refactor to OOP
This commit is contained in:
Daniel Mevec
parent
afcce3b98b
commit
7b8a2dae26
1 changed files with 269 additions and 237 deletions
506
torus.py
506
torus.py
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@ -1,272 +1,304 @@
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import numpy as np
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import numpy as np
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from numpy.polynomial.polynomial import Polynomial
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from numpy.polynomial.polynomial import Polynomial
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import matplotlib.pyplot as plt
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import matplotlib.pyplot as plt
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import matplotlib.colors as colors
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from matplotlib.widgets import Slider, Button
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from matplotlib.widgets import Slider, Button
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# The parametrized function to be plotted
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def mantle(rfrac, n=1000):
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theta = np.linspace(-np.pi, np.pi, n)
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rmaj = 1
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rmin = rmaj*rfrac
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u = theta * rmin
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func = (np.pi)*(rmaj - rmin*np.cos(theta))
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data = np.array([func, u])
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data2 = np.array([-func, u[::-1]])
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data = np.append(data, data2, axis=1)
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data = np.append(data, data[:, 0:1], axis=1)
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return data
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def crossection(rfrac, n=1000):
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theta = np.linspace(0, 2*np.pi, n)
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rmaj = 1
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rmin = rmaj * rfrac
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x = rmaj + rmin*np.cos(theta)
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y = rmin*np.sin(theta)
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data = np.array([x, y])
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data2 = np.array([-x, y])
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data = np.append(data, [[np.nan,], [np.nan,]], axis=1)
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data = np.append(data, data2, axis=1)
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return data
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def sunpath_side(rfrac, n=1000):
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theta = np.linspace(0, 2*np.pi, n)
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rmaj = 1
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x = rmaj + rmaj*np.cos(theta)
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y = rmaj*np.sin(theta)
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return np.array([x, y])
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def sunpath_top(rfrac, n=1000):
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theta = np.linspace(0, np.pi, n)
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rmaj = 1
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x = rmaj + rmaj*np.cos(theta)
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y = np.zeros_like(theta)
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return np.array([x, y])
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def sun_side(rfrac, sunpos):
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rmaj = 1
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x = rmaj - rmaj*np.cos(sunpos)
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y = rmaj*np.sin(sunpos)
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return [x, y]
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def sun_top(rfrac, sunpos):
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rmaj = 1
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x = rmaj - rmaj*np.cos(sunpos)
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y = 0
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return [x, y]
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def sun_map(rfrac, sunpos):
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rmaj = 1
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rmin = rmaj*rfrac
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y = sunpos * rmin
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x = 0
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return [x, y]
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def topview(rfrac, n=1000):
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theta = np.linspace(0, np.pi, n)
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rmaj = 1
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rmin = rmaj*rfrac
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x1 = (rmaj + rmin) * np.cos(theta)
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y1 = -1 * (rmaj + rmin) * np.sin(theta)
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data1 = np.array([x1, y1])
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x2 = (rmaj - rmin) * np.cos(theta)
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y2 = -1 * (rmaj - rmin) * np.sin(theta)
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data2 = np.array([x2, y2])
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data = np.append(data1, [[np.nan,], [np.nan,]], axis=1)
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data = np.append(data, data2, axis=1)
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return data
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def contour_map(rfrac, sunpos, n=100):
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rmaj = 1
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rmin = rmaj*rfrac
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phi = np.linspace(-np.pi, np.pi, n)
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theta = np.linspace(-np.pi, np.pi, int(n*rfrac))
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y = np.array([[w]*n for w in rmin*theta])
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func = (np.pi)*(rmaj - rmin*np.cos(theta))
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x = np.array([np.linspace(-f, f, n) for f in func])
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# x, y = np.meshgrid(np.linspace(-func[0], func[0], n), rmin*theta)
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sun = [rmaj - rmaj*np.cos(sunpos), 0, rmaj*np.sin(sunpos)]
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def raytraced(ph, th):
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def r(ph, th):
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rx = (rmaj - rmin*np.cos(th)) * np.cos(ph)
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ry = (rmaj - rmin*np.cos(th)) * np.sin(ph)
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rz = rmin * np.sin(th)
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return rx, ry, rz
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def n(ph, th):
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rx, ry, rz = r(ph, th)
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cx = rmaj * np.cos(ph)
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cy = rmaj * np.sin(ph)
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cz = 0
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retx, rety, retz = rx-cx, ry-cy, rz-cz
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return -1*np.array([retx, rety, retz])/np.linalg.norm([retx, rety, retz])
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def b(ph, th):
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rx, ry, rz = r(ph, th)
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sx, sy, sz = sun
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retx, rety, retz = rx-sx, ry-sy, rz-sz
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return np.array([retx, rety, retz])/np.linalg.norm([retx, rety, retz])
