Bokeh Blur with Light Leaks

Math essence

For each circle c with centre (cx_c, cy_c), radius r_c, colour col_c and peak i_c: stamp(c) = col_c * i_c * exp(-((p - centre_c) / r_c)^2 * tightness). canvas = background + sum_c stamp(c). canvas := canvas / (1 + 0.6 * canvas) (Reinhard tonemap), then multiply by a soft radial vignette.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/shader_legends_3/TaterBokeh/reference.py

from __future__ import annotations

from typing import ClassVar

import numpy as np


def _hash11(x: np.ndarray, seed: int) -> np.ndarray:
    p = np.int64(x) * np.int64(374761393) + np.int64(seed) * np.int64(668265263)
    p = p & np.int64(0xFFFFFFFF)
    p = (p ^ (p >> np.int64(13))) * np.int64(1274126177)
    p = p & np.int64(0xFFFFFFFF)
    p = p ^ (p >> np.int64(16))
    return (p & np.int64(0xFFFFFFFF)).astype(np.float32) / np.float32(0xFFFFFFFF)


def _hash12(x: np.ndarray, y: np.ndarray, seed: int) -> np.ndarray:
    p = np.int64(x) * np.int64(374761393) + np.int64(y) * np.int64(668265263) + np.int64(seed)
    p = p & np.int64(0xFFFFFFFF)
    p = (p ^ (p >> np.int64(13))) * np.int64(1274126177)
    p = p & np.int64(0xFFFFFFFF)
    p = p ^ (p >> np.int64(16))
    return (p & np.int64(0xFFFFFFFF)).astype(np.float32) / np.float32(0xFFFFFFFF)


class TaterBokeh:
    """Bokeh blur with light leaks — Dave "Tater" Hoskins (Shadertoy).

    Tater (Dave Hoskins) wrote several *bokeh* shaders that draw
    50-200 soft Gaussian circles on a dark backdrop, where each
    circle's colour is drawn from a warm-to-cool palette and
    overlapping circles add their intensities (additive blending)
    to produce a *light leak* effect at the intersection.  The
    trick is that the circles are *not* all the same size: a
    per-circle hash picks both a centre, a radius, and a colour,
    and a slow per-circle drift animates each disc in a slightly
    different direction.

    The output looks like out-of-focus Christmas lights or a
    lens-flare test chart.

    Math essence:

        for each circle c:
            h = hash(c)
            centre_c = (h.x, h.y)
            r_c = base_radius * (0.4 + 0.9 * h.r)
            col_c = palette(h.hue)
            drift_c = (h.dx, h.dy) * speed
            for each pixel p:
                d = |p - centre_c(t)|
                intensity = exp(-(d/r_c)^2)
                canvas += col_c * intensity

    We render the additive accumulation efficiently by stamping
    each circle into its own per-circle buffer and summing them.
    """

    family: ClassVar[str] = "shader_legends_3"
    sketch: ClassVar[str] = "taterbokeh"