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pendulum.py
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pendulum.py
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import numpy
import random
import math
import argparse
import os
os.environ['PYGAME_HIDE_SUPPORT_PROMPT'] = "hide"
import pygame
import pygame.gfxdraw
# Double Pendulum with Pygame + pyOpenGL
# by Ghast ~ https://github.com/davidpendergast
USE_GL = True # if False, will use pure pygame
if USE_GL:
import OpenGL as OpenGL
import OpenGL.GL as GL
import OpenGL.GLU as GLU
# Params (can be set via the command line)
N = 1000 # Number of pendulums
L = 20 # Length of pendulum arms
M = 5 # Mass of pendulum arms
G = 2 * 9.8 # Gravity
FPS = 60
ZOOM = 5
SPREAD = (6.283 / 360) / 4
ML2 = M * L * L
# OpenGL-Only Params
COLOR_CHANNELS = 4 # must be 3 or 4
RAINBOW = True
OPACITY = 0.1
def get_initial_conds():
theta1 = 3.1415 * (random.random() + 0.5)
theta2 = random.random() * 6.283
return theta1, theta2, SPREAD
class State:
def __init__(self):
theta1, theta2, spread = get_initial_conds()
self.theta1 = numpy.linspace(theta1, theta1 + spread, N)
self.theta2 = numpy.linspace(theta2, theta2 + spread, N)
self.p1 = numpy.zeros(N)
self.p2 = numpy.zeros(N)
self.colors = [hsv_to_rgb(360 * i / N, 0.75, 1) for i in range(N)]
self.colors.reverse()
# arrays for temp storage (to avoid reallocating arrays constantly)
self.sub = numpy.zeros(N)
self.cos = numpy.zeros(N)
self.cos2 = numpy.zeros(N)
self.sin = numpy.zeros(N)
self.temp1 = numpy.zeros(N)
self.temp2 = numpy.zeros(N)
self.temp3 = numpy.zeros(N)
self.temp4 = numpy.zeros(N)
self.denom = numpy.zeros(N)
self.num = numpy.zeros(N)
self.dtheta1 = numpy.zeros(N)
self.dtheta2 = numpy.zeros(N)
self.dp1 = numpy.zeros(N)
self.dp2 = numpy.zeros(N)
self.x1 = numpy.zeros(N, dtype=numpy.int16)
self.y1 = numpy.zeros(N, dtype=numpy.int16)
self.x2 = numpy.zeros(N, dtype=numpy.int16)
self.y2 = numpy.zeros(N, dtype=numpy.int16)
if USE_GL:
self.vertex_data = numpy.zeros((N * 2 + 1) * 2, dtype=float)
self.color_data = numpy.ones((N * 2 + 1) * COLOR_CHANNELS, dtype=float)
if RAINBOW:
for i in range(0, N * 2):
c = self.colors[i // 2]
self.color_data[i * COLOR_CHANNELS + 0] = c[0] / 256
self.color_data[i * COLOR_CHANNELS + 1] = c[1] / 256
self.color_data[i * COLOR_CHANNELS + 2] = c[2] / 256
if COLOR_CHANNELS > 3:
self.color_data[3::COLOR_CHANNELS] = OPACITY
self.index_data = numpy.arange(0, N * 4, dtype=int)
self.index_data[0::4] = N * 2 # center point is stored as the Nth vertex
self.index_data[1::4] = numpy.arange(0, N * 2, 2, dtype=int)
self.index_data[2::4] = numpy.arange(0, N * 2, 2, dtype=int)
self.index_data[3::4] = numpy.arange(1, N * 2, 2, dtype=int)
def euler_update(self, dt):
numpy.subtract(self.theta1, self.theta2, out=self.sub)
numpy.cos(self.sub, out=self.cos)
numpy.square(self.cos, out=self.cos2)
numpy.sin(self.sub, out=self.sin)
self.calc_dtheta1(self.p1, self.p2, self.cos, self.cos2)
self.calc_dtheta2(self.p1, self.p2, self.cos, self.cos2)
self.calc_dp1(self.theta1, self.dtheta1, self.dtheta2, self.sin)
self.calc_dp2(self.theta2, self.dtheta1, self.dtheta2, self.sin)
self.theta1 = self.theta1 + dt * self.dtheta1
self.theta2 = self.theta2 + dt * self.dtheta2
self.p1 = self.p1 + dt * self.dp1
self.p2 = self.p2 + dt * self.dp2
def calc_dtheta1(self, p1, p2, cos, cos2):
# self.dtheta1 = (6 / ML2) * (2 * p1 - 3 * cos * p2) / (16 - 9 * cos2)
numpy.multiply(2, p1, out=self.temp1)
numpy.multiply(3, cos, out=self.temp2)
