Smooth-Minimum SDF field

Math essence

smin_quadratic(a, b, k) = min(a, b) - h*h*k/4 with h = max(k - |a-b|, 0)/k. The blend weight m = h*h*0.5 linearly interpolates the two primitives' materials. Field shading uses 0.5 - smin/k to highlight the zero-isosurface, with iso-contours drawn at fixed step intervals to evoke Quilez's SDF debug visualisations.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/hodgin_iquilezles/SmoothMinSDF/reference.py

from __future__ import annotations

from typing import ClassVar

import numpy as np


def _smin_quadratic(a: np.ndarray, b: np.ndarray, k: float) -> np.ndarray:
    kk = k * 4.0
    h = np.maximum(kk - np.abs(a - b), 0.0) / kk
    return np.minimum(a, b) - h * h * kk * 0.25


class SmoothMinSDF:
    """Smooth-Minimum SDF field — Inigo Quilez (iquilezles.org).

    The "smooth-minimum" or "smooth-union" operator combines two signed
    distance fields into a single field whose iso-zero surface melts and
    blends the two primitives together (Quilez's *smin* article,
    https://iquilezles.org/articles/smin/).

    We render the *scalar field itself*: two animated 2D SDF metaballs —
    a circle and a horizontal slab — blended with the popular
    *quadratic-polynomial* smooth-minimum

        smin(a, b, k) = min(a, b) - h*h*k/4,  h = max(k-|a-b|, 0)/k.

    Pixels are shaded by the field value using the "mix factor" trick
    (the original Quilez vec2 smin that also returns the blend weight)
    so the two primitives are coloured in their own hues across the
    smooth transition.
    """

    family: ClassVar[str] = "hodgin_iquilezles"
    sketch: ClassVar[str] = "smoothminsdf"

    def __init__(
        self,
        dim: int = 360,
        radius_a: float = 60.0,
        radius_b: float = 50.0,
        k: float = 35.0,
        slab_halfwidth: float = 24.0,
        color_a: tuple[float, float, float] = (1.00, 0.42, 0.32),
        color_b: tuple[float, float, float] = (0.30, 0.62, 1.00),
        background: tuple[float, float, float] = (0.04, 0.04, 0.08),
        contour_step: float = 4.0,
        **_,
    ) -> None:
        self.dim = dim
        self.radius_a = float(radius_a)
        self.radius_b = float(radius_b)
        self.k = float(k)
        self.slab_halfwidth = float(slab_halfwidth)
        self.color_a = np.array(color_a, dtype=np.float32)
        self.color_b = np.array(color_b, dtype=np.float32)
        self.bg_color = np.array(background, dtype=np.float32)
        self.contour_step = float(contour_step)
        self.reset()