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o = sun
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d = b(ph, th)
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s = r(ph, th)
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pol = Polynomial(coef(rmaj, rmin, d, o))
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roots = uproot(pol.roots())
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if len(roots) == 0:
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return 0
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poi = o + roots[0]*d
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return (1 if np.allclose(s, poi) else -1)
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z = np.array([[raytraced(ph, th) for ph in phi] for th in theta])
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# z = np.array([[np.dot(b(ph, th), n(ph, th)) for ph in phi] for th in theta])
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return x, y, z
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def coef(rmaj, rmin, d, o):
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k1 = np.inner(d, d)
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k2 = np.inner(o, d)
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k3 = np.inner(o, o) - (rmin**2 + rmaj**2)
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c4 = k1**2
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c3 = 4*k1*k2
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c2 = 2*k1*k3 + 4*k2**2 + 4*(rmaj*d[2])**2
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c1 = 4*k3*k2 + 8*(rmaj**2)*o[2]*d[2]
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c0 = k3**2 - 4*(rmaj**2)*(rmin**2 - o[2]**2)
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return [c0, c1, c2, c3, c4]
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def uproot(arr):
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def uproot(arr):
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mask = np.logical_and(arr > 0, np.isreal(arr))
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mask = np.logical_and(arr > 0, np.isreal(arr))
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masked = arr[mask]
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masked = arr[mask]
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return np.real(sorted(masked))
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return np.real(sorted(masked))
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r_fraction = 0.5
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class TorusWorld:
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sun_pos = np.pi/2
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# Create the figure and the line that we will manipulate
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@staticmethod
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fig, (ax_side, ax_top, ax_map) = plt.subplots(3, 1, gridspec_kw={'height_ratios': [1, 1, 1]})
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def coef(rmaj, rmin, d, o):
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"""
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curtesy of: http://blog.marcinchwedczuk.pl/ray-tracing-torus
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"""
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k1 = np.inner(d, d)
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k2 = np.inner(o, d)
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k3 = np.inner(o, o) - (rmin**2 + rmaj**2)
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circles_top, = ax_top.plot(*topview(r_fraction), 'k')
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c4 = k1**2
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path_top, = ax_top.plot(*sunpath_top(r_fraction), 'k:')
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c3 = 4*k1*k2
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pos_top, = ax_top.plot(*sun_top(r_fraction, sun_pos), marker='o', color='r', markersize=10,)
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c2 = 2*k1*k3 + 4*k2**2 + 4*(rmaj*d[2])**2
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ax_top.set_xlim(-2.05, 2.05)
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c1 = 4*k3*k2 + 8*(rmaj**2)*o[2]*d[2]
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ax_top.set_ylim(-2.05, None)
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c0 = k3**2 - 4*(rmaj**2)*(rmin**2 - o[2]**2)
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ax_top.set_aspect('equal')
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return [c0, c1, c2, c3, c4]
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ax_top.axis('off')
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def __init__(self, rfrac):
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self.r_maj = 1
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self.r_min = rfrac
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self.sun = np.array([self.r_maj, 0, self.r_maj])
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self.sun_r = np.array([np.pi/2, 0])
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self.surface_map = None
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circles_side, = ax_side.plot(*crossection(r_fraction), 'k')
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def update(self, rfrac=None):
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path_side, = ax_side.plot(*sunpath_side(r_fraction), 'k:')
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rfrac = rfrac if rfrac else self.r_min
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pos_side, = ax_side.plot(*sun_side(r_fraction, sun_pos), marker='o', color='r', markersize=10,)
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self.r_min = rfrac
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ax_side.set_xlim(-2.05, 2.05)
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self.put_sun(*self.sun_r)
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ax_side.set_aspect('equal')
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# ax_side.set_ylim(-r_min, None)
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ax_side.axis('off')
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map_border, = ax_map.plot(*mantle(r_fraction), 'k')
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def put_sun(self, phi, theta):
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pos_map, = ax_map.plot(*sun_map(r_fraction, sun_pos), marker='o', color='r', markersize=10,)
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self.sun_r = np.array([phi, theta])
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dawnline_map = [ax_map.contourf(*contour_map(r_fraction, sun_pos), [-1, 0, 1], cmap='YlOrBr_r')]
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self.sun = np.array([
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ax_map.set_aspect('equal')
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(self.r_maj - self.r_maj*np.cos(phi))*np.cos(theta),
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ax_map.set_ylabel('Longitude')
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(self.r_maj - self.r_maj*np.cos(phi))*np.sin(theta),
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ax_map.set_xlabel('Lattitude')
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self.r_maj * np.sin(phi),
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ax_map.axis('off')
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])
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# cbar = fig.colorbar(dawnline_map[0])
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# adjust the main plot to make room for the sliders
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def surface_point(self, phi, theta):
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fig.subplots_adjust(left=0.25, bottom=0.25)
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rx = (self.r_maj - self.r_min*np.cos(phi)) * np.cos(theta)
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ry = (self.r_maj - self.r_min*np.cos(phi)) * np.sin(theta)
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rz = self.r_min * np.sin(phi)
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return rx, ry, rz
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# Make a horizontal slider to control the frequency.