numpy.multiply(self.temp2, p2, out=self.temp2)
numpy.subtract(self.temp1, self.temp2, out=self.num)
numpy.multiply((6 / ML2), self.num, out=self.num)
numpy.multiply(9, cos2, out=self.temp3)
numpy.subtract(16, self.temp3, out=self.denom)
numpy.divide(self.num, self.denom, out=self.dtheta1)
def calc_dtheta2(self, p1, p2, cos, cos2):
# self.dtheta2 = (6 / ML2) * (8 * p2 - 3 * cos * p1) / (16 - 9 * cos2)
numpy.multiply(8, p2, out=self.temp1)
numpy.multiply(3, cos, out=self.temp2)
numpy.multiply(self.temp2, p1, out=self.temp2)
numpy.subtract(self.temp1, self.temp2, out=self.num)
numpy.multiply((6 / ML2), self.num, out=self.num)
numpy.multiply(9, cos2, out=self.temp3)
numpy.subtract(16, self.temp3, out=self.denom)
numpy.divide(self.num, self.denom, out=self.dtheta2)
def calc_dp1(self, theta1, dtheta1, dtheta2, sin):
# self.dp1 = (-ML2 / 2) * (dtheta1 * dtheta2 * sin + 3 * G / L * numpy.sin(theta1))
numpy.multiply(dtheta1, dtheta2, out=self.temp1)
numpy.multiply(self.temp1, sin, out=self.temp1)
numpy.sin(theta1, out=self.temp2)
numpy.multiply(3 * G / L, self.temp2, out=self.temp2)
numpy.add(self.temp1, self.temp2, out=self.temp3)
numpy.multiply(-ML2 / 2, self.temp3, out=self.dp1)
def calc_dp2(self, theta2, dtheta1, dtheta2, sin):
# self.dp2 = (-ML2 / 2) * (-dtheta1 * dtheta2 * sin + G / L * numpy.sin(theta2))
numpy.multiply(dtheta1, dtheta2, out=self.temp1)
numpy.multiply(self.temp1, sin, out=self.temp1)
numpy.sin(theta2, out=self.temp2)
numpy.multiply(G / L, self.temp2, out=self.temp2)
numpy.subtract(self.temp2, self.temp1, out=self.temp3)
numpy.multiply(-ML2 / 2, self.temp3, out=self.dp2)
def render_all(self, screen):
x0 = screen.get_width() // 2
y0 = screen.get_height() // 2
# self.x1 = x0 + ZOOM * L * numpy.cos(self.theta1 + 3.1429 / 2)
numpy.add(self.theta1, 3.1429 / 2, out=self.temp1)
numpy.cos(self.temp1, out=self.temp1)
numpy.multiply(ZOOM * L, self.temp1, out=self.temp1)
numpy.add(x0, self.temp1, out=self.x1, casting='unsafe')
# self.y1 = y0 + ZOOM * L * numpy.sin(self.theta1 + 3.1429 / 2)
numpy.add(self.theta1, 3.1429 / 2, out=self.temp2)
numpy.sin(self.temp2, out=self.temp2)
numpy.multiply(ZOOM * L, self.temp2, out=self.temp2)
numpy.add(y0, self.temp2, out=self.y1, casting='unsafe')
# self.x2 = self.x1 + ZOOM * L * numpy.cos(self.theta2 + 3.1429 / 2)
numpy.add(self.theta2, 3.1429 / 2, out=self.temp3)
numpy.cos(self.temp3, out=self.temp3)
numpy.multiply(ZOOM * L, self.temp3, out=self.temp3)
numpy.add(self.x1, self.temp3, out=self.x2, casting='unsafe')
# self.y2 = self.y1 + ZOOM * L * numpy.sin(self.theta2 + 3.1429 / 2)
numpy.add(self.theta2, 3.1429 / 2, out=self.temp4)
numpy.sin(self.temp4, out=self.temp4)
numpy.multiply(ZOOM * L, self.temp4, out=self.temp4)
numpy.add(self.y1, self.temp4, out=self.y2, casting='unsafe')
if USE_GL:
self.vertex_data[0:N*4:4] = self.x1
self.vertex_data[1:N*4:4] = self.y1
self.vertex_data[2:N*4:4] = self.x2
self.vertex_data[3:N*4:4] = self.y2
self.vertex_data[N*4] = x0
self.vertex_data[N*4 + 1] = y0
GL.glClear(GL.GL_COLOR_BUFFER_BIT)
GL.glEnableClientState(GL.GL_VERTEX_ARRAY)
GL.glEnableClientState(GL.GL_COLOR_ARRAY)
GL.glVertexPointer(2, GL.GL_FLOAT, 0, self.vertex_data)
GL.glColorPointer(COLOR_CHANNELS, GL.GL_FLOAT, 0, self.color_data)
GL.glDrawElements(GL.GL_LINES, len(self.index_data), GL.GL_UNSIGNED_INT, self.index_data);
GL.glDisableClientState(GL.GL_VERTEX_ARRAY)
GL.glDisableClientState(GL.GL_COLOR_ARRAY)
else:
screen.fill((0, 0, 0))
