kusano/render.py

## render.py
from PIL import Image, ImageDraw
import math

def render(name, F):
    size = 4096
    im = Image.new("RGB", (size, size), (255, 255, 255))
    draw = ImageDraw.Draw(im)

    def trans(x, y, z):
        t = math.pi*0.05
        x, y, z = (
            x*math.cos(t)+y*math.sin(t),
            -x*math.sin(t)+y*math.cos(t),
            z,
        )
        t = math.pi*0.2
        x, y, z = (
            x*math.cos(t)+z*math.sin(t),
            y,
            -x*math.sin(t)+z*math.cos(t),
        )
        t = 0.1
        x, y = (
            y*(1+x*t),
            -z*(1+x*t),
        )
        t = 1200
        x, y = (
            size/2+x*t,
            size/2+y*t,
        )
        return x, y

    # https://www.jstage.jst.go.jp/article/jsgs1967/18/2/18_2_15/_pdf/-char/ja
    L = 1. # 5角形の1辺。
    d54 = 54./180.*math.pi
    L1 = (1.+math.sin(d54))/(2*math.cos(d54))*L
    R = L/(2*math.cos(d54))
    a = math.acos(math.sin(d54)/(1+math.sin(d54)))
    R1 = R*math.sin(d54)+L1*math.cos(a)
    H1 = L1*math.sin(a)
    H2 = (R1-R)*math.sin(d54)*math.tan(a)
    H = (H1+H2)/2

    V = [
        (-R*math.cos(0.0*math.pi), R*math.sin(0.0*math.pi), H), # 0
        (-R*math.cos(0.4*math.pi), R*math.sin(0.4*math.pi), H),
        (-R*math.cos(0.8*math.pi), R*math.sin(0.8*math.pi), H),
        (-R*math.cos(1.2*math.pi), R*math.sin(1.2*math.pi), H),
        (-R*math.cos(1.6*math.pi), R*math.sin(1.6*math.pi), H),
        (-R1*math.cos(0.0*math.pi), R1*math.sin(0.0*math.pi), H-H2), # 5
        (-R1*math.cos(0.4*math.pi), R1*math.sin(0.4*math.pi), H-H2),
        (-R1*math.cos(0.8*math.pi), R1*math.sin(0.8*math.pi), H-H2),
        (-R1*math.cos(1.2*math.pi), R1*math.sin(1.2*math.pi), H-H2),
        (-R1*math.cos(1.6*math.pi), R1*math.sin(1.6*math.pi), H-H2),
        (-R1*math.cos(0.2*math.pi), R1*math.sin(0.2*math.pi), -H+H2), # 10
        (-R1*math.cos(0.6*math.pi), R1*math.sin(0.6*math.pi), -H+H2),
        (-R1*math.cos(1.0*math.pi), R1*math.sin(1.0*math.pi), -H+H2),
        (-R1*math.cos(1.4*math.pi), R1*math.sin(1.4*math.pi), -H+H2),
        (-R1*math.cos(1.8*math.pi), R1*math.sin(1.8*math.pi), -H+H2),
        (-R*math.cos(0.2*math.pi), R*math.sin(0.2*math.pi), -H), # 10
        (-R*math.cos(0.6*math.pi), R*math.sin(0.6*math.pi), -H),
        (-R*math.cos(1.0*math.pi), R*math.sin(1.0*math.pi), -H),
        (-R*math.cos(1.4*math.pi), R*math.sin(1.4*math.pi), -H),
        (-R*math.cos(1.8*math.pi), R*math.sin(1.8*math.pi), -H),
    ]

    S = [
        ( 0,  1,  2,  3,  4),
        ( 1,  0,  5, 10,  6),
        ( 2,  1,  6, 11,  7),
        ( 3,  2,  7, 12,  8),
        ( 4,  3,  8, 13,  9),
        ( 0,  4,  9, 14,  5),
        (17, 16, 15, 19, 18),
        (16, 17, 12,  7, 11),
        (15, 16, 11,  6, 10),
        (19, 15, 10,  5, 14),
        (18, 19, 14,  9, 13),
        (17, 18, 13,  8, 12),
    ]

    C = {
        "W": "#ffffff",
        "R": "#f80808",
        "G": "#088008",
        "P": "#800880",
        "Y": "#ffff00",
        "B": "#0808f8",
        "w": "#c0c0c0",
        "r": "#f88008",
        "g": "#80f880",
        "p": "#f88080",
        "y": "#ffffc0",
        "b": "#80c0f8",
        " ": "#404040",
    }

    for si in [0, 2, 3, 4, 7, 11]:
        s = S[si]
        VF = [V[p] for p in s]
        for i in range(5):
            VF += [
                (
                    VF[i][0]*0.6+VF[(i+1)%5][0]*0.4,
                    VF[i][1]*0.6+VF[(i+1)%5][1]*0.4,
                    VF[i][2]*0.6+VF[(i+1)%5][2]*0.4,
                ), (
                    VF[i][0]*0.4+VF[(i+1)%5][0]*0.6,
                    VF[i][1]*0.4+VF[(i+1)%5][1]*0.6,
                    VF[i][2]*0.4+VF[(i+1)%5][2]*0.6,
                )
            ]
        for i in range(5):
            VF += [
                (
                    VF[i*2+5][0]+VF[(i*2+9)%10+5][0]-VF[i][0],
                    VF[i*2+5][1]+VF[(i*2+9)%10+5][1]-VF[i][1],
                    VF[i*2+5][2]+VF[(i*2+9)%10+5][2]-VF[i][2],
                )
            ]

