knotchy/scripts/icons/knot.py

#!/usr/bin/env python3
"""Generates the knot icons' geometry; run via scripts/make-icons.sh."""
import json
import math
import os

ROOT = os.path.dirname(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
NAVY = "#132441"
CORAL = "#FF8A5B"


def trefoil(cx, cy, size, gap):
    n = 1200
    pts = []
    for i in range(n):
        t = 2 * math.pi * i / n
        pts.append((math.sin(t) + 2 * math.sin(2 * t), -(math.cos(t) - 2 * math.cos(2 * t))))
    xs = [p[0] for p in pts]
    ys = [p[1] for p in pts]
    mx, my = (max(xs) + min(xs)) / 2, (max(ys) + min(ys)) / 2
    span = max(max(xs) - min(xs), max(ys) - min(ys))
    p = [(cx + (x - mx) / span * size, cy + (y - my) / span * size) for x, y in pts]

    # Self-crossings: points far apart along the curve that land on each other.
    cands = []
    for i in range(n):
        for j in range(i + n // 6, n):
            if j - i > n - n // 6:
                continue
            d = (p[i][0] - p[j][0]) ** 2 + (p[i][1] - p[j][1]) ** 2
            if d < (size * 0.004) ** 2:
                cands.append((d, i, j))
    cands.sort()
    crossings = []
    for _, i, j in cands:
        far = lambda a, b: min(abs(a - b) % n, n - abs(a - b) % n) > 40
        if all(far(i, a) and far(j, b) for a, b in crossings):
            crossings.append((i, j))
        if len(crossings) == 3:
            break
    assert len(crossings) == 3, crossings

    # Alternate crossings go under; hide points within `gap` (straight-line) of each.
    visits = sorted([i for i, _ in crossings] + [j for _, j in crossings])
    under = visits[1::2]
    hidden = set()
    for u in under:
        for d in range(-n // 10, n // 10 + 1):
            k = (u + d) % n
            if math.dist(p[k], p[u]) < gap:
                hidden.add(k)

    strands, cur = [], []
    start = next(i for i in range(n) if i in hidden)
    for k in range(1, n + 1):
        i = (start + k) % n
        if i in hidden:
            if len(cur) > 1:
                strands.append(cur)
            cur = []
        else:
            cur.append(p[i])
    if len(cur) > 1:
        strands.append(cur)
    assert len(strands) == 3
    return [s[::3] + [s[-1]] for s in strands]


def path(strand):
    return "M" + " L".join(f"{x:.2f},{y:.2f}" for x, y in strand)


# Each gap is half the crossing strand's width, plus the round cap, plus clear space.
ICON_STROKE, GLYPH_STROKE = 8.5, 1.9
icon = trefoil(50, 51, 62, ICON_STROKE + 1.3)
glyph = trefoil(9, 9.3, 14.2, GLYPH_STROKE + 0.6)

os.makedirs(os.path.join(ROOT, "assets"), exist_ok=True)
json.dump({"icon": icon, "iconStroke": ICON_STROKE, "glyph": glyph, "glyphStroke": GLYPH_STROKE,
           "navy": NAVY, "coral": CORAL},
          open(os.path.join(ROOT, "scripts/icons/knot.json"), "w"))

strokes = "".join(f'<path d="{path(s)}"/>' for s in icon)
open(os.path.join(ROOT, "assets/knotchy-icon.svg"), "w").write(
    f'<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100">'
    f'<rect width="100" height="100" rx="22.5" fill="{NAVY}"/>'
    f'<g fill="none" stroke="{CORAL}" stroke-width="8.5" stroke-linecap="round" stroke-linejoin="round">{strokes}</g></svg>\n')
open(os.path.join(ROOT, "assets/knotchy-mark.svg"), "w").write(
    f'<svg xmlns="http://www.w3.org/2000/svg" viewBox="15 18 70 66">'
    f'<g fill="none" stroke="{CORAL}" stroke-width="8.5" stroke-linecap="round" stroke-linejoin="round">{strokes}</g></svg>\n')

points = ",\n".join(
    "        [" + ", ".join(f"CGPoint(x: {x:.2f}, y: {y:.2f})" for x, y in s) + "]" for s in glyph)
open(os.path.join(ROOT, "Sources/Knotchy/KnotGlyph.swift"), "w").write(f'''// Generated by scripts/icons/knot.py; run scripts/make-icons.sh to change it.
import AppKit

enum KnotGlyph {{
    static let strands: [[CGPoint]] = [
{points},
    ]

    static let menuBarImage: NSImage = {{
        let image = NSImage(size: NSSize(width: 18, height: 18), flipped: true) {{ _ in
            NSColor.black.setStroke()
            for strand in strands {{
                let path = NSBezierPath()
                path.move(to: strand[0])
                for point in strand.dropFirst() {{ path.line(to: point) }}
                path.lineWidth = 1.9
                path.lineCapStyle = .round
                path.lineJoinStyle = .round
                path.stroke()
            }}
            return true
        }}
        image.isTemplate = true
        image.accessibilityDescription = "Knotchy"
        return image
    }}()
}}
''')
print("knot: 3 strands; wrote knot.json, assets/*.svg, Sources/Knotchy/KnotGlyph.swift")