Melodies from the Area of the Triangle Swept Out by Bodies on Circular Orbits

matsobco.py

import matplotlib.pyplot as plt
import math

# Radii of the bodies.
RAD0 = 7
RAD1 = 11
RAD2 = 15

# How many cycles to compute.
CYC = 1

# Sample/Hold conditions. The least restrictive condition is chosen.
SH = {
    #"always": True, # Uncomment for smooth, unS&H'd output
    #"timer": 13, # Uncomment to sample every N steps. Primes are the best.
    "triggers": True, # Uncomment to trigger on zeniths
}

class Body:
    def __init__(self, radius, angle):
        self.radius = radius
        self.angle = angle
    
    def position(self):
        return [self.radius * math.cos(self.angle), self.radius * math.sin(self.angle)]

fig, ax = plt.subplots()

def positions_of_body_at_radius(radius):
    positions = []
    body = Body(radius, 0)
    time_multiplier = 100 / radius
    
    for angle in range(0, 360 * CYC):
        body.angle = math.radians(angle * time_multiplier)
        positions += [body.position()]
    
    return positions

positions_zip = zip(positions_of_body_at_radius(RAD0), positions_of_body_at_radius(RAD1), positions_of_body_at_radius(RAD2))

def distance(p0, p1):
    return math.sqrt((p0[0] - p1[0])**2 + (p0[1] - p1[1])**2)

def close(x0, x1):
    return abs(x0 - x1) < 0.01

def condition(a, b, c, tak):
    if "always" in SH:
        return True
    if "timer" in SH:
        return tak % SH["timer"] == 0
    if "triggers" in SH:
        return close(RAD0 - RAD1, a) or close(RAD1 - RAD2, b) or close(RAD2 - RAD0, c) or close(RAD0 + RAD1, a) or close(RAD1 + RAD2, b) or close(RAD2 + RAD0, c)

areas = []
xs = []
lastarea = 0
for (tak, (p0, p1, p2)) in enumerate(positions_zip):
    a = distance(p0, p1)
    b = distance(p1, p2)
    c = distance(p2, p0)
    s = (a + b + c)/2
    if condition(a, b, c, tak):
        lastarea = [(s*(s-a)*(s-b)*(s-c)) ** 0.5]
    
    xs += [tak]
    areas += [lastarea]

ax.plot(xs, areas)