        for i, p in enumerate([
            [15, 16, 17, 18, 19],
            [ 0,  5, 15, 14],
            [ 5,  6, 16, 15],
            [ 1,  7, 16,  6],
            [ 7,  8, 17, 16],
            [ 2,  9, 17,  8],
            [ 9, 10, 18, 17],
            [ 3, 11, 18, 10],
            [11, 12, 19, 18],
            [ 4, 13, 19, 12],
            [13, 14, 15, 19],
        ]):
            draw.polygon([trans(*VF[x]) for x in p], C[F[si*11+i]], "black", 5)
        draw.polygon([trans(*V[x]) for x in s], None, "black", 15)

    im = im.resize((1024, 1024), Image.Resampling.BICUBIC)
    im.save(name)

def renderLL(name, F, center=False):
    size = 4096
    im = Image.new("RGB", (size, size), (255, 255, 255))
    draw = ImageDraw.Draw(im)

    def trans(x, y, z):
        if center:
            t = 1600
            x, y = (
                size/2+y*t,
                size/2+x*t,
            )
        else:
            t = 1800
            x, y = (
                size/2+y*t,
                size/2+x*t+200,
            )
        return x, y

    # https://www.jstage.jst.go.jp/article/jsgs1967/18/2/18_2_15/_pdf/-char/ja
    L = 1. # 5角形の1辺。
    d54 = 54./180.*math.pi
    L1 = (1.+math.sin(d54))/(2*math.cos(d54))*L
    R = L/(2*math.cos(d54))
    a = math.acos(math.sin(d54)/(1+math.sin(d54)))
    R1 = R*math.sin(d54)+L1*math.cos(a)
    H1 = L1*math.sin(a)
    H2 = (R1-R)*math.sin(d54)*math.tan(a)
    H = (H1+H2)/2

    V = [
        (-R*math.cos(0.0*math.pi), R*math.sin(0.0*math.pi), H), # 0
        (-R*math.cos(0.4*math.pi), R*math.sin(0.4*math.pi), H),
        (-R*math.cos(0.8*math.pi), R*math.sin(0.8*math.pi), H),
        (-R*math.cos(1.2*math.pi), R*math.sin(1.2*math.pi), H),
        (-R*math.cos(1.6*math.pi), R*math.sin(1.6*math.pi), H),
        (-R1*math.cos(0.0*math.pi), R1*math.sin(0.0*math.pi), H-H2), # 5
        (-R1*math.cos(0.4*math.pi), R1*math.sin(0.4*math.pi), H-H2),
        (-R1*math.cos(0.8*math.pi), R1*math.sin(0.8*math.pi), H-H2),
        (-R1*math.cos(1.2*math.pi), R1*math.sin(1.2*math.pi), H-H2),
        (-R1*math.cos(1.6*math.pi), R1*math.sin(1.6*math.pi), H-H2),
        (-R1*math.cos(0.2*math.pi), R1*math.sin(0.2*math.pi), -H+H2), # 10
        (-R1*math.cos(0.6*math.pi), R1*math.sin(0.6*math.pi), -H+H2),
        (-R1*math.cos(1.0*math.pi), R1*math.sin(1.0*math.pi), -H+H2),
        (-R1*math.cos(1.4*math.pi), R1*math.sin(1.4*math.pi), -H+H2),
        (-R1*math.cos(1.8*math.pi), R1*math.sin(1.8*math.pi), -H+H2),
        (-R*math.cos(0.2*math.pi), R*math.sin(0.2*math.pi), -H), # 10
        (-R*math.cos(0.6*math.pi), R*math.sin(0.6*math.pi), -H),
        (-R*math.cos(1.0*math.pi), R*math.sin(1.0*math.pi), -H),
        (-R*math.cos(1.4*math.pi), R*math.sin(1.4*math.pi), -H),
        (-R*math.cos(1.8*math.pi), R*math.sin(1.8*math.pi), -H),
    ]

    S = [
        ( 0,  1,  2,  3,  4),
        ( 1,  0,  5, 10,  6),
        ( 2,  1,  6, 11,  7),
        ( 3,  2,  7, 12,  8),
        ( 4,  3,  8, 13,  9),
        ( 0,  4,  9, 14,  5),
        (17, 16, 15, 19, 18),
        (16, 17, 12,  7, 11),
        (15, 16, 11,  6, 10),
        (19, 15, 10,  5, 14),
        (18, 19, 14,  9, 13),
        (17, 18, 13,  8, 12),
    ]

