figure.py
5.8 kB · python · 169 lines
1import math2import os34# STYLE56FONT = "Helvetica,Arial,sans-serif"7# PALETTE8INK = "#000000"9MUTED = "#8e8e93"10PALE = "#bababf"11PAPER = "#ffffff"12CONCEPT = {13 "gasket": "#00cad8",14 "carpet": "#008cff",15 "sponge": "#6768fa",16 "prime": "#ff325a",17 "bound": "#ff8f2c",18 "window": "#ff3d40",19 "control": "#8e8e93",20}21PALETTE = {22 "black": "#000000",23 "white": "#ffffff",24 "red": "#ff3d40",25 "red-light": "#ff9d95",26 "red-dark": "#a80016",27 "orange": "#ff8f2c",28 "orange-light": "#ffc093",29 "orange-dark": "#a25400",30 "yellow": "#ffd100",31 "yellow-light": "#ffe591",32 "yellow-dark": "#9e8100",33 "green": "#32cc58",34 "green-light": "#5eee79",35 "green-dark": "#007f2c",36 "mint": "#00d1bb",37 "mint-light": "#48efd8",38 "mint-dark": "#008173",39 "teal": "#00cad8",40 "teal-light": "#48e9f7",41 "teal-dark": "#007c85",42 "cyan": "#1ec9f3",43 "cyan-light": "#86e2ff",44 "cyan-dark": "#007c98",45 "blue": "#008cff",46 "blue-light": "#84bdff",47 "blue-dark": "#00559f",48 "indigo": "#6768fa",49 "indigo-light": "#9ea9ff",50 "indigo-dark": "#3c2abc",51 "purple": "#d332e9",52 "purple-light": "#f08aff",53 "purple-dark": "#870097",54 "pink": "#ff325a",55 "pink-light": "#ff9a9f",56 "pink-dark": "#a50030",57 "brown": "#b18462",58 "brown-light": "#dfaf8c",59 "brown-dark": "#754c2b",60 "gray": "#8e8e93",61 "gray-light": "#bababf",62 "gray-dark": "#56565a",63}64# PALETTE END65STROKE = 1.266THIN = 0.667MARGIN = 366869def esc(s):70 return s.replace("&", "&").replace("<", "<").replace(">", ">")7172def header(width, height):73 return ['<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 %d %d" width="%d" height="%d">' % (width, height, width, height), '<rect width="%d" height="%d" fill="%s"/>' % (width, height, PAPER)]7475def text(x, y, s, size=11, fill=INK, anchor="start", weight=None):76 w = ' font-weight="%s"' % weight if weight else ""77 return '<text x="%.1f" y="%.1f" font-family="%s" font-size="%d" fill="%s" text-anchor="%s"%s>%s</text>' % (x, y, FONT, size, fill, anchor, w, esc(s))7879def line(x1, y1, x2, y2, stroke=INK, width=STROKE):80 return '<line x1="%.1f" y1="%.1f" x2="%.1f" y2="%.1f" stroke="%s" stroke-width="%.1f"/>' % (x1, y1, x2, y2, stroke, width)8182def rect(x, y, w, h, fill, opacity=1.0):83 return '<rect x="%.1f" y="%.1f" width="%.1f" height="%.1f" fill="%s" opacity="%.2f"/>' % (x, y, w, h, fill, opacity)8485def circle(x, y, r, fill):86 return '<circle cx="%.1f" cy="%.1f" r="%.1f" fill="%s"/>' % (x, y, r, fill)8788def save(parts, path):89 with open(path, "w") as handle:90 handle.write("\n".join(parts + ["</svg>"]) + "\n")9192# STYLE END9394# DRAW9596Q = 2197DIGITS = (0, 10)98SAMPLES = 180099TIKZ = 900100101def hat(q, a0, t):102 d = math.sin(math.pi * q * t) / math.sin(math.pi * t)103 e = d * d - 2.0 * d * math.cos(math.pi * (2 * a0 - q + 1) * t) + 1.0104 return math.sqrt(e) / (q - 1) if e > 0.0 else 0.0105106def cap(q, t):107 