acdream/tools/IconForge/ac_glyph.py

"""The Asheron's Call sigil geometry, rebuilt from the retail wordmark.

Measured off the logo rather than guessed:

* the ring is a **thin, complete** circle -- roughly 1/16 of its diameter in
  thickness -- not a thick band with a gap. It passes *behind* the glyph.
* both ring and glyph are chiselled relief with a raised centre ridge, which is
  why every stroke shows a bright spine and two darker chamfers.
* the glyph is a crescent opening to the right. Its upper terminal extends into
  a barbed hook that crosses over the ring; its lower terminal tapers to a fine
  point.

Everything here produces masks; chisel.shade() turns them into metal.
"""
import numpy as np
from PIL import Image, ImageDraw, ImageFilter

SS = 4  # supersample factor for all mask drawing


def _canvas(size):
    return Image.new("L", (size * SS, size * SS), 0)


def _down(img, size):
    return np.asarray(img.resize((size, size), Image.LANCZOS), dtype=np.float32) / 255.0


def _px(size, v):
    """normalised (-1..1) -> pixel on the supersampled canvas"""
    return (v * 0.5 + 0.5) * size * SS


def thin_ring(size=1024, R=0.86, thick=0.055, wobble=0.0, seed=3):
    """Complete slender circle, the AC ring proportion."""
    W = size * SS
    y, x = np.mgrid[0:W, 0:W].astype(np.float32)
    x = (x / (W - 1)) * 2 - 1
    y = (y / (W - 1)) * 2 - 1
    r = np.sqrt(x * x + y * y)
    if wobble > 0:
        th = np.arctan2(y, x)
        rng = np.random.default_rng(seed)
        r = r - wobble * (np.sin(6 * th + rng.uniform(0, 6)) * 0.6
                          + np.sin(11 * th + rng.uniform(0, 6)) * 0.4)
    m = (np.abs(r - R) < thick / 2).astype(np.float32)
    im = Image.fromarray((m * 255).astype(np.uint8), "L")
    return _down(im, size)


def crescent(size=1024, R=0.66, inner_r=0.60, offset=0.30, cy=0.0,
             rot_deg=-18.0):
    """Classic two-circle crescent: outer disc minus an offset inner disc.

    The two intersection points give naturally sharp cusps -- exactly the
    terminals the AC glyph has, before the barb is added on top.
    """
    W = size * SS
    y, x = np.mgrid[0:W, 0:W].astype(np.float32)
    x = (x / (W - 1)) * 2 - 1
    y = (y / (W - 1)) * 2 - 1
    a = np.radians(rot_deg)
    xr = x * np.cos(a) - y * np.sin(a)
    yr = x * np.sin(a) + y * np.cos(a)
    outer = (xr * xr + (yr - cy) ** 2) < R * R
    inner = ((xr - offset) ** 2 + (yr - cy) ** 2) < inner_r * inner_r
    m = (outer & ~inner).astype(np.float32)
    return _down(Image.fromarray((m * 255).astype(np.uint8), "L"), size)


def _tapered_arc(draw, size, cx, cy, r0, r1, a0_deg, a1_deg,
                 w0, w1, steps=90, curl=0.0):
    """Draw a tapering curved stroke as a polygon strip."""
    t = np.linspace(0, 1, steps)
    ang = np.radians(a0_deg + (a1_deg - a0_deg) * t)
    rad = r0 + (r1 - r0) * t + curl * np.sin(np.pi * t)
    cxs = cx + np.cos(ang) * rad
    cys = cy + np.sin(ang) * rad
    w = w0 + (w1 - w0) * (t ** 1.35)
    dx = np.gradient(cxs); dy = np.gradient(cys)
    ln = np.sqrt(dx * dx + dy * dy); ln = np.where(ln < 1e-9, 1, ln)
    nx, ny = -dy / ln, dx / ln
    left = [( _px(size, cxs[i] + nx[i] * w[i]), _px(size, cys[i] + ny[i] * w[i]) )
            for i in range(steps)]
    right = [( _px(size, cxs[i] - nx[i] * w[i]), _px(size, cys[i] - ny[i] * w[i]) )
             for i in range(steps)][::-1]
    draw.polygon(left + right, fill=255)


def cusp_angles(R, inner_r, offset):
    """Where the two circles meet -- the crescent's two sharp terminals.

    Solving the circle intersection gives the exact attachment points, so the
    barb and tail grow out of the cusps instead of floating near them.
    """
    x = (R * R - inner_r * inner_r + offset * offset) / (2 * offset)
    y2 = R * R - x * x
    if y2 <= 0:
        return None
    y = np.sqrt(y2)
    return np.degrees(np.arctan2(-y, x)), np.degrees(np.arctan2(y, x))


def ac_glyph(size=1024, R=0.66, inner_r=0.60, offset=0.30, rot_deg=-18.0,
             barb=True, tail=True, fork=True):
    """Crescent + barbed upper hook + tapering lower tail, as one mask."""
    # Build crescent and spikes in ONE unrotated frame, then rotate the combined
    # mask once. Rotating them separately mixed two sign conventions and left the
    # tail floating clear of the cusp it is supposed to grow out of.
    m = crescent(size, R, inner_r, offset, 0.0, 0.0)
    cu = cusp_angles(R, inner_r, offset)
    if cu is None:
        return m
    upper, lower = cu

    img = _canvas(size)
    d = ImageDraw.Draw(img)
    if barb:
        # main spike: leaves the cusp thin, swells, then needles out past the ring
        _tapered_arc(d, size, 0.0, 0.0, R, R * 1.34, upper, upper - 62.0,
                     0.030, 0.004, curl=0.085)
        if fork:
            # the second, shorter prong that makes the terminal read as barbed
            _tapered_arc(d, size, 0.0, 0.0, R * 1.02, R * 1.16, upper - 26.0,
                         upper - 54.0, 0.022, 0.003, curl=-0.055)
    if tail:
        _tapered_arc(d, size, 0.0, 0.0, R, R * 1.14, lower, lower + 34.0,
                     0.028, 0.003, curl=0.030)
    spikes = _down(img, size)
    return np.clip(_rot(np.maximum(m, spikes), rot_deg, size), 0, 1)


def _rot(mask, deg, size):
    im = Image.fromarray((mask * 255).astype(np.uint8), "L")
    im = im.rotate(-deg, resample=Image.BICUBIC, center=(size / 2, size / 2))
    return np.asarray(im, dtype=np.float32) / 255.0


def soften(mask, px=1.0):
    im = Image.fromarray((np.clip(mask, 0, 1) * 255).astype(np.uint8), "L")
    return np.asarray(im.filter(ImageFilter.GaussianBlur(px)), dtype=np.float32) / 255.0