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def normal_vector(self, phi, theta):
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axsun = fig.add_axes([0.25, 0.1, 0.65, 0.03])
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rx, ry, rz = self.surface_point(phi, theta)
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slider_sun = Slider(
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cx = self.r_maj * np.cos(theta)
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ax=axsun,
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cy = self.r_maj * np.sin(theta)
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label='Angle of Sun',
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cz = 0
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valmin=-np.pi,
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retx, rety, retz = rx-cx, ry-cy, rz-cz
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valmax=np.pi,
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return np.array([retx, rety, retz])/np.linalg.norm([retx, rety, retz])
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valinit=sun_pos,
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)
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# Make a vertically oriented slider to control the amplitude
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def ray_vector(self, phi, theta):
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axrad = fig.add_axes([0.1, 0.25, 0.0225, 0.63])
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rx, ry, rz = self.surface_point(phi, theta)
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slider_rf = Slider(
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sx, sy, sz = self.sun
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ax=axrad,
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retx, rety, retz = rx-sx, ry-sy, rz-sz
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label="Fraction of Radii (r/R)",
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return np.array([retx, rety, retz])/np.linalg.norm([retx, rety, retz])
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valmin=0,
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valmax=1,
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def is_illuminated(self, phi, theta):
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valinit=r_fraction,
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ray = self.ray_vector(phi, theta)
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orientation="vertical"
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pol = Polynomial(self.coef(self.r_maj, self.r_min, ray, self.sun))
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)
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roots = uproot(pol.roots())
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if len(roots) == 0:
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return False
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return np.allclose(self.surface_point(phi, theta), self.sun+roots[0]*ray)
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def illumination(self, phi, theta):
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# return np.dot(self.ray_vector(phi, theta), -self.normal_vector(phi, theta))
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return np.dot(self.ray_vector(phi, theta), -self.normal_vector(phi, theta)) * self.is_illuminated(phi, theta)
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# The function to be called anytime a slider's value changes
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class NoInamge():
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def update_torus(val):
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def __init__(self, rfrac_init=0.5, sun_init=np.pi/2):
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def update(ax, line, func):
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fig, (ax_side, ax_top, ax_map) = plt.subplots(3, 1, gridspec_kw={'height_ratios': [2, 2, 1]})
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u, m = func(slider_rf.val)
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self.fig = fig
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line.set_ydata(m)