d = abs(math.sin(math.pi * q * t) / math.sin(math.pi * t))108 return min(1.0, (d + 1.0) / (q - 1))109110def samples(n):111 return [0.5 * (j + 0.5) / n for j in range(n)]112113def curves(n):114 ts = samples(n)115 rows = [("majorant", [cap(Q, t) for t in ts])]116 for a0 in DIGITS:117 rows.append((f"digit {a0}", [hat(Q, a0, t) for t in ts]))118 return ts, rows119120def svg(path):121 width, height = 640, 280122 left, right, top, foot = MARGIN + 4, width - MARGIN - 96, MARGIN - 12, height - MARGIN123 parts = header(width, height)124 ts, rows = curves(SAMPLES)125 place = lambda t, v: (left + (right - left) * (t / 0.5), foot - (foot - top) * v)126 parts.append(line(left, foot, right, foot, PALE, THIN))127 parts.append(line(left, top, left, foot, PALE, THIN))128 parts.append(line(left, top, right, top, PALE, THIN))129 keys = (CONCEPT["bound"], CONCEPT["gasket"], CONCEPT["carpet"])130 for (_, values), color in zip(rows, keys):131 pts = " ".join("%.2f,%.2f" % place(t, v) for t, v in zip(ts, values))132 parts.append('<polyline points="%s" fill="none" stroke="%s" stroke-width="%.1f"/>' % (pts, color, STROKE))133 labels = ("majorant u_q", "|F| missing 0", "|F| missing 10")134 for i, (text_line, color) in enumerate(zip(labels, keys)):135 y = top + 18 + 18 * i136 parts.append(line(right + 12, y - 4, right + 30, y - 4, color, STROKE))137 parts.append(text(right + 36, y, text_line, size=10, fill=color))138 parts.append(text(left, foot + 16, "0", size=9, fill=MUTED))139 parts.append(text(right, foot + 16, "1/2", size=9, fill=MUTED, anchor="end"))140 parts.append(text(left - 6, top + 4, "1", size=9, fill=MUTED, anchor="end"))141 parts.append(text(left, top - 8, "base 21, one digit removed", size=11, weight="bold"))142 save(parts, path)143144def tikz(path):145 ts, rows = curves(TIKZ)146 names = ("bound", "gasket", "carpet")147 body = ["\\begin{tikzpicture}[x=23cm,y=4.4cm]"]148 for key in names:149 body.append("\\definecolor{tone%s}{HTML}{%s}" % (key, CONCEPT[key][1:].upper()))150 body.append("\\draw[gray!45,line width=0.3pt] (0,0) rectangle (0.5,1);")151 for (_, values), key in zip(rows, names):152 pts = " ".join("(%.5f,%.5f)" % (t, v) for t, v in zip(ts, values))153 body.append("\\draw[tone%s,line width=0.4pt] plot coordinates {%s};" % (key, pts))154 body.append("\\node[anchor=north] at (0,0) {\\footnotesize $0$};")155 body.append("\\node[anchor=north] at (0.5,0) {\\footnotesize $\\tfrac12$};")156 body.append("\\node[anchor=east] at (0,1) {\\footnotesize $1$};")157 body.append("\\end{tikzpicture}")158 with open(path, "w") as handle:159 handle.write("\n".join(body) + "\n")160161def main():162 out = os.path.join(os.path.dirname(os.path.abspath(__file__)), "..", "figures")163 os.makedirs(out, exist_ok=True)164 svg(os.path.join(out, "figure.svg"))165 tikz(os.path.join(out, "lemma.tex"))166 print("drew figures/figure.svg and figures/lemma.tex")167168if __name__ == "__main__":169 main()