    C = {
        "W": "#ffffff",
        "R": "#f80808",
        "G": "#088008",
        "P": "#800880",
        "Y": "#ffff00",
        "B": "#0808f8",
        "w": "#c0c0c0",
        "r": "#f88008",
        "g": "#80f880",
        "p": "#f88080",
        "y": "#ffffc0",
        "b": "#80c0f8",
        " ": "#404040",
    }

    for si in [0, 1, 2, 3, 4, 5]:
        s = S[si]
        VF = [V[p] for p in s]
        for i in range(5):
            VF += [
                (
                    VF[i][0]*0.6+VF[(i+1)%5][0]*0.4,
                    VF[i][1]*0.6+VF[(i+1)%5][1]*0.4,
                    VF[i][2]*0.6+VF[(i+1)%5][2]*0.4,
                ), (
                    VF[i][0]*0.4+VF[(i+1)%5][0]*0.6,
                    VF[i][1]*0.4+VF[(i+1)%5][1]*0.6,
                    VF[i][2]*0.4+VF[(i+1)%5][2]*0.6,
                )
            ]
        for i in range(5):
            VF += [
                (
                    VF[i*2+5][0]+VF[(i*2+9)%10+5][0]-VF[i][0],
                    VF[i*2+5][1]+VF[(i*2+9)%10+5][1]-VF[i][1],
                    VF[i*2+5][2]+VF[(i*2+9)%10+5][2]-VF[i][2],
                )
            ]

        for i, p in enumerate([
            [15, 16, 17, 18, 19],
            [ 0,  5, 15, 14],
            [ 5,  6, 16, 15],
            [ 1,  7, 16,  6],
            [ 7,  8, 17, 16],
            [ 2,  9, 17,  8],
            [ 9, 10, 18, 17],
            [ 3, 11, 18, 10],
            [11, 12, 19, 18],
            [ 4, 13, 19, 12],
            [13, 14, 15, 19],
        ]):
            if si==0 or i in ((0, 1, 2, 3) if center else (1, 2, 3)):
                draw.polygon([trans(*VF[x]) for x in p], C[F[si*11+i]], "black", 8)
        if si==0:
            draw.polygon([trans(*V[x]) for x in s], None, "black", 24)

    im = im.resize((1024, 1024), Image.Resampling.BICUBIC)
    im.save(name)

render("sample.png",
    "WBRPYwypgrb"+
    "BBBBBBBBBBB"+
    "RRRRRRRRRRR"+
    "GGGGGGGGGGG"+
    "PPPPPPPPPPP"+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

renderLL("sample_ll.png",
    "WBRPYwypgrb"+
    "BBBBBBBBBBB"+
    "RRRRRRRRRRR"+
    "GGGGGGGGGGG"+
    "PPPPPPPPPPP"+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

render("megaminx.png",
    "WWWWWWWWWWW"+
    "BBBBBBBBBBB"+
    "RRRRRRRRRRR"+
    "GGGGGGGGGGG"+
    "PPPPPPPPPPP"+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

render("scramble_r.png",
    "pppppppwwwp"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "pwpppppppWW"+
    "WwwwWWWWWWW"+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "ppppppppppp"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "pppppWWWppp")

render("scramble_d.png",
    "WWWWWWWwwwW"+
    "BBBBBBBBBBB"+
    "pWWWppppppp"+
    "pwWWppppppp"+
    "pwwwppppppp"+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "ppppppppppp"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "ppppppppppp")

render("scramble_u.png",
    "ppppppppppp"+
    "BBBBBBBBBBB"+
    "WpppWWWWWWW"+
    "WpppWWWWWWW"+
    "WpppWWWWWWW"+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "WWWWWWWWWWW"+
    "WWWWWWWWWWW"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "WWWWWWWWWWW")

render("scramble_example.png",
    "BrrWYPgpbPP"+
    "BBBBBBBBBBB"+
    "WWWBrBrPyPR"+
    "YwpGGrRRyyB"+
    "gYPyYbWpbgw"+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "PBgBgGBbbYY"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "rWygGyRwpWY")

render("star.png",
    "B     B    "+
    "BBBBBBBBBBB"+
    "R         R"+
    "W W W W W W"+
    "Y   Y      "+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "G     G    "+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "P       P  ")

render("f2l.png",
    "B   BBBBB  "+
    "BBBBBBBBBBB"+
    "RRR     RRR"+
    "WWWWWWWWWWW"+
    "Y YYYYY    "+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "G   GGGGG  "+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "P     PPPPP")

render("f2l_i.png",
    "      BB   "+
    "BBBBBBBBBBB"+
    "R   RRRRR  "+
    "BRR   BBB  "+
    "   W       "+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "WWWWWWW WWW"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYY     YYY")

render("f2l_center.png",
    "     W    B"+
    "BBBBBBBBBBB"+
    "RB  RRRRR  "+
    "B  R  BBB  "+
    "           "+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "WWWWWWW WWW"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYY     YYY")

render("s2l.png",
    "           "+
    "y   yyyyyyy"+
    "p   ppppppp"+
    "g   ggggggg"+
    "r   rrrrrrr"+
    "b   bbbbbbb"+
    "wwwwwwwwwww"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYYYYYYYYYY")

render("s2l.png",
    "           "+
    "B   BBBBBBB"+
    "R   RRRRRRR"+
    "G   GGGGGGG"+
    "P   PPPPPPP"+
    "Y   YYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

render("s2l_1.png",
    "w          "+
    "BBBBBBBBBBB"+
    "b     bbbbb"+
    "y   yyyyy  "+
    "p          "+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "GGGGGGGGGGG"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "RRRRR   RRR")

