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113 lines
No EOL
3.5 KiB
Python
113 lines
No EOL
3.5 KiB
Python
import numpy as np
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import itertools as it
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from mobject.mobject import Mobject, Mobject1D, Mobject2D, Mobject
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from geometry import Line
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from constants import *
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class Stars(Mobject1D):
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CONFIG = {
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"stroke_width" : 1,
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"radius" : FRAME_X_RADIUS,
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"num_points" : 1000,
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}
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def generate_points(self):
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radii, phis, thetas = [
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scalar*np.random.random(self.num_points)
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for scalar in [self.radius, np.pi, 2*np.pi]
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]
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self.add_points([
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(
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r * np.sin(phi)*np.cos(theta),
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r * np.sin(phi)*np.sin(theta),
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r * np.cos(phi)
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)
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for r, phi, theta in zip(radii, phis, thetas)
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])
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class CubeWithFaces(Mobject2D):
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def generate_points(self):
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self.add_points([
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sgn * np.array(coords)
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for x in np.arange(-1, 1, self.epsilon)
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for y in np.arange(x, 1, self.epsilon)
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for coords in it.permutations([x, y, 1])
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for sgn in [-1, 1]
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])
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self.pose_at_angle()
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self.set_color(BLUE)
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def unit_normal(self, coords):
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return np.array(map(lambda x : 1 if abs(x) == 1 else 0, coords))
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class Cube(Mobject1D):
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def generate_points(self):
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self.add_points([
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([a, b, c][p[0]], [a, b, c][p[1]], [a, b, c][p[2]])
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for p in [(0, 1, 2), (2, 0, 1), (1, 2, 0)]
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for a, b, c in it.product([-1, 1], [-1, 1], np.arange(-1, 1, self.epsilon))
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])
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self.pose_at_angle()
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self.set_color(YELLOW)
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class Octohedron(Mobject1D):
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def generate_points(self):
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x = np.array([1, 0, 0])
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y = np.array([0, 1, 0])
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z = np.array([0, 0, 1])
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vertex_pairs = [(x+y, x-y), (x+y,-x+y), (-x-y,-x+y), (-x-y,x-y)]
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vertex_pairs += [
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(b[0]*x+b[1]*y, b[2]*np.sqrt(2)*z)
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for b in it.product(*[(-1, 1)]*3)
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]
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for pair in vertex_pairs:
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self.add_points(
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Line(pair[0], pair[1], density = 1/self.epsilon).points
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)
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self.pose_at_angle()
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self.set_color(MAROON_D)
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class Dodecahedron(Mobject1D):
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def generate_points(self):
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phi = (1 + np.sqrt(5)) / 2
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x = np.array([1, 0, 0])
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y = np.array([0, 1, 0])
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z = np.array([0, 0, 1])
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v1, v2 = (phi, 1/phi, 0), (phi, -1/phi, 0)
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vertex_pairs = [
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(v1, v2),
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(x+y+z, v1),
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(x+y-z, v1),
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(x-y+z, v2),
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(x-y-z, v2),
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]
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five_lines_points = Mobject(*[
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Line(pair[0], pair[1], density = 1.0/self.epsilon)
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for pair in vertex_pairs
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]).points
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#Rotate those 5 edges into all 30.
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for i in range(3):
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perm = map(lambda j : j%3, range(i, i+3))
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for b in [-1, 1]:
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matrix = b*np.array([x[perm], y[perm], z[perm]])
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self.add_points(np.dot(five_lines_points, matrix))
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self.pose_at_angle()
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self.set_color(GREEN)
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class Sphere(Mobject2D):
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def generate_points(self):
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self.add_points([
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(
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np.sin(phi) * np.cos(theta),
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np.sin(phi) * np.sin(theta),
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np.cos(phi)
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)
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for phi in np.arange(self.epsilon, np.pi, self.epsilon)
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for theta in np.arange(0, 2 * np.pi, 2 * self.epsilon / np.sin(phi))
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])
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self.set_color(BLUE)
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def unit_normal(self, coords):
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return np.array(coords) / np.linalg.norm(coords)
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