max=isqr(xmin,xmax)
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local y2min,y2max=isqr(ymin,ymax)
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local xymin,xymax=imul(xmin,xmax,ymin,ymax)
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return x2min-y2max+cx,x2max-y2min+cx,2.0*xymin+cy,2.0*xymax+cy
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end
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local function outside(xmin,xmax,ymin,ymax)
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local x,y
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if 0.0<xmin then x=xmin elseif 0.0<xmax then x=0.0 else x=xmax end
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if 0.0<ymin then y=ymin elseif 0.0<ymax then y=0.0 else y=ymax end
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return x^2+y^2>4.0
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end
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local function inside(xmin,xmax,ymin,ymax)
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return xmin^2+ymin^2<=4.0 and xmin^2+ymax^2<=4.0 and
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xmax^2+ymin^2<=4.0 and xmax^2+ymax^2<=4.0
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end
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local function newcell()
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return {nil,nil,nil,nil,color=gray}
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end
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local function addedge(a,b)
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nE=nE+1
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E[nE]=b
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end
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local function refine(q)
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if q.color==gray then
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if q[1]==nil then
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q[1]=newcell()
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q[2]=newcell()
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q[3]=newcell()
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q[4]=newcell()
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else
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refine(q[1])
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refine(q[2])
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refine(q[3])
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refine(q[4])
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end
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end
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end
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local function clip(q,xmin,xmax,ymin,ymax,o,oxmin,oxmax,oymin,oymax)
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local ixmin,ixmax,iymin,iymax
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if xmin>oxmin then ixmin=xmin else ixmin=oxmin end
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if xmax<oxmax then ixmax=xmax else ixmax=oxmax end
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if ixmin>=ixmax then return end
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if ymin>oymin then iymin=ymin else iymin=oymin end
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if ymax<oymax then iymax=ymax else iymax=oymax end
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--if ixmin<=ixmax and iymin<=iymax then
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if iymin<iymax then
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if q[1]==nil then
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addedge(o,q)
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else
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local xmid=(xmin+xmax)/2.0
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local ymid=(ymin+ymax)/2.0
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clip(q[1],xmin,xmid,ymid,ymax,o,oxmin,oxmax,oymin,oymax)
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clip(q[2],xmid,xmax,ymid,ymax,o,oxmin,oxmax,oymin,oymax)
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clip(q[3],xmin,xmid,ymin,ymid,o,oxmin,oxmax,oymin,oymax)
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clip(q[4],xmid,xmax,ymin,ymid,o,oxmin,oxmax,oymin,oymax)
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end
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end
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end
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local function map(q,xmin,xmax,ymin,ymax)
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--xmin,xmax,ymin,ymax=f(xmin,xmax,ymin,ymax,cx,cy)
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xmin,xmax,ymin,ymax=f(xmin,xmax,ymin,ymax)
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if outside(xmin,xmax,ymin,ymax) then
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q.color=white
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else
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if not inside(xmin,xmax,ymin,ymax) then addedge(q,exterior) end
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clip(root,Rxmin,Rxmax,Rymin,Rymax,q,xmin,xmax,ymin,ymax)
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end
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end
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local function update(q,xmin,xmax,ymin,ymax)
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if q.color==gray then
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if q[1]==nil then
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local b=nE
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q[2]=nE+1
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map(q,xmin,xmax,ymin,ymax)
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q[3]=nE
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else
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local xmid=(xmin+xmax)/2.0
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local ymid=(ymin+ymax)/2.0
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update(q[1],xmin,xmid,ymid,ymax)
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update(q[2],xmid,xmax,ymid,ymax)
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update(q[3],xmin,xmid,ymin,ymid)
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update(q[4],xmid,xmax,ymin,ymid)
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end
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end
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end
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local function color(q)
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if q.color==gray then
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if q[1]==nil then
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for i=q[2],q[3] do
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if E[i].color~=white then return end
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end
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q.color=white N=N+1
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else
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color(q[1])
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color(q[2])
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color(q[3])
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color(q[4])
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end
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end
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end
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local function prewhite(q)
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if q.color==gray then
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if q[1]==nil then
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for i=q[2],q[3] do
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local c=E[i].color
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if c==white or c==-gray then
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q.color=-gray
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N=N+1
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return
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end
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end
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else
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prewhite(q[1])
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prewhite(q[2])
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prewhite(q[3])
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prewhite(q[4])