render("s2l_2.png",
    "w          "+
    "BBBBBBBBBBB"+
    "g     ggggg"+
    "r   rrrrrrr"+
    "b   bbbbbbb"+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "YYYYYYYYYYY"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "PPPPPPPPPPP")

render("s2l_3.png",
    "w          "+
    "BBBBBBBBBBB"+
    "y   yyyyyyy"+
    "p   ppppppp"+
    "g   ggggggg"+
    "YYYYYYYYYYY"+
    "wwwwwwwwwww"+
    "RRRRRRRRRRR"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "BBBBBBBBBBB")

render("eoll.png",
    "w w w w w w"+
    "y   yyyyyyy"+
    "p   ppppppp"+
    "g   ggggggg"+
    "r   rrrrrrr"+
    "b   bbbbbbb"+
    "wwwwwwwwwww"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYYYYYYYYYY")

renderLL("eoll_1.png",
    "w   w   w w"+
    "B w BBBBBBB"+
    "R   RRRRRRR"+
    "G w GGGGGGG"+
    "P   PPPPPPP"+
    "Y   YYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

renderLL("eoll_2.png",
    "w w     w w"+
    "B   BBBBBBB"+
    "R w RRRRRRR"+
    "G w GGGGGGG"+
    "P   PPPPPPP"+
    "Y   YYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

renderLL("eoll_3.png",
    "w         w"+
    "B w BBBBBBB"+
    "R w RRRRRRR"+
    "G w GGGGGGG"+
    "P w PPPPPPP"+
    "Y   YYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

renderLL("eoll_4.png",
    "w       w  "+
    "B w BBBBBBB"+
    "R w RRRRRRR"+
    "G w GGGGGGG"+
    "P   PPPPPPP"+
    "Y w YYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

render("coll.png",
    "wwwwwwwwwww"+
    "y   yyyyyyy"+
    "p   ppppppp"+
    "g   ggggggg"+
    "r   rrrrrrr"+
    "b   bbbbbbb"+
    "wwwwwwwwwww"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYYYYYYYYYY")

renderLL("coll_1.png",
    "w w w w w w"+
    "B  wBBBBBBB"+
    "R  wRRRRRRR"+
    "G  wGGGGGGG"+
    "P   PPPPPPP"+
    "Y   YYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

renderLL("coll_2.png",
    "w w w w w w"+
    "Bw  BBBBBBB"+
    "Rw  RRRRRRR"+
    "Gw  GGGGGGG"+
    "P   PPPPPPP"+
    "Y   YYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

renderLL("coll_3.png",
    "w w w w w w"+
    "B   BBBBBBB"+
    "Rw  RRRRRRR"+
    "G   GGGGGGG"+
    "Pw  PPPPPPP"+
    "Yw  YYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

renderLL("coll_4.png",
    "w w w w w w"+
    "B   BBBBBBB"+
    "R  wRRRRRRR"+
    "G   GGGGGGG"+
    "P  wPPPPPPP"+
    "Y  wYYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

renderLL("coll_5.png",
    "w w w w w w"+
    "B   BBBBBBB"+
    "R  wRRRRRRR"+
    "G  wGGGGGGG"+
    "P  wPPPPPPP"+
    "Yw wYYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

renderLL("coll_6.png",
    "w w w w w w"+
    "Bw wBBBBBBB"+
    "Rw  RRRRRRR"+
    "Gw  GGGGGGG"+
    "Pw  PPPPPPP"+
    "Y   YYYYYYY"+
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb")

render("epll.png",
    "wwwwwwwwwww"+
    "y y yyyyyyy"+
    "p p ppppppp"+
    "g g ggggggg"+
    "r r rrrrrrr"+
    "b b bbbbbbb"+
    "wwwwwwwwwww"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYYYYYYYYYY")

renderLL("epll_1.png",
    "wwwwwwwwwww"+
    "y p yyyyyyy"+
    "p b ppppppp"+
    "g g ggggggg"+
    "r r rrrrrrr"+
    "b y bbbbbbb"+
    "wwwwwwwwwww"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYYYYYYYYYY",
    True)

renderLL("epll_2.png",
    "wwwwwwwwwww"+
    "y y yyyyyyy"+
    "p r ppppppp"+
    "g p ggggggg"+
    "r g rrrrrrr"+
    "b b bbbbbbb"+
    "wwwwwwwwwww"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYYYYYYYYYY",
    True)

renderLL("epll_3.png",
    "wwwwwwwwwww"+
    "y y yyyyyyy"+
    "p r ppppppp"+
    "g g ggggggg"+
    "r b rrrrrrr"+
    "b p bbbbbbb"+
    "wwwwwwwwwww"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYYYYYYYYYY",
    True)

renderLL("epll_4.png",
    "wwwwwwwwwww"+
    "y p yyyyyyy"+
    "p r ppppppp"+
    "g y ggggggg"+
    "r g rrrrrrr"+
    "b b bbbbbbb"+
    "wwwwwwwwwww"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYYYYYYYYYY",
    True)

renderLL("epll_5.png",
    "wwwwwwwwwww"+
    "y y yyyyyyy"+
    "p b ppppppp"+
    "g r ggggggg"+
    "r g rrrrrrr"+
    "b p bbbbbbb"+
    "wwwwwwwwwww"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYYYYYYYYYY",
    True)

