Particle-Spring Cloth (Verlet + Hooke)

Math essence

Velocity is implicit: v = (x - x_prev)*damping. Spring correction: d = ||p1-p0||; offset = (p1-p0)/d * (rest - d)*spring_k/2; distribute +/- offset between the two endpoints respecting anchor pinning. Fully vectorized over all edges via numpy.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/reas_processing/particleSpring/reference.py

from __future__ import annotations

from typing import ClassVar

import numpy as np


class ParticleSpring:
    """Particle-spring mass network with Verlet integration.

    A grid of free particles is connected to its 4-neighbors by linear
    Hooke's-law springs at rest length ``spacing``. A handful of points
    are marked as anchors (pinned to fixed positions). Per step:
    integrate with Verlet (x_new = 2*x - x_prev + a*dt^2), then
    relax each spring a fixed number of constraint iterations so the
    structure settles toward its rest-length network.
    """

    family: ClassVar[str] = "reas_processing"
    sketch: ClassVar[str] = "particleSpring"

    def __init__(
        self,
        dim: int = 500,
        grid_w: int = 32,
        grid_h: int = 24,
        spacing: float = 20.0,
        spring_k: float = 0.04,
        damping: float = 0.985,
        gravity: float = 60.0,
        constraint_iterations: int = 6,
        anchor_top: bool = True,
        anchor_bottom_corners: bool = True,
        center_anchor: bool = False,
        bg_color: tuple[int, int, int] = (245, 240, 230),
        link_color: tuple[int, int, int] = (60, 70, 90),
        node_color: tuple[int, int, int] = (220, 80, 70),
        line_alpha: float = 0.85,
        seed: int | None = None,
    ) -> None:
        self.dim = dim
        self.grid_w = grid_w
        self.grid_h = grid_h
        self.spacing = spacing
        self.spring_k = spring_k
        self.damping = damping
        self.gravity = gravity
        self.constraint_iterations = constraint_iterations
        self._anchor_top = anchor_top
        self._anchor_bottom_corners = anchor_bottom_corners
        self._center_anchor = center_anchor
        self.bg_color = np.array(bg_color, dtype=np.float32)
        self.link_color = np.array(link_color, dtype=np.float32)
        self.node_color = np.array(node_color, dtype=np.float32)
        self.line_alpha = line_alpha
        self._seed = seed
        self.reset()

    def reset(self, seed: int | None = None) -> None:
        if seed is not None: