Plotter Trajectories (Hébert)

Math essence

Each curve is x(t) = cx + r(t)·cos(2π·b·t)·cos(2π·a·t + δ) − r(t)·sin(2π·b·t)·sin(2π·a·t + δ)·½ (and y symmetric), with r(t) a slow radial modulation. Local pixel alpha ∝ 1 / (1 + speed / v_ref), so the line darkens where the pen slows.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/generative_pioneers/hebert_plotter_trajectory/reference.py

from __future__ import annotations

from typing import ClassVar

import imageio.v2 as imageio
import numpy as np


class HebertPlotterTrajectory:
    family: ClassVar[str] = "generative_pioneers"
    sketch: ClassVar[str] = "hebert_plotter_trajectory"

    def __init__(
        self,
        dim: int = 512,
        n_passes: int = 3,
        n_curves: int = 18,
        length: float = 12000.0,
        a: float = 3.0,
        b: float = 4.0,
        delta: float = 1.5707963,
        d_phase_per_pass: float = 0.05,
        velocity_amp: float = 0.45,
        thickness: float = 1.0,
        bg_color: tuple[int, int, int] = (245, 240, 230),
        ink_color: tuple[int, int, int] = (20, 20, 30),
        seed: int | None = None,
    ) -> None:
        self.dim = dim
        self.n_passes = n_passes
        self.n_curves = n_curves
        self.length = length
        self.a = a
        self.b = b
        self.delta = delta
        self.d_phase_per_pass = d_phase_per_pass
        self.velocity_amp = velocity_amp
        self.thickness = thickness
        self.bg_color = np.array(bg_color, dtype=np.uint8)
        self.ink_color = np.array(ink_color, dtype=np.uint8)
        self._seed = seed
        self.rng = np.random.default_rng(seed)
        self.canvas = np.full((dim, dim, 3), self.bg_color, dtype=np.uint8)
        self.time = 0
        self._dirty = True

    def reset(self, seed: int | None = None) -> None:
        if seed is not None:
            self._seed = seed
        self.rng = np.random.default_rng(self._seed)
        self.canvas = np.full((self.dim, self.dim, 3), self.bg_color, dtype=np.uint8)
        self.time = 0
        self._dirty = True

    def _plot_one_curve(
        self,
        a: float,
        b: float,
        delta: float,
        length: float,