File size: 3,514 Bytes
06b3545 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 | """Minimal 2D rigid-body physics: discs in a box with elastic collisions.
Cubes and cylinders are *rendered* as squares / rings (top-down view, like
looking down on the CLEVRER scene) but use a circular footprint for physics.
This keeps the engine tiny, stable and fast while preserving the causal event
structure (collisions, starts/stops of motion) that CLEVRER questions need.
"""
from dataclasses import dataclass, field
import numpy as np
from . import config
@dataclass
class Body:
idx: int
color: str
shape: str
material: str
size: str
radius: float
pos: np.ndarray # (2,) world coordinates
vel: np.ndarray # (2,)
spin: float = 0.0 # visual angular velocity (rad/s)
angle: float = 0.0 # visual rotation angle (rad)
mass: float = 1.0
is_probe: bool = False
@property
def speed(self) -> float:
return float(np.linalg.norm(self.vel))
def mass_of(radius: float, material: str) -> float:
# all shapes use a circular footprint: m = density * pi * r^2
return config.DENSITY[material] * np.pi * radius ** 2
class World:
"""A box arena with elastic object-object and object-wall collisions."""
def __init__(self, bodies, half: float = config.WORLD_HALF):
self.bodies = list(bodies)
self.half = half
def step(self, h: float):
"""Advance physics by h seconds.
Returns:
contacts: list of (idx_a, idx_b) pairs that collided this step
wall_hits: list of (idx, axis, side) with side in {-1, +1}
"""
contacts, wall_hits = [], []
# integrate
for b in self.bodies:
b.pos = b.pos + b.vel * h
b.vel = b.vel * config.DRAG
b.angle = (b.angle + b.spin * h) % (2.0 * np.pi)
# pairwise object collisions
bs = self.bodies
for i in range(len(bs)):
for j in range(i + 1, len(bs)):
A, B = bs[i], bs[j]
d = B.pos - A.pos
dist = float(np.linalg.norm(d))
rsum = A.radius + B.radius
if dist < rsum and dist > 1e-9:
n = d / dist
# impulse along the normal if approaching
v_rel_n = float(np.dot(B.vel - A.vel, n))
if v_rel_n < 0.0:
e = config.RESTITUTION
jimp = -(1.0 + e) * v_rel_n / (1.0 / A.mass + 1.0 / B.mass)
A.vel = A.vel - (jimp / A.mass) * n
B.vel = B.vel + (jimp / B.mass) * n
contacts.append((A.idx, B.idx))
# positional correction so objects never sink into each other
push = n * (0.5 * (rsum - dist))
A.pos = A.pos - push
B.pos = B.pos + push
# walls
for b in self.bodies:
for ax in range(2):
lim = self.half - b.radius
if b.pos[ax] > lim and b.vel[ax] > 0:
b.pos[ax] = lim
b.vel[ax] = -b.vel[ax] * config.WALL_RESTITUTION
wall_hits.append((b.idx, ax, +1))
elif b.pos[ax] < -lim and b.vel[ax] < 0:
b.pos[ax] = -lim
b.vel[ax] = -b.vel[ax] * config.WALL_RESTITUTION
wall_hits.append((b.idx, ax, -1))
return contacts, wall_hits
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