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from scipy.integrate import solve_ivp
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import math
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import numpy as np
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from scipy.constants import pi
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from scipy.interpolate import interp1d
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import copy
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from PIL import Image
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Rs = 8 # in au
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D = 50 # -"-
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accuracy = 100 # amount of iterations of solver
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res = 500 #as pixel on X-Axis
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fovX = 180 #in ° ####vorläufig über 180
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fovY = 180 # -"-
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maxDeviation = .01 # bei zu kleinem wert, knick in interpolation. ?photonensphäre? später lösen!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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bg = Image.open("old/images/background.jpg")
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#test = []
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def solver(alpha):
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if alpha == 0: # skip divided by 0 error
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return [0], [0] # r and phi=0
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if alpha == 180:
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return [D], [0] # if angle= pi then, tan(pi)=0 so 1/tan=1/0
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# initial value for position and angular speed
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y0 = [1/D, 1/(D*math.tan(math.radians(alpha)))]
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sol = solve_ivp(fun=_diff_eq, t_span=[0, 10*pi], y0=y0, method='DOP853', events=[_eventRs]) #, self._eventR])#,t_eval=np.linspace(0, t_max, 10000)) #dense_output=False
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if sol.t[-1] == 10*pi:
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raise StopIteration("solver error, alpha reached computation limit (loop number)")
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phi = np.array(sol.t)
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r = np.abs(1/sol.y[0, :]) # must use this because solver can't be stop before infinity because negative
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#print("alpha:", alpha)
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#print(phi, r)
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print("I AM DOING SOMETHING!!", alpha)
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return r, phi
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def _diff_eq(phi, u):
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"""Represent the differential equation : d²u(ɸ)/dɸ²=3/2*Rs*u²(ɸ)-u(ɸ)
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"""
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v0 = u[1] #correspond to u'
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v1 = 3/2*Rs*u[0]**2 - u[0] #correspond to u"
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return v0, v1
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def _eventRs(phi, u):
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"""stop solver if radius < black hole radius"""
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with np.errstate(all='ignore'):
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return 1/u[0] - Rs
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_eventRs.terminal = True
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def apperentSize(a1, a2):
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if a2-a1 <= maxDeviation:
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print(a2)
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return a2
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points = np.linspace(a1, a2, 3)
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point = solver(points[1])
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test = point[0][len(point[0]) - 1 ]
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if test > Rs:
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print("1")
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return apperentSize(a1, points[1])
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elif test <= Rs:
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print("2")
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return apperentSize(points[1], a2)
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else:
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print("Fehler")
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def getAllAngles():
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maxA = 0# 180 - math.degrees( math.acos(math.cos(math.radians(fovX)) * math.cos(math.radians(fovY)))) #math.sqrt(((fovX/2)**2) + ((fovY/2)**2))
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print("MAX_____________________", maxA)
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maxA = fovX
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#maxA = 90
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minA = apperentSize(0, 180)
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print(minA)
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# minA = 24.2086
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linspace = np.linspace(0, 1, accuracy)
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angles = minA + (maxA - minA) * linspace**6 #beser als **6 finden !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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#angles = np.geomspace(minA, maxA, accuracy)
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array = []
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for i in range(accuracy):
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sol = solver(angles[i])
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deviatedAngle = sol[1][len(sol[1]) - 1]
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array.append([angles[i], np.degrees(deviatedAngle)])
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#print(array)
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#interpolierung der punkte
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points = np.array(array)
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f = interp1d(points[:, 0], points[:, 1], kind='cubic')
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#x_new = np.linspace(points[:, 0].min(), points[:, 0].max(), 5000)
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#y_new = f(x_new)
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#
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#plt.figure()
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#plt.scatter(points[:, 0], points[:, 1])
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#plt.plot(x_new, y_new, '-', label='Kubische Interpolation', color= 'orange')
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#plt.xlabel("Seen angle")
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#plt.ylabel("deviated angle")
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#plt.title("Punkte aus array")
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#plt.grid(True)
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#plt.show()
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#berechnung der einzelnen Pixel
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resX = res