# (-_-) don't think there's a good way to avoid this loop without gl...
for i in range(0, N):
pygame.gfxdraw.line(screen, x0, y0, self.x1[i], self.y1[i], self.colors[i])
pygame.gfxdraw.line(screen, self.x1[i], self.y1[i], self.x2[i], self.y2[i], self.colors[i])
import cProfile
import pstats
class Profiler:
def __init__(self):
self.is_running = False
self.pr = cProfile.Profile(builtins=False)
def toggle(self):
self.is_running = not self.is_running
if not self.is_running:
self.pr.disable()
ps = pstats.Stats(self.pr)
ps.strip_dirs()
ps.sort_stats('cumulative')
ps.print_stats(35)
else:
print("Started profiling...")
self.pr.clear()
self.pr.enable()
def initialize_display(size):
pygame.init()
if USE_GL:
display = size
flags = pygame.DOUBLEBUF | pygame.OPENGL
screen = pygame.display.set_mode(display, flags)
GL.glClearColor(0, 0, 0, 1)
GL.glViewport(0, 0, display[0], display[1])
GL.glOrtho(0.0, display[0], display[1], 0.0, 0.0, 1.0);
if COLOR_CHANNELS > 3:
GL.glEnable(GL.GL_BLEND)
GL.glBlendFunc(GL.GL_SRC_ALPHA, GL.GL_ONE_MINUS_SRC_ALPHA);
return screen
else:
return pygame.display.set_mode(size, 0, 8)
def start(size):
screen = initialize_display(size)
clock = pygame.time.Clock()
state = State()
profiler = Profiler()
running = True
last_update_time = pygame.time.get_ticks()
while running:
current_time = pygame.time.get_ticks()
dt = (current_time - last_update_time) / 1000
state.euler_update(dt)
state.render_all(screen)
pygame.display.flip()
for event in pygame.event.get():
if event.type == pygame.QUIT or (event.type == pygame.KEYDOWN and event.key == pygame.K_ESCAPE):
running = False
elif event.type == pygame.KEYDOWN:
if event.key == pygame.K_r:
print("Reseting...")
state = State()
elif event.key == pygame.K_p:
profiler.toggle()
if current_time // 1000 > last_update_time // 1000:
pygame.display.set_caption("Double Pendulum (FPS={:.1f}, N={})".format(clock.get_fps(), N))
last_update_time = current_time
clock.tick(FPS)
def hsv_to_rgb(h, s, v):
"""
:param h: 0 <= h < 360
:param s: 0 <= s <= 1
:param v: 0 <= v <= 1
:return: (r, g, b) as floats
"""
C = v * s
X = C * (1 - abs((h / 60) % 2 - 1))
m = v - C
if h < 60:
rgb_prime = (C, X, 0)
elif h < 120:
rgb_prime = (X, C, 0)
elif h < 180:
rgb_prime = (0, C, X)
elif h < 240:
rgb_prime = (0, X, C)
elif h < 300:
rgb_prime = (X, 0, C)
else:
rgb_prime = (C, 0, X)
return (int(256 * rgb_prime[0] + m),
int(256 * rgb_prime[1] + m),
int(256 * rgb_prime[2] + m))
if __name__ == "__main__":
parser = argparse.ArgumentParser(description='A double pendulum simulation made with pygame, PyOpenGL, and numpy.')
parser.add_argument('-n', type=int, metavar="int", default=N, help=f'the number of pendulums (default {N})')
parser.add_argument('--opacity', type=float, metavar="float", default=OPACITY, help=f'the opacity of the pendulums (default {OPACITY})')
parser.add_argument('--length', type=int, metavar="int", default=L, help=f'the length of the pendulum arms (default {L})')
parser.add_argument('--mass', type=int, metavar="float", default=M, help=f'the mass of the pendulum arms (default {M})')
parser.add_argument('--fps', type=int, metavar="int", default=FPS, help=f'the target FPS for the simulation (default {FPS})')
parser.add_argument('--zoom', type=int, metavar="int", default=ZOOM, help=f'the target FPS for the simulation (default {ZOOM})')
parser.add_argument('--size', type=int, metavar="int", default=[800, 600], nargs=2, help='the window size for the simulation (default 800 600)')
parser.add_argument('--spread', type=float, metavar="float", default=SPREAD, help=f'the initial spread, in radians (default {SPREAD:.4f})')
args = parser.parse_args()
N = args.n
OPACITY = args.opacity
L = args.length
M = args.mass
FPS = args.fps
ZOOM = args.zoom
SPREAD = args.spread
start(args.size)