Restitution

15 · Impacts and penetration

Balls with e = 0, 0.3, 0.6 and 0.9 drop from 1 m onto a ground with e = 0. An impact replaces the contact's position bias with a rebound target of −e times the closing speed. With the default average combine, the ground's 0 halves every coefficient. With restitution_combine="max" each ball keeps its own.

drag to orbit · scroll to zoom

0.00 s

What to look at

Average: even the e = 0.9 ball bounces only about 20 cm.
Max: it bounces back to about 80 cm.

Key parameter

ShapeConfig.restitution

Per shape, 0 to 1, default 0. Pairs combine with restitution_combine.

Try changing

Give the ground e = 1 and keep "average".
Set enable_restitution=False to turn bouncing off everywhere.

Concept

Restitution

What it is

On impact, a contact's position correction is replaced by a target: the separating velocity must be at least e times the closing velocity at the start of the step. The combined coefficient comes from restitution_combine.

u_after ≥ −e · u_start

In this scene

With the default average, the ground's e = 0 halves the e = 0.9 ball's bounce to about 20 cm; with max it returns to about 80 cm.

Considerations

Cost: No extra rows.
Accuracy: The target uses the start-of-step velocity, so forces in the step do not enlarge the bounce. Large steps make the impact time less precise.
Interactions: contact_compliance rejects positive restitution unless enable_restitution=False.
Use it when: Balls and dropped parts; leave e = 0 for grasping and stacking.

The script

cd tutorials && python 15_restitution.py prints each variant's final metric; --record out.json also writes the replay. Every tutorial imports replay.py from the same folder.

15_restitution.py
replay.py

# SPDX-FileCopyrightText: Copyright (c) 2026 Skild AI and the Steel contributors
# SPDX-License-Identifier: Apache-2.0

"""Restitution: per-shape coefficients and the restitution_combine mode."""

import newton
import warp as wp
from newton.solvers import SolverSteel

from replay import Recorder

DT = 1.0 / 240.0
SUBSTEPS = 8
BALL_E = [0.0, 0.3, 0.6, 0.9]


def build():
    builder = newton.ModelBuilder()
    builder.add_ground_plane(cfg=newton.ModelBuilder.ShapeConfig(restitution=0.0))
    for i, e in enumerate(BALL_E):
        ball = builder.add_body(xform=wp.transform((0.3 * i - 0.45, 0.0, 1.06), wp.quat_identity()))
        builder.add_shape_sphere(
            ball, radius=0.06, cfg=newton.ModelBuilder.ShapeConfig(density=500.0, restitution=e)
        )
    return builder.finalize()


def simulate(rec, combine):
    model = build()
    solver = SolverSteel(model, restitution_combine=combine)
    pipeline = newton.CollisionPipeline(model)
    contacts = pipeline.contacts()
    state_0, state_1, control = model.state(), model.state(), model.control()

    run = rec.variant(f'restitution_combine="{combine}"', model)
    for _ in range(rec.frames(4.0)):
        heights = state_0.body_q.numpy()[:, 2] - 0.06
        run.frame(state_0, **{f"e_{e}": h for e, h in zip(BALL_E, heights)})
        for _ in range(SUBSTEPS):
            pipeline.collide(state_0, contacts)
            solver.step(state_0, state_1, control, contacts, DT)
            state_0, state_1 = state_1, state_0
    run.check(solver)


if __name__ == "__main__":
    rec = Recorder()
    simulate(rec, "average")  # default: the ground's 0 halves every coefficient
    simulate(rec, "max")
    rec.save()

# SPDX-FileCopyrightText: Copyright (c) 2026 Skild AI and the Steel contributors
# SPDX-License-Identifier: Apache-2.0

"""Record Steel tutorial runs as replay JSON for the tutorials page, or print a summary.

Every tutorial imports this module. ``python NN_name.py`` runs the variants and prints
the final metric of each; ``--record out.json`` also writes body poses, shapes and metric
series that the page replays in 3D.
"""

import argparse
import base64
import json
import os
import subprocess
import sys
import time

import newton
import numpy as np
import warp as wp

from source_hash import source_sha256

_RENDERED_TYPES = {
    newton.GeoType.PLANE,
    newton.GeoType.SPHERE,
    newton.GeoType.CAPSULE,
    newton.GeoType.ELLIPSOID,
    newton.GeoType.CYLINDER,
    newton.GeoType.BOX,
    newton.GeoType.MESH,
    newton.GeoType.CONE,
    newton.GeoType.CONVEX_MESH,
}


class Recorder:
    """Collect the variants of one tutorial; ``fps`` is the replay frame rate."""

    def __init__(self, fps: int = 30):
        parser = argparse.ArgumentParser()
        parser.add_argument(
            "--record", metavar="OUT.json", help="write a replay file for the tutorials page"
        )
        parser.add_argument("--device", default=None, help="Warp device, for example cuda:0")
        self.args = parser.parse_args()
        if self.args.device:
            wp.set_device(self.args.device)
        self.fps = fps
        self.script = os.path.abspath(sys.argv[0])
        self.variants: list[Variant] = []

    def frames(self, seconds: float) -> int:
        """Number of replay frames in ``seconds``, including the first."""
        return int(round(seconds * self.fps)) + 1

    def variant(
        self,
        label: str,
        model: newton.Model,
        *,
        ghost: bool = False,
        slot: int | None = None,
        scene: str | None = None,
    ) -> "Variant":
        """Start one run; ``ghost`` overlays run ``slot``, ``scene`` groups runs for charts."""
        variant = Variant(label, model, self.fps, ghost, slot, scene)
        self.variants.append(variant)
        return variant

