replace noise with tileable perlin; use pixel-space sampling for fixed scale

generate_noise.py

@@ -0,0 +1,153 @@
+#!/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 ✓)")