render("cpll.png",
    "wwwwwwwwwww"+
    "yyyyyyyyyyy"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "bbbbbbbbbbb"+
    "wwwwwwwwwww"+
    "BBBBBBBBBBB"+
    "ppppppppppp"+
    "ggggggggggg"+
    "rrrrrrrrrrr"+
    "YYYYYYYYYYY")
	from PIL import Image, ImageDraw
	import math

	def render(name, F):
	size = 4096
	im = Image.new("RGB", (size, size), (255, 255, 255))
	draw = ImageDraw.Draw(im)

	def trans(x, y, z):
	t = math.pi*0.05
	x, y, z = (
	xmath.cos(t)+ymath.sin(t),
	-xmath.sin(t)+ymath.cos(t),
	z,
	)
	t = math.pi*0.2
	x, y, z = (
	xmath.cos(t)+zmath.sin(t),
	y,
	-xmath.sin(t)+zmath.cos(t),
	)
	t = 0.1
	x, y = (
	y(1+xt),
	-z(1+xt),
	)
	t = 1200
	x, y = (
	size/2+x*t,
	size/2+y*t,
	)
	return x, y

	# https://www.jstage.jst.go.jp/article/jsgs1967/18/2/18_2_15/_pdf/-char/ja
	L = 1. # 5角形の1辺。
	d54 = 54./180.*math.pi
	L1 = (1.+math.sin(d54))/(2math.cos(d54))L
	R = L/(2*math.cos(d54))
	a = math.acos(math.sin(d54)/(1+math.sin(d54)))
	R1 = Rmath.sin(d54)+L1math.cos(a)
	H1 = L1*math.sin(a)
	H2 = (R1-R)math.sin(d54)math.tan(a)
	H = (H1+H2)/2

	V = [
	(-Rmath.cos(0.0math.pi), Rmath.sin(0.0math.pi), H), # 0
	(-Rmath.cos(0.4math.pi), Rmath.sin(0.4math.pi), H),
	(-Rmath.cos(0.8math.pi), Rmath.sin(0.8math.pi), H),
	(-Rmath.cos(1.2math.pi), Rmath.sin(1.2math.pi), H),
	(-Rmath.cos(1.6math.pi), Rmath.sin(1.6math.pi), H),
	(-R1math.cos(0.0math.pi), R1math.sin(0.0math.pi), H-H2), # 5
	(-R1math.cos(0.4math.pi), R1math.sin(0.4math.pi), H-H2),
	(-R1math.cos(0.8math.pi), R1math.sin(0.8math.pi), H-H2),
	(-R1math.cos(1.2math.pi), R1math.sin(1.2math.pi), H-H2),
	(-R1math.cos(1.6math.pi), R1math.sin(1.6math.pi), H-H2),
	(-R1math.cos(0.2math.pi), R1math.sin(0.2math.pi), -H+H2), # 10
	(-R1math.cos(0.6math.pi), R1math.sin(0.6math.pi), -H+H2),
	(-R1math.cos(1.0math.pi), R1math.sin(1.0math.pi), -H+H2),
	(-R1math.cos(1.4math.pi), R1math.sin(1.4math.pi), -H+H2),
	(-R1math.cos(1.8math.pi), R1math.sin(1.8math.pi), -H+H2),
	(-Rmath.cos(0.2math.pi), Rmath.sin(0.2math.pi), -H), # 10
	(-Rmath.cos(0.6math.pi), Rmath.sin(0.6math.pi), -H),
	(-Rmath.cos(1.0math.pi), Rmath.sin(1.0math.pi), -H),
	(-Rmath.cos(1.4math.pi), Rmath.sin(1.4math.pi), -H),
	(-Rmath.cos(1.8math.pi), Rmath.sin(1.8math.pi), -H),
	]

	S = [
	( 0, 1, 2, 3, 4),
	( 1, 0, 5, 10, 6),
	( 2, 1, 6, 11, 7),
	( 3, 2, 7, 12, 8),
	( 4, 3, 8, 13, 9),
	( 0, 4, 9, 14, 5),
	(17, 16, 15, 19, 18),
	(16, 17, 12, 7, 11),
	(15, 16, 11, 6, 10),
	(19, 15, 10, 5, 14),
	(18, 19, 14, 9, 13),
	(17, 18, 13, 8, 12),
	]

	C = {
	"W": "#ffffff",
	"R": "#f80808",
	"G": "#088008",
	"P": "#800880",
	"Y": "#ffff00",
	"B": "#0808f8",
	"w": "#c0c0c0",
	"r": "#f88008",
	"g": "#80f880",
	"p": "#f88080",
	"y": "#ffffc0",
	"b": "#80c0f8",
	" ": "#404040",
	}

	for si in [0, 2, 3, 4, 7, 11]:
	s = S[si]
	VF = [V[p] for p in s]
	for i in range(5):
	VF += [
	(
	VF[i][0]0.6+VF[(i+1)%5][0]0.4,
	VF[i][1]0.6+VF[(i+1)%5][1]0.4,
	VF[i][2]0.6+VF[(i+1)%5][2]0.4,
	), (
	VF[i][0]0.4+VF[(i+1)%5][0]0.6,
	VF[i][1]0.4+VF[(i+1)%5][1]0.6,
	VF[i][2]0.4+VF[(i+1)%5][2]0.6,
	)
	]
	for i in range(5):
	VF += [
	(
	VF[i2+5][0]+VF[(i2+9)%10+5][0]-VF[i][0],
	VF[i2+5][1]+VF[(i2+9)%10+5][1]-VF[i][1],
	VF[i2+5][2]+VF[(i2+9)%10+5][2]-VF[i][2],
	)
	]