    def save(self) -> None:
        """Print a summary and, with ``--record``, write the replay file."""
        for variant in self.variants:
            last = variant.metrics[-1] if variant.metrics else {}
            flag = "  (rows dropped)" if variant.overflow else ""
            print(f"{variant.label:<48} {json.dumps(last)}  {variant.wall:.2f} s{flag}")
        if not self.args.record:
            return
        source_sha = source_sha256(self.script)
        doc = {
            "script": os.path.basename(self.script),
            "script_sha256": source_sha,
            "newton_commit": _newton_commit(),
            "newton_version": newton.__version__,
            "warp_version": wp.config.version,
            "gpu": wp.get_device().name,
            "fps": self.fps,
            "variants": [v.to_json() for v in self.variants],
        }
        with open(self.args.record, "w") as f:
            json.dump(doc, f, separators=(",", ":"))
        print(f"wrote {self.args.record}")


class Variant:
    """One recorded run: a pose per frame for every body, plus named metric values."""

    def __init__(self, label, model, fps, ghost, slot, scene):
        self.label, self.model, self.fps, self.ghost, self.slot = label, model, fps, ghost, slot
        self.scene = scene
        self.poses: list[np.ndarray] = []
        self.metrics: list[dict] = []
        self.awake: list[list[int]] = []
        self.particles: list[np.ndarray] = []
        self.overflow = False
        self.start = time.perf_counter()
        self.wall = 0.0

    def frame(self, state: newton.State, awake=None, particles=None, **metrics) -> None:
        """Record ``state.body_q``, optional awake flags, particle positions and metric values."""
        self.poses.append(state.body_q.numpy().astype(np.float32).copy())
        if particles is not None:
            self.particles.append(particles.numpy().astype(np.float32).copy())
        self.metrics.append({k: _round(v) for k, v in metrics.items()})
        if awake is not None:
            self.awake.append([int(x) for x in awake.numpy()])
        self.wall = time.perf_counter() - self.start

    def check(self, solver) -> None:
        """Note whether the solver dropped rows; call once after the run."""
        try:
            solver.check_constraint_capacity()
        except RuntimeError:
            self.overflow = True

    def to_json(self) -> dict:
        poses = (
            np.stack(self.poses)
            if self.poses
            else np.zeros((0, self.model.body_count, 7), np.float32)
        )
        return {
            "label": self.label,
            "fps": self.fps,
            "ghost": self.ghost,
            "slot": self.slot,
            "scene": self.scene,
            "bodies": int(self.model.body_count),
            "frames": int(poses.shape[0]),
            "poses": base64.b64encode(poses.astype(np.float32).tobytes()).decode(),
            "shapes": _shape_table(self.model),
            "metric": self.metrics,
            "awake": self.awake or None,
            "particles": self._particles_json(),
            "wall_s": round(self.wall, 3),
            "overflow": self.overflow,
        }

    def _particles_json(self):
        if not self.particles:
            return None
        frames = np.stack(self.particles)
        tris = self.model.tri_indices
        radius = self.model.particle_radius.numpy()
        return {
            "count": int(frames.shape[1]),
            "frames": base64.b64encode(frames.astype(np.float32).tobytes()).decode(),
            "radius": round(float(radius.mean()), 5) if radius.size else 0.0,
            "tris": [int(v) for v in tris.numpy().reshape(-1)]
            if tris is not None and tris.shape[0]
            else None,
        }


def _shape_table(model):
    types = model.shape_type.numpy()
    scales = model.shape_scale.numpy()
    xforms = model.shape_transform.numpy()
    bodies = model.shape_body.numpy()
    flags = model.shape_flags.numpy()
    shapes = []
    for i, t in enumerate(types):
        if int(t) not in _RENDERED_TYPES or not flags[i] & int(newton.ShapeFlags.VISIBLE):
            continue
        shape = {
            "b": int(bodies[i]),
            "t": int(t),
            "s": [round(float(v), 5) for v in scales[i]],
            "x": [round(float(v), 6) for v in xforms[i]],
        }
        if int(t) in (newton.GeoType.MESH, newton.GeoType.CONVEX_MESH):
            mesh = model.shape_source[i]
            shape["v"] = [round(float(v), 5) for v in np.asarray(mesh.vertices).reshape(-1)]
            shape["i"] = [int(v) for v in np.asarray(mesh.indices).reshape(-1)]
        shapes.append(shape)
    return shapes


def _round(value):
    value = float(value)
    return round(value, 5) if np.isfinite(value) else None


def _newton_commit():
    if os.environ.get("NEWTON_COMMIT"):
        return os.environ["NEWTON_COMMIT"]
    try:
        root = os.path.dirname(os.path.dirname(newton.__file__))
        return subprocess.check_output(["git", "-C", root, "rev-parse", "HEAD"], text=True).strip()
    except (OSError, subprocess.CalledProcessError):
        return None

Recorded with SolverSteel on Newton 1.9.0.dev0, Warp 1.19.0, NVIDIA RTX PRO 6000 Blackwell Server Edition. Replays read the state back every frame, so they are not a speed benchmark. Script · page text

Steel docs and tutorials are licensed under Apache-2.0. Third-party notices. "Skild", "Skild AI" and the Skild logo are trademarks of Skild AI and are not licensed under Apache-2.0.