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resY = int(res * fovY / fovX)
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deviationOfPixels = []
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conversion = maxA / math.degrees( math.acos(math.cos(math.radians(resX) / 2) * math.cos(math.radians(resY) / 2))) #####################################################################
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for x in range(int(resX / 2)):
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deviationOfPixels.append([])
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for y in range(int(resY / 2)):
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deviationOfPixels[x].append([])
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d = math.degrees( math.acos(math.cos(math.radians(x/int(resX / 2) * fovX / 2)) * math.cos(math.radians(y/int(resY / 2) * fovY / 2))))#% maxA #* conversion
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if d >= minA:
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beta = math.atan2(y, x)
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deviation = f(d) % 360 #unnötige umdrehungen durch subtrahieren von auf 360 gerundeten Wert ignorieren
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alpha = x/int(resX / 2) * fovX / 2
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beta = y/int(resY / 2) * fovY / 2
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phi = math.degrees(math.atan2(math.sin(math.radians(deviation)) * (math.cos(math.radians(beta)) * math.sin(math.radians(alpha))) / math.sqrt((math.cos(math.radians(beta)) * math.sin(math.radians(alpha)))**2 + math.sin(math.radians(beta))**2), math.cos(math.radians(deviation))))
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theta = 2 * math.degrees(math.asin(math.sin(math.radians(deviation)) * math.sin(math.radians(beta)) / math.sqrt((math.cos(math.radians(beta)) * math.sin(math.radians(alpha)))**2 + math.sin(math.radians(beta))**2)))
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deviationX = theta
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deviationY = phi
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deviationOfPixels[x][y] = ([deviationX, deviationY])
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else:
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deviationOfPixels[x][y] = None
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print("ARRAY")
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doc = open("del3.txt", "w")
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for i in range(len(deviationOfPixels)):
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doc.write(str(deviationOfPixels[i]))
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doc.write('\n')
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doc.close()
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return deviationOfPixels
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def fullArray(array):
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arr = array
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arr.reverse()
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arr2 = copy.deepcopy(arr)
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result =[]
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result2 = []
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for i in range(len(arr2)):
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arr2[i].reverse()
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for j in range(len(arr2[i])):
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if arr2[i][j] != None:
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zahl1, zahl2 = arr2[i][j]
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arr2[i][j] = [-zahl1, zahl2]
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result.append((arr2[i]) + arr[i])
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res = copy.deepcopy(result)
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for i in range(len(res)):
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for j in range(len(res[i])):
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if res[i][j] != None:
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zahl1, zahl2 = res[i][j]
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res[i][j] = [zahl1, -zahl2]
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res.reverse()
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result2.append(result + res)
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#result2.append(result)
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return result2[0]
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def allPixel(deviations):
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Img = []
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bgY, bgX = bg.size
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conversionX = bgX / 360
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print("len", len(deviations))
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print("con", conversionX)
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conversionY = bgY / 360
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print("len", len(deviations[0]))
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print("con", conversionY)
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test = .5
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print(" max X:", )
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for x in range(len(deviations)):
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Img.append([])
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for y in range(len(deviations[x])):
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Img[x].append([])
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if deviations[x][y] == None:
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pixel = (0, 0, 0)
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else:
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px = int(deviations[x][y][0] % 360 * conversionX - (bgX / 2)) - 1
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py = int(deviations[x][y][1] % 360 * conversionY) - 1
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pixel = bg.getpixel((py ,px))
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Img[x][y] = pixel
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#print(Img)
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return Img
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def showImage(arrayx):
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# Beispiel: array ist dein Pixel-Array
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# Achtung: Pillow erwartet (height, width), also [y][x]
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height = len(arrayx[0])
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width = len(arrayx)
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# In ein flaches Array umwandeln
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pixels = []
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for y in range(height):
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for x in range(width):
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pixels.append(arrayx[x][y])
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# Bild erzeugen
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img = Image.new("RGB", (width, height))
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img.putdata(pixels)
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img.show()
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deviationOfPixels = getAllAngles()
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array = fullArray(deviationOfPixels)
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showImage(allPixel(array))
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