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self.ax = dict(
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line.set_xdata(u)
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map=ax_map,
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top=ax_top,
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side=ax_side,
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)
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self.lines = dict()
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self.sun_kwargs = dict(marker='o', color='r', markersize=10,)
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self.contour_kwargs = dict(cmap=plt.colormaps['hot'], vmin=0, vmax=1)
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self.levels = 25 # [-1, 0, 1]
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self.torus = TorusWorld(rfrac_init)
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self.init_top_view()
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self.init_side_view()
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self.init_map_view()
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def init_map_view(self):
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self.lines['map_border'], = self.ax['map'].plot(*self._mantle_map(), 'k')
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self.lines['pos_map'], = self.ax['map'].plot(*self._sunpos_map(), marker='o', color='r', markersize=10,)
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self.lines['dawnline_map'] = [
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self.ax['map'].contourf(*self._contour_map(), self.levels, **self.contour_kwargs),
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]
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self.ax['map'].set_aspect('equal')
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self.ax['map'].set_ylabel('Longitude')
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self.ax['map'].set_xlabel('Lattitude')
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self.ax['map'].axis('off')
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def init_top_view(self):
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self.lines['circles_top'], = self.ax['top'].plot(*self._top_section(), 'k')
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self.lines['path_top'], = self.ax['top'].plot(*self._sunpath_top(), 'k:')
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self.lines['pos_top'], = self.ax['top'].plot(*self._sunpos_top(), **self.sun_kwargs)
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self.ax['top'].set_xlim(-2.05, 2.05)
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self.ax['top'].set_ylim(-2.05, None)
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self.ax['top'].set_aspect('equal')
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self.ax['top'].axis('off')
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def init_side_view(self):
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self.lines['circles_side'], = self.ax['side'].plot(*self._crossection(), 'k')
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self.lines['path_side'], = self.ax['side'].plot(*self._sunpath_side(), 'k:')
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self.lines['pos_side'], = self.ax['side'].plot(*self._sunpos_side(), **self.sun_kwargs)
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self.ax['side'].set_xlim(-2.05, 2.05)
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self.ax['side'].set_aspect('equal')
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# self.ax['side'].set_ylim(-self.torus.r_min, None)
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self.ax['side'].axis('off')
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def _mantle_map(self, n=1000):
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phi = np.linspace(-np.pi, np.pi, n)
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u = phi * self.torus.r_min
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width = np.pi*(self.torus.r_maj - self.torus.r_min*np.cos(phi))
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data = np.array([width, u])