	for i, p in enumerate([
	[15, 16, 17, 18, 19],
	[ 0, 5, 15, 14],
	[ 5, 6, 16, 15],
	[ 1, 7, 16, 6],
	[ 7, 8, 17, 16],
	[ 2, 9, 17, 8],
	[ 9, 10, 18, 17],
	[ 3, 11, 18, 10],
	[11, 12, 19, 18],
	[ 4, 13, 19, 12],
	[13, 14, 15, 19],
	]):
	draw.polygon([trans(VF[x]) for x in p], C[F[si11+i]], "black", 5)
	draw.polygon([trans(*V[x]) for x in s], None, "black", 15)

	im = im.resize((1024, 1024), Image.Resampling.BICUBIC)
	im.save(name)

	def renderLL(name, F, center=False):
	size = 4096
	im = Image.new("RGB", (size, size), (255, 255, 255))
	draw = ImageDraw.Draw(im)

	def trans(x, y, z):
	if center:
	t = 1600
	x, y = (
	size/2+y*t,
	size/2+x*t,
	)
	else:
	t = 1800
	x, y = (
	size/2+y*t,
	size/2+x*t+200,
	)
	return x, y

	# https://www.jstage.jst.go.jp/article/jsgs1967/18/2/18_2_15/_pdf/-char/ja
	L = 1. # 5角形の1辺。
	d54 = 54./180.*math.pi
	L1 = (1.+math.sin(d54))/(2math.cos(d54))L
	R = L/(2*math.cos(d54))
	a = math.acos(math.sin(d54)/(1+math.sin(d54)))
	R1 = Rmath.sin(d54)+L1math.cos(a)
	H1 = L1*math.sin(a)
	H2 = (R1-R)math.sin(d54)math.tan(a)
	H = (H1+H2)/2

	V = [
	(-Rmath.cos(0.0math.pi), Rmath.sin(0.0math.pi), H), # 0
	(-Rmath.cos(0.4math.pi), Rmath.sin(0.4math.pi), H),
	(-Rmath.cos(0.8math.pi), Rmath.sin(0.8math.pi), H),
	(-Rmath.cos(1.2math.pi), Rmath.sin(1.2math.pi), H),
	(-Rmath.cos(1.6math.pi), Rmath.sin(1.6math.pi), H),
	(-R1math.cos(0.0math.pi), R1math.sin(0.0math.pi), H-H2), # 5
	(-R1math.cos(0.4math.pi), R1math.sin(0.4math.pi), H-H2),
	(-R1math.cos(0.8math.pi), R1math.sin(0.8math.pi), H-H2),
	(-R1math.cos(1.2math.pi), R1math.sin(1.2math.pi), H-H2),
	(-R1math.cos(1.6math.pi), R1math.sin(1.6math.pi), H-H2),
	(-R1math.cos(0.2math.pi), R1math.sin(0.2math.pi), -H+H2), # 10
	(-R1math.cos(0.6math.pi), R1math.sin(0.6math.pi), -H+H2),
	(-R1math.cos(1.0math.pi), R1math.sin(1.0math.pi), -H+H2),
	(-R1math.cos(1.4math.pi), R1math.sin(1.4math.pi), -H+H2),
	(-R1math.cos(1.8math.pi), R1math.sin(1.8math.pi), -H+H2),
	(-Rmath.cos(0.2math.pi), Rmath.sin(0.2math.pi), -H), # 10
	(-Rmath.cos(0.6math.pi), Rmath.sin(0.6math.pi), -H),
	(-Rmath.cos(1.0math.pi), Rmath.sin(1.0math.pi), -H),
	(-Rmath.cos(1.4math.pi), Rmath.sin(1.4math.pi), -H),
	(-Rmath.cos(1.8math.pi), Rmath.sin(1.8math.pi), -H),
	]

	S = [
	( 0, 1, 2, 3, 4),
	( 1, 0, 5, 10, 6),
	( 2, 1, 6, 11, 7),
	( 3, 2, 7, 12, 8),
	( 4, 3, 8, 13, 9),
	( 0, 4, 9, 14, 5),
	(17, 16, 15, 19, 18),
	(16, 17, 12, 7, 11),
	(15, 16, 11, 6, 10),
	(19, 15, 10, 5, 14),
	(18, 19, 14, 9, 13),
	(17, 18, 13, 8, 12),
	]

