Penne Ringers (Aaron Penne concentric ring extrusion)

Math essence

For ring i: r_i = lerp(r_max, r_min, i / (N-1)), z_i = i * z_step, theta_i = i * rotate_per_ring (radians), scale_i = z_far / (z_far + z_i). Project to 2D: draw a polyline of M points on a circle of radius r_i * scale_i, centred at (cx, cy), phase-shifted by theta_i. Sort rings by scale descending (front-to-back) so the front rings are drawn on top. For each adjacent pair of rings, draw a single connecting line between their phase-0 points.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/hobbs_cherniak_penne_deep/PenneRingers/reference.py

"""PenneRingers — Aaron Penne concentric ring extrusion (3D -> 2D).

A direct homage to Aaron Penne's take on the *Ringers* idiom
(best known from Cherniak's Art Blocks release, 2021).  Penne's
version is geometrically different: instead of "string around
pegs", it's "concentric rings extruded along the Z axis,
rotated about a common axis, projected to 2D".

The kernel we implement:

    1. Build N concentric rings of varying radii, all sharing
       a common centre.  Each ring has its own radius r_i.
    2. Each ring is "extruded" along the Z axis by a small
       amount z_i, and *rotated* about the Z axis by an angle
       theta_i.
    3. The 2D projection of the ring at (r_i, z_i, theta_i) is
       a circle of radius r_i * (z_far / (z_far + z_i)) (the
       standard perspective projection) but with a phase shift
       of theta_i.  So the projected ring is a circle of
       radius proportional to (1 / (1 + z_i / z_far)), drawn
       with an offset that depends on theta_i.
    4. Each ring is drawn as a closed polyline of M points
       (default 64), with the line colour sampled from a
       palette (Penne's signature: muted, low-saturation
       colours inspired by 1980s data visualisations and
       vintage infographics).
    5. A line connects each ring to the next one at one point
       on each ring (the "string" Penne adds to make the rings
       feel like a connected 3D form).

The visual is a stack of concentric rings, each rotated by a
small angle, with the rings closest to the viewer (smallest z)
the largest on screen, and the rings furthest from the viewer
the smallest.  The 1° per-ring rotation creates the slow
"spiral" feeling of a 3D form being viewed from the side.

Reference:
- Cherniak's *Ringers* (2021) for the underlying idiom.
  https://www.artblocks.io/collection/ringers-by-dmitri-cherniak
- Penne's *Apparitions* (2021) for the muted palette and the
  "layered form" aesthetic:
  https://www.artxcode.io/journal/aaron-penne-apparitions-on-art-blocks
"""
from __future__ import annotations

from typing import ClassVar

import numpy as np


# ---------------------------------------------------------------------------
class PenneRingers:
    """Penne-style concentric ring extrusion (3D -> 2D).

    Parameters
    ----------
    dim : int
        Square canvas side length (px).
    num_rings : int
        Number of rings N to draw.