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data2 = np.array([-width, u[::-1]])
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data = np.append(data, data2, axis=1)
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data = np.append(data, data[:, 0:1], axis=1)
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return data
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def _contour_map(self, n=100):
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theta = np.linspace(-np.pi, np.pi, n)
|
||||||
|
phi = np.linspace(-np.pi, np.pi, int(n*self.torus.r_min))
|
||||||
|
|
||||||
|
y = np.array([[w]*n for w in self.torus.r_min*phi])
|
||||||
|
func = (np.pi)*(self.torus.r_maj - self.torus.r_min*np.cos(phi))
|
||||||
|
x = np.array([np.linspace(-f, f, n) for f in func])
|
||||||
|
# x, y = np.meshgrid(np.linspace(-func[0], func[0], n), rmin*theta)
|
||||||
|
|
||||||
|
z = np.array([[self.torus.illumination(ph, th) for th in theta] for ph in phi])
|
||||||
|
|
||||||
|
return x, y, z
|
||||||
|
|
||||||
|
def _sunpos_map(self):
|
||||||
|
phi, theta = self.torus.sun_r
|
||||||
|
x = (self.torus.r_maj - self.torus.r_min*np.cos(phi)) * theta
|
||||||
|
y = self.torus.r_min * phi
|
||||||
|
return x, y
|
||||||
|
|
||||||
|
def _top_section(self, n=1000):
|
||||||
|
phi = np.linspace(0, np.pi, n)
|
||||||
|
x1 = (self.torus.r_maj + self.torus.r_min) * np.cos(phi)
|
||||||
|
y1 = -1 * (self.torus.r_maj + self.torus.r_min) * np.sin(phi)
|
||||||
|
data1 = np.array([x1, y1])
|
||||||
|
x2 = (self.torus.r_maj - self.torus.r_min) * np.cos(phi)
|
||||||
|
y2 = -1 * (self.torus.r_maj - self.torus.r_min) * np.sin(phi)
|
||||||
|
data2 = np.array([x2, y2])
|
||||||
|
|
||||||
|
data = np.append(data1, [[np.nan,], [np.nan,]], axis=1)
|
||||||
|
data = np.append(data, data2, axis=1)
|
||||||
|
return data
|
||||||
|
|
||||||
|
def _sunpath_top(self, n=1000):
|
||||||
|
phi = np.linspace(0, np.pi, n)
|
||||||
|
x = self.torus.r_maj + self.torus.r_maj*np.cos(phi)
|
||||||
|
y = np.zeros_like(phi)
|
||||||
|
return np.array([x, y])
|
||||||
|
|
||||||
|
def _sunpos_top(self):
|
||||||
|
phi, theta = self.torus.sun_r
|
||||||
|
x = self.torus.r_maj + self.torus.r_maj*np.cos(phi)
|
||||||
|
y = 0
|
||||||
|
return x, y
|
||||||
|
|
||||||
|
def _crossection(self, n=1000):
|
||||||
|
phi = np.linspace(0, 2*np.pi, n)
|
||||||
|
x = self.torus.r_maj + self.torus.r_min*np.cos(phi)
|
||||||
|
y = self.torus.r_min*np.sin(phi)
|
||||||
|
data = np.array([x, y])
|
||||||
|
data2 = np.array([-x, y])
|
||||||
|
data = np.append(data, [[np.nan,], [np.nan,]], axis=1)
|
||||||
|
data = np.append(data, data2, axis=1)
|
||||||
|
return data
|
||||||
|
|
||||||
|
def _sunpath_side(self, n=1000):
|
||||||
|
phi = np.linspace(0, 2*np.pi, n)
|
||||||
|
x = self.torus.r_maj + self.torus.r_maj*np.cos(phi)
|
||||||
|
y = self.torus.r_maj*np.sin(phi)
|
||||||
|
return np.array([x, y])
|
||||||
|
|
||||||
|
def _sunpos_side(self):
|
||||||
|
phi, theta = self.torus.sun_r
|
||||||
|
x = self.torus.r_maj - self.torus.r_maj*np.cos(phi)
|
||||||
|
y = self.torus.r_maj*np.sin(phi)
|
||||||
|
return x, y
|
||||||
|
|
||||||
|
@staticmethod
|
||||||
|
def redraw_plot(ax, line, func):
|
||||||
|
x, y = func()
|
||||||
|
line.set_xdata(x)
|
||||||
|
line.set_ydata(y)
|
||||||
ax.relim()
|
ax.relim()
|
||||||
ax.autoscale_view()
|
ax.autoscale_view()
|
||||||
|
|
||||||
update(ax_map, map_border, mantle)
|
@staticmethod
|
||||||
update(ax_side, circles_side, crossection)
|
def redraw_contourf(ax, container, func, levels=None, contour_kwargs=None):
|
||||||
update(ax_side, path_side, sunpath_side)
|
levels = levels if levels else [-1, 0, 1]
|
||||||
update(ax_top, circles_top, topview)
|
contour_kwargs = contour_kwargs if contour_kwargs else {}
|
||||||
update(ax_top, path_top, sunpath_top)
|
for coll in container[0].collections:
|
||||||
|
coll.remove()
|
||||||
|
container[0] = ax.contourf(*func(), levels, **contour_kwargs)
|
||||||
|
|
||||||
for coll in dawnline_map[0].collections:
|
def update_torus(self, rfrac):
|
||||||
coll.remove()
|
self.torus.update(rfrac)
|
||||||
dawnline_map[0] = ax_map.contourf(*contour_map(slider_rf.val, slider_sun.val), [-1, 0, 1], cmap='YlOrBr_r')
|
self.redraw_plot(self.ax['map'], self.lines['map_border'], self._mantle_map)