	C = {
	"W": "#ffffff",
	"R": "#f80808",
	"G": "#088008",
	"P": "#800880",
	"Y": "#ffff00",
	"B": "#0808f8",
	"w": "#c0c0c0",
	"r": "#f88008",
	"g": "#80f880",
	"p": "#f88080",
	"y": "#ffffc0",
	"b": "#80c0f8",
	" ": "#404040",
	}

	for si in [0, 1, 2, 3, 4, 5]:
	s = S[si]
	VF = [V[p] for p in s]
	for i in range(5):
	VF += [
	(
	VF[i][0]0.6+VF[(i+1)%5][0]0.4,
	VF[i][1]0.6+VF[(i+1)%5][1]0.4,
	VF[i][2]0.6+VF[(i+1)%5][2]0.4,
	), (
	VF[i][0]0.4+VF[(i+1)%5][0]0.6,
	VF[i][1]0.4+VF[(i+1)%5][1]0.6,
	VF[i][2]0.4+VF[(i+1)%5][2]0.6,
	)
	]
	for i in range(5):
	VF += [
	(
	VF[i2+5][0]+VF[(i2+9)%10+5][0]-VF[i][0],
	VF[i2+5][1]+VF[(i2+9)%10+5][1]-VF[i][1],
	VF[i2+5][2]+VF[(i2+9)%10+5][2]-VF[i][2],
	)
	]

	for i, p in enumerate([
	[15, 16, 17, 18, 19],
	[ 0, 5, 15, 14],
	[ 5, 6, 16, 15],
	[ 1, 7, 16, 6],
	[ 7, 8, 17, 16],
	[ 2, 9, 17, 8],
	[ 9, 10, 18, 17],
	[ 3, 11, 18, 10],
	[11, 12, 19, 18],
	[ 4, 13, 19, 12],
	[13, 14, 15, 19],
	]):
	if si==0 or i in ((0, 1, 2, 3) if center else (1, 2, 3)):
	draw.polygon([trans(VF[x]) for x in p], C[F[si11+i]], "black", 8)
	if si==0:
	draw.polygon([trans(*V[x]) for x in s], None, "black", 24)

	im = im.resize((1024, 1024), Image.Resampling.BICUBIC)
	im.save(name)

	render("sample.png",
	"WBRPYwypgrb"+
	"BBBBBBBBBBB"+
	"RRRRRRRRRRR"+
	"GGGGGGGGGGG"+
	"PPPPPPPPPPP"+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	renderLL("sample_ll.png",
	"WBRPYwypgrb"+
	"BBBBBBBBBBB"+
	"RRRRRRRRRRR"+
	"GGGGGGGGGGG"+
	"PPPPPPPPPPP"+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	render("megaminx.png",
	"WWWWWWWWWWW"+
	"BBBBBBBBBBB"+
	"RRRRRRRRRRR"+
	"GGGGGGGGGGG"+
	"PPPPPPPPPPP"+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	render("scramble_r.png",
	"pppppppwwwp"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"pwpppppppWW"+
	"WwwwWWWWWWW"+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"ppppppppppp"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"pppppWWWppp")

	render("scramble_d.png",
	"WWWWWWWwwwW"+
	"BBBBBBBBBBB"+
	"pWWWppppppp"+
	"pwWWppppppp"+
	"pwwwppppppp"+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"ppppppppppp"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"ppppppppppp")

	render("scramble_u.png",
	"ppppppppppp"+
	"BBBBBBBBBBB"+
	"WpppWWWWWWW"+
	"WpppWWWWWWW"+
	"WpppWWWWWWW"+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"WWWWWWWWWWW"+
	"WWWWWWWWWWW"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"WWWWWWWWWWW")

	render("scramble_example.png",
	"BrrWYPgpbPP"+
	"BBBBBBBBBBB"+
	"WWWBrBrPyPR"+
	"YwpGGrRRyyB"+
	"gYPyYbWpbgw"+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"PBgBgGBbbYY"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"rWygGyRwpWY")

	render("star.png",
	"B B "+
	"BBBBBBBBBBB"+
	"R R"+
	"W W W W W W"+
	"Y Y "+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"G G "+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"P P ")

	render("f2l.png",
	"B BBBBB "+
	"BBBBBBBBBBB"+
	"RRR RRR"+
	"WWWWWWWWWWW"+
	"Y YYYYY "+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"G GGGGG "+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"P PPPPP")

	render("f2l_i.png",
	" BB "+
	"BBBBBBBBBBB"+
	"R RRRRR "+
	"BRR BBB "+
	" W "+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"WWWWWWW WWW"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYY YYY")

	render("f2l_center.png",
	" W B"+
	"BBBBBBBBBBB"+
	"RB RRRRR "+
	"B R BBB "+
	" "+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"WWWWWWW WWW"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYY YYY")

	render("s2l.png",
	" "+
	"y yyyyyyy"+
	"p ppppppp"+
	"g ggggggg"+
	"r rrrrrrr"+
	"b bbbbbbb"+
	"wwwwwwwwwww"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYYYYYYYYYY")

	render("s2l.png",
	" "+
	"B BBBBBBB"+
	"R RRRRRRR"+
	"G GGGGGGG"+
	"P PPPPPPP"+
	"Y YYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	render("s2l_1.png",
	"w "+
	"BBBBBBBBBBB"+
	"b bbbbb"+
	"y yyyyy "+
	"p "+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"GGGGGGGGGGG"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"RRRRR RRR")

	render("s2l_2.png",
	"w "+
	"BBBBBBBBBBB"+
	"g ggggg"+
	"r rrrrrrr"+
	"b bbbbbbb"+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"YYYYYYYYYYY"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"PPPPPPPPPPP")