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end
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end
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end
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local function recolor(q)
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if q.color==-gray then
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q.color=gray
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elseif q.color==gray then
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if q[1]==nil then
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q.color=black
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else
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recolor(q[1])
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recolor(q[2])
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recolor(q[3])
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recolor(q[4])
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end
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end
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end
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local function area(q)
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if q[1]==nil then
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if q.color==white then return 0.0,0.0
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elseif q.color==black then return 0.0,1.0
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else return 1.0,0.0 end
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else
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local g1,b1=area(q[1])
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local g2,b2=area(q[2])
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local g3,b3=area(q[3])
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local g4,b4=area(q[4])
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return (g1+g2+g3+g4)/4.0, (b1+b2+b3+b4)/4.0
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end
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end
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local function colorup(q)
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if q[1]~=nil and q.color==gray then
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local c1=colorup(q[1])
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local c2=colorup(q[2])
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local c3=colorup(q[3])
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local c4=colorup(q[4])
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if c1==c2 and c1==c3 and c1==c4 then
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if c1~=gray then
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q[1]=nil; --q[2]=nil; q[3]=nil; q[4]=nil
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N=N+1 end
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q.color=c1
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end
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end
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return q.color
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end
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local function save(q,xmin,ymin,N)
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if q[1]==nil or N==1 then
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output(xmin,ymin,N,q.color)
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else
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N=N/2
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local xmid=xmin+N
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local ymid=ymin+N
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save(q[1],xmin,ymin,N)
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save(q[2],xmid,ymin,N)
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save(q[3],xmin,ymid,N)
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save(q[4],xmid,ymid,N)
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end
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end
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local function show(p)
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local N=2^10
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-- io.output(p..".box")
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output(N)
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save(root,0,0,N)
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-- io.close()
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end
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local t0=0
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local function memory(s)
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local t=os.clock()
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--local dt=string.format("%f",t-t0)
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local dt=t-t0
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--io.stdout:write(s,"\t",dt," sec\t",t," sec\t",math.floor(collectgarbage"count"/1024),"M\n")
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t0=t
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end
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local function do_(f,s)
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local a,b=f(root,Rxmin,Rxmax,Rymin,Rymax)
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memory(s)
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return a,b
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end
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local function julia(l,a,b)
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memory"begin"
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cx=a cy=b
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root=newcell()
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exterior=newcell() exterior.color=white
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show(0)
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for i=1,l do --print("\nstep",i)
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nE=0
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do_(refine,"refine")
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do_(update,"update")
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repeat
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N=0 color(root,Rxmin,Rxmax,Rymin,Rymax) --print("color",N)
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until N==0 memory"color"
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repeat
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N=0 prewhite(root,Rxmin,Rxmax,Rymin,Rymax) --print("prewhite",N)
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until N==0 memory"prewhite"
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do_(recolor,"recolor")
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do_(colorup,"colorup") --print("colorup",N)
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local g,b=do_(area,"area") --print("area",g,b,g+b)
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show(i) memory"output"
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--print("edges",nE)
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end
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end
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--julia(14,0.25,0.35)
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--julia(14, -.12, .74 )
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--julia(14,0,0)
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--julia(12,0.25,0)
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--julia(9,0.24,0)
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--julia(9,0.26,0)
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--julia(13,0,1)
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--julia(12,-1.1,0)
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--julia(9,-0.12,0.5)
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-- figures for paper
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--julia(14,0,1)
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--julia(14,-1,0)
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--julia(12,-0.12, 0.64)
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--julia(14,-0.12, 0.60)
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--julia(14,-0.12, 0.30)
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-- julia (level, a, b) -- julia set de c= a + b i
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julia(8,-0.25, 0.74)
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end
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bench.runCode(test, "qt")
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