|
||||||
|
self.redraw_plot(self.ax['side'], self.lines['circles_side'], self._crossection)
|
||||||
|
self.redraw_plot(self.ax['side'], self.lines['path_side'], self._sunpath_side)
|
||||||
|
self.redraw_plot(self.ax['top'], self.lines['circles_top'], self._top_section)
|
||||||
|
self.redraw_plot(self.ax['top'], self.lines['path_top'], self._sunpath_top)
|
||||||
|
self.redraw_contourf(self.ax['map'], self.lines['dawnline_map'],
|
||||||
|
self._contour_map, self.levels, self.contour_kwargs)
|
||||||
|
self.fig.canvas.draw_idle()
|
||||||
|
|
||||||
fig.canvas.draw_idle()
|
def update_sun(self, phi, theta):
|
||||||
|
self.torus.put_sun(phi, theta)
|
||||||
|
self.redraw_plot(self.ax['map'], self.lines['pos_map'], self._sunpos_map)
|
||||||
|
self.redraw_plot(self.ax['side'], self.lines['pos_side'], self._sunpos_side)
|
||||||
|
self.redraw_plot(self.ax['top'], self.lines['pos_top'], self._sunpos_top)
|
||||||
|
self.redraw_contourf(self.ax['map'], self.lines['dawnline_map'],
|
||||||
|
self._contour_map, self.levels, self.contour_kwargs)
|
||||||
|
self.fig.canvas.draw_idle()
|
||||||
|
|
||||||
|
|
||||||
# The function to be called anytime a slider's value changes
|
class ImageStatic(NoInamge):
|
||||||
def update_sun(val):
|
|
||||||
def update(ax, line, func):
|
|
||||||
u, m = func(slider_rf.val, slider_sun.val)
|
|
||||||
line.set_ydata(m)
|
|
||||||
line.set_xdata(u)
|
|
||||||
|
|
||||||
update(ax_map, pos_map, sun_map)
|
def __init__(self, rfrac_init=0.5, sun_init=np.pi/2):
|
||||||
update(ax_side, pos_side, sun_side)
|
super().__init__(rfrac_init, sun_init)
|
||||||
update(ax_top, pos_top, sun_top)
|
plt.show()
|
||||||
|
|
||||||
for coll in dawnline_map[0].collections:
|
|
||||||
coll.remove()
|
|
||||||
dawnline_map[0] = ax_map.contourf(*contour_map(slider_rf.val, slider_sun.val), [-1, 0, 1], cmap='YlOrBr_r')
|
|
||||||
|
|
||||||
fig.canvas.draw_idle()
|
|
||||||
|
|
||||||
|
|
||||||
# register the update function with each slider
|
class ImageInteractive(NoInamge):
|
||||||
slider_sun.on_changed(update_sun)
|
|
||||||
slider_rf.on_changed(update_torus)
|
|
||||||
|
|
||||||
# Create a `matplotlib.widgets.Button` to reset the sliders to initial values.
|
def __init__(self, rfrac_init=0.5, sun_init=np.pi/2):
|
||||||
resetax = fig.add_axes([0.8, 0.025, 0.1, 0.04])
|
super().__init__(rfrac_init, sun_init)
|
||||||
button = Button(resetax, 'Reset', hovercolor='0.975')
|
self.init_interactivity(rfrac_init, sun_init)
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
def init_interactivity(self, rfrac_init, sun_init):
|
||||||
|
self.fig.subplots_adjust(left=0.25, bottom=0.25)
|
||||||
|
self.ax['slider_sun'] = self.fig.add_axes([0.25, 0.1, 0.65, 0.03])
|
||||||
|
self.ax['slider_rf'] = self.fig.add_axes([0.1, 0.25, 0.0225, 0.63])
|
||||||
|
self.ax['button_reset'] = self.fig.add_axes([0.8, 0.025, 0.1, 0.04])
|
||||||
|
self.sliders = dict(
|
||||||
|
sun_phi=Slider(
|
||||||
|
ax=self.ax['slider_sun'],
|
||||||
|
label='Angle of Sun',
|
||||||
|
valmin=-np.pi,
|
||||||
|
valmax=np.pi,
|
||||||
|
valinit=sun_init,
|
||||||
|
),
|
||||||
|
rfrac=Slider(
|
||||||
|
ax=self.ax['slider_rf'],
|
||||||
|
label="Fraction of Radii (r/R)",
|
||||||
|
valmin=0,
|
||||||
|
valmax=1,
|
||||||
|
valinit=rfrac_init,
|
||||||
|
orientation="vertical"
|
||||||
|
)
|
||||||
|
|
||||||
|
)
|
||||||
|
self.sliders['sun_phi'].on_changed(self._slider_update_sun)
|
||||||
|
self.sliders['rfrac'].on_changed(self._slider_update_torus)
|
||||||
|
button = Button(self.ax['button_reset'], 'Reset', hovercolor='0.975')
|
||||||
|
button.on_clicked(self._reset)
|
||||||
|
|
||||||
|
def _slider_update_torus(self, val):
|
||||||
|
self.update_torus(val)
|
||||||
|
|
||||||
|
def _slider_update_sun(self, val):
|
||||||
|
self.update_sun(val, 0)
|
||||||
|
|
||||||
|
def _reset(self, event):
|
||||||
|
self.sliders['sun_phi'].reset()
|
||||||
|
self.sliders['rfrac'].reset()
|
||||||
|
|
||||||
|
|
||||||
def reset(event):
|
if __name__ == '__main__':
|
||||||
slider_sun.reset()
|
# ImageStatic()
|
||||||
slider_rf.reset()
|
ImageInteractive()
|
||||||
|
|
||||||
|
|
||||||
button.on_clicked(reset)
|
|
||||||
|
|
||||||
plt.show()
|
|
||||||
|
|
|
||||||
Loading…
Add table
Reference in a new issue