	render("s2l_3.png",
	"w "+
	"BBBBBBBBBBB"+
	"y yyyyyyy"+
	"p ppppppp"+
	"g ggggggg"+
	"YYYYYYYYYYY"+
	"wwwwwwwwwww"+
	"RRRRRRRRRRR"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"BBBBBBBBBBB")

	render("eoll.png",
	"w w w w w w"+
	"y yyyyyyy"+
	"p ppppppp"+
	"g ggggggg"+
	"r rrrrrrr"+
	"b bbbbbbb"+
	"wwwwwwwwwww"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYYYYYYYYYY")

	renderLL("eoll_1.png",
	"w w w w"+
	"B w BBBBBBB"+
	"R RRRRRRR"+
	"G w GGGGGGG"+
	"P PPPPPPP"+
	"Y YYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	renderLL("eoll_2.png",
	"w w w w"+
	"B BBBBBBB"+
	"R w RRRRRRR"+
	"G w GGGGGGG"+
	"P PPPPPPP"+
	"Y YYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	renderLL("eoll_3.png",
	"w w"+
	"B w BBBBBBB"+
	"R w RRRRRRR"+
	"G w GGGGGGG"+
	"P w PPPPPPP"+
	"Y YYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	renderLL("eoll_4.png",
	"w w "+
	"B w BBBBBBB"+
	"R w RRRRRRR"+
	"G w GGGGGGG"+
	"P PPPPPPP"+
	"Y w YYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	render("coll.png",
	"wwwwwwwwwww"+
	"y yyyyyyy"+
	"p ppppppp"+
	"g ggggggg"+
	"r rrrrrrr"+
	"b bbbbbbb"+
	"wwwwwwwwwww"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYYYYYYYYYY")

	renderLL("coll_1.png",
	"w w w w w w"+
	"B wBBBBBBB"+
	"R wRRRRRRR"+
	"G wGGGGGGG"+
	"P PPPPPPP"+
	"Y YYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	renderLL("coll_2.png",
	"w w w w w w"+
	"Bw BBBBBBB"+
	"Rw RRRRRRR"+
	"Gw GGGGGGG"+
	"P PPPPPPP"+
	"Y YYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	renderLL("coll_3.png",
	"w w w w w w"+
	"B BBBBBBB"+
	"Rw RRRRRRR"+
	"G GGGGGGG"+
	"Pw PPPPPPP"+
	"Yw YYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	renderLL("coll_4.png",
	"w w w w w w"+
	"B BBBBBBB"+
	"R wRRRRRRR"+
	"G GGGGGGG"+
	"P wPPPPPPP"+
	"Y wYYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	renderLL("coll_5.png",
	"w w w w w w"+
	"B BBBBBBB"+
	"R wRRRRRRR"+
	"G wGGGGGGG"+
	"P wPPPPPPP"+
	"Yw wYYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	renderLL("coll_6.png",
	"w w w w w w"+
	"Bw wBBBBBBB"+
	"Rw RRRRRRR"+
	"Gw GGGGGGG"+
	"Pw PPPPPPP"+
	"Y YYYYYYY"+
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb")

	render("epll.png",
	"wwwwwwwwwww"+
	"y y yyyyyyy"+
	"p p ppppppp"+
	"g g ggggggg"+
	"r r rrrrrrr"+
	"b b bbbbbbb"+
	"wwwwwwwwwww"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYYYYYYYYYY")

	renderLL("epll_1.png",
	"wwwwwwwwwww"+
	"y p yyyyyyy"+
	"p b ppppppp"+
	"g g ggggggg"+
	"r r rrrrrrr"+
	"b y bbbbbbb"+
	"wwwwwwwwwww"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYYYYYYYYYY",
	True)

	renderLL("epll_2.png",
	"wwwwwwwwwww"+
	"y y yyyyyyy"+
	"p r ppppppp"+
	"g p ggggggg"+
	"r g rrrrrrr"+
	"b b bbbbbbb"+
	"wwwwwwwwwww"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYYYYYYYYYY",
	True)

	renderLL("epll_3.png",
	"wwwwwwwwwww"+
	"y y yyyyyyy"+
	"p r ppppppp"+
	"g g ggggggg"+
	"r b rrrrrrr"+
	"b p bbbbbbb"+
	"wwwwwwwwwww"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYYYYYYYYYY",
	True)

	renderLL("epll_4.png",
	"wwwwwwwwwww"+
	"y p yyyyyyy"+
	"p r ppppppp"+
	"g y ggggggg"+
	"r g rrrrrrr"+
	"b b bbbbbbb"+
	"wwwwwwwwwww"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYYYYYYYYYY",
	True)

	renderLL("epll_5.png",
	"wwwwwwwwwww"+
	"y y yyyyyyy"+
	"p b ppppppp"+
	"g r ggggggg"+
	"r g rrrrrrr"+
	"b p bbbbbbb"+
	"wwwwwwwwwww"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYYYYYYYYYY",
	True)

	render("cpll.png",
	"wwwwwwwwwww"+
	"yyyyyyyyyyy"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"bbbbbbbbbbb"+
	"wwwwwwwwwww"+
	"BBBBBBBBBBB"+
	"ppppppppppp"+
	"ggggggggggg"+
	"rrrrrrrrrrr"+
	"YYYYYYYYYYY")
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