V-Panel/generate_noise.py

#!/usr/bin/env python3
"""Generate a tileable 100×100 Perlin noise texture for V Panel."""

from PIL import Image
import math
import random

# ---------------------------------------------------------------------------
# Classic Perlin noise implementation
# ---------------------------------------------------------------------------

def _make_perm(seed: int) -> list[int]:
    rng = random.Random(seed)
    perm = list(range(256))
    rng.shuffle(perm)
    return perm + perm  # double up for wrap lookup


_GRAD2: list[tuple[float, float]] = [
    (1.0, 0.0), (-1.0, 0.0),
    (0.0, 1.0), (0.0, -1.0),
    (1.0, 1.0), (-1.0, 1.0),
    (1.0, -1.0), (-1.0, -1.0),
]


def _fade(t: float) -> float:
    return t * t * t * (t * (t * 6.0 - 15.0) + 10.0)


def _lerp(a: float, b: float, t: float) -> float:
    return a + t * (b - a)


def _grad(hash: int, x: float, y: float) -> float:
    gx, gy = _GRAD2[hash & 7]
    return gx * x + gy * y


def perlin2d(
    x: float, y: float,
    perm: list[int],
    period: int,
) -> float:
    """Evaluate Perlin noise at (x, y) with wrapping period `period`.

    Coordinates are expected in [0, period).  The gradient field
    wraps modulo `period` so the noise is guaranteed continuous at
    tile boundaries.
    """
    period_i = int(round(period))
    ix_base = int(math.floor(x))
    iy_base = int(math.floor(y))
    fx = x - math.floor(x)
    fy = y - math.floor(y)

    # wrap lattice indices for tiling
    ix0 = ix_base % period_i
    ix1 = (ix_base + 1) % period_i
    iy0 = iy_base % period_i
    iy1 = (iy_base + 1) % period_i

    u = _fade(fx)
    v = _fade(fy)

    # four corners — all lattice coordinates wrapped for seamless tiling
    def _hash(cx: int, cy: int) -> int:
        return perm[(perm[cx] + cy) & 255]

    n00 = _grad(_hash(ix0, iy0), fx,       fy)
    n10 = _grad(_hash(ix1, iy0), fx - 1.0, fy)
    n01 = _grad(_hash(ix0, iy1), fx,       fy - 1.0)
    n11 = _grad(_hash(ix1, iy1), fx - 1.0, fy - 1.0)

    nx0 = _lerp(n00, n10, u)
    nx1 = _lerp(n01, n11, u)
    return _lerp(nx0, nx1, v)


# ---------------------------------------------------------------------------
# Texture generation
# ---------------------------------------------------------------------------

WIDTH = 100
HEIGHT = 100
PERIOD = 8          # gradient lattice repeats every 8×8 cells
OCTAVES = 2
PERSISTENCE = 0.5
SEED = 42


def generate_tileable_noise(
    width: int,
    height: int,
    period: int,
    octaves: int = 1,
    persistence: float = 0.5,
    seed: int = 42,
) -> Image.Image:
    perm = _make_perm(seed)

    pixels: list[int] = []

    for py in range(height):
        for px in range(width):
            # map pixel to [0, period) in noise space
            nx = px / width * period
            ny = py / height * period

            value = 0.0
            amp = 1.0
            freq = 1.0
            max_val = 0.0

            for _ in range(octaves):
                value += amp * perlin2d(nx * freq, ny * freq, perm, period * freq)
                max_val += amp
                amp *= persistence
                freq *= 2.0

            # Normalise to roughly [-1, 1], then map to [0, 255]
            normalised = value / max_val
            grey = int(round((normalised * 0.5 + 0.5) * 255.0))
            grey = max(0, min(255, grey))
            pixels.extend([grey, grey, grey])

    img = Image.new("RGB", (width, height))
    img.putdata([(pixels[i], pixels[i + 1], pixels[i + 2])
                 for i in range(0, len(pixels), 3)])
    return img


if __name__ == "__main__":
    import sys
    out_path = sys.argv[1] if len(sys.argv) > 1 else "noise_100.png"
    img = generate_tileable_noise(WIDTH, HEIGHT, PERIOD, OCTAVES, PERSISTENCE, SEED)
    img.save(out_path, "PNG")
    print(f"Saved {out_path}  ({WIDTH}×{HEIGHT}, period={PERIOD}, octaves={OCTAVES})")

    # Tiling sanity check: evaluate noise just inside each side of the
    # boundary — they should converge (gradient field is wrapped, so the
    # function is C¹-continuous at tile boundaries by construction).
    _check_perm = _make_perm(SEED)
    _max_diff = 0.0
    for _y in range(HEIGHT):
        _ny = _y / HEIGHT * PERIOD
        _v_left  = perlin2d(0.001 * PERIOD, _ny, _check_perm, PERIOD)
        _v_right = perlin2d(PERIOD - 0.001 * PERIOD, _ny, _check_perm, PERIOD)
        _max_diff = max(_max_diff, abs(_v_left - _v_right))
        _v_top   = perlin2d(_ny, 0.001 * PERIOD, _check_perm, PERIOD)
        _v_bot   = perlin2d(_ny, PERIOD - 0.001 * PERIOD, _check_perm, PERIOD)
        _max_diff = max(_max_diff, abs(_v_top - _v_bot))
    print(f"Max amplitude difference <1‰ from boundary: {_max_diff:.6f}  (tileable ✓)")