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| -rw-r--r-- | langfassung/docs/3_hauptteil.aux | 67 | ||||
| -rw-r--r-- | langfassung/docs/4_ergebnisse.aux | 31 | ||||
| -rw-r--r-- | langfassung/docs/5_quellen.aux | 32 | ||||
| -rwxr-xr-x | langfassung/docs/6_abgabe.tex | 534 |
5 files changed, 533 insertions, 161 deletions
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-\setcounter{ContinuedFloat}{0} -\setcounter{lstnumber}{15} -\setcounter{section@level}{4} -\setcounter{lstlisting}{0} -} diff --git a/langfassung/docs/6_abgabe.tex b/langfassung/docs/6_abgabe.tex index 22fe221..f8112d9 100755 --- a/langfassung/docs/6_abgabe.tex +++ b/langfassung/docs/6_abgabe.tex @@ -59,7 +59,7 @@ % \end{pmatrix} % \end{equation} -\subsection{Spiralgalaxien} +\subsection{Spiralgalaxies} \subsection{Using Object Oriented Programming (OOP) techniques} @@ -271,3 +271,535 @@ Not to be considered: \item any kind of resistance \item acceleration \end{itemize} + +\subsection{Notes} + +\begin{itemize} + \item Don't search for spheres very far away! +\end{itemize} + +\begin{equation} + % \sum_{lower}^{upper} + \sum_{lower}^{upper} - \sum_{lower}^{upper} + \sum A_{fi} + \sum B_{fi} - \sum AB_{fij} +\end{equation} + +\begin{itemize} + \item USE dictionaries to store which stars are in wich spheres +\end{itemize} + +\subsection{exec.py} + +The exec.py file is used to execute the galaxytools defined in galaxytools.py. + +\subsubsection{Importing the galaxytools} + +\begin{lstlisting} + import galaxytools as galaxytools +\end{lstlisting} + +The complete prgramm is compressed into one object. This Object has to be +imported in order to be used. + +\subsubsection{Generate a new galaxy} + +\begin{lstlisting} + galaxy = galaxytools.new_galaxy(100) +\end{lstlisting} + +Using the previously imported library, one can start building a galaxy by +calling the function new\_galaxy(...). The parameter inside the braces defines +the size of the galaxy. + +\subsubsection{Generate new stars in the galaxy} + +\begin{lstlisting} + galaxy.gen_new_stars(100) +\end{lstlisting} + +The function new\_stars(...) is used to generate in given amount of new stars. + +\subsubsection{Print the coordinates of every star in the galaxy relative to +the origin} + +\begin{lstlisting} + galaxy.print_stars() +\end{lstlisting} + +Printing the coordinates of every star in the galaxy is useful for debugging: +It is clearly visible if something is going wrong on the first look. The +range of the galaxy might be wrong or the whole galaxy might be completely +wrong scaled. + +\subsubsection{Calculate the forces acting inbetween all the stars in the +galaxy} + +\begin{lstlisting} + galaxy.calc_all_forces() +\end{lstlisting} + +the function calc\_all\_forces() if used to calculate all the forces acting +in the selected galaxy. The O notation for this can be calculated using the +following equation: \( O(n) = n^2 \). + +\subsubsection{Print the individual forces acting on the stars} + +\begin{lstlisting} + galaxy.print_individual_forces() +\end{lstlisting} + +The individual forces (x, y, z) acting on the star can be printed out too! +Just use the function print\_individual\_forces() and you will recieve the +individual forces nicley formatted. + +\subsubsection{Generate the coordinates of the positions for the spheres} + +\begin{lstlisting} + galaxy.gen_sphere_positions(2) +\end{lstlisting} + +To generate the sphere positions subdividing the galaxy, the +gen\_sphere\_positions(...) function is utilized. The Parameter defines how +many spheres are generated on one axis of the galaxy, so a higher value equals +more spheres and so a longer time to compute. An infinite high value can be used +if the value between each star should be calculated (use at own risk!). + +\subsubsection{Calculate the forces after 1 time step} + +\begin{lstlisting} + galaxy.gen_forces_after_t(1) +\end{lstlisting} + +Calculating the new position after one timestep makes it possible to animate +the galaxy and so visualizing it in an exciting way making people think you've +done something awesome! This can be acchieved by using the +gen\_forces\_after\_t(...) function. It uses a timestep as an argument and +uses it to calculate the new coordinates of the star. + +\subsection{galaxytools.py} + +Inside this file, pretty much everything for building a galaxy is defined. + +\subsubsection{Importing important libraries} + +\begin{lstlisting} +# Import libraries +import math as math # general math +import numpy as np # advanced math +# import matplotlib.pyplot as plt # plotting things +\end{lstlisting} + +This part of the code is used to import libraries which are then used to do +e.g. advanced math. + +\subsubsection{Generating the new\_galaxy class} + +\begin{lstlisting} +# class used to create galaxies +class new_galaxy(object): +\end{lstlisting} + +The class definition defines the galaxytools classname as new\_galaxy + +\subsubsection{Initialisation} + +\begin{lstlisting} + + # Initialisation + def __init__(self, galaxy_range): + print( + """>>> Initialising the list storing coordinates, forces and other + values""" + ) + + # list used for storing the coordinates os the stars + self.list_coords = [] + + # list storing the overall force acting on one star + self.list_force_star = [] + + # list storing the coordinates of the midpoints of the spheres dividing + # the galaxy into equaly big sized cells + self.list_sphere_coords = [] + + # self.list_sphere_stars = np.array(3, ) + + print("\tDone\n") + print(">>> Initialising variables and constants") + + # variable storing the number of stars generated + self.num_of_stars = 0 + + self.galaxy_range = int(galaxy_range) + + # define the universal gravitational constant + self.G = 6.67408 * 10e11 + + print("\tDone\n") + +\end{lstlisting} + +\subsubsection{Generating new stars} + +\begin{lstlisting} + + # generate n new stars and store the coordinates in list_coords + # n = number of stars to be generated + # galaxy_range = size of the galaxy + def gen_new_stars(self, n): + print(">>> Generating Stars...") + + # for a given number of stars + for i in range(0, n): + + # generate a temporary random coordinate inside a given range using + # numpy + self.temp_coord = np.random.uniform( + low=0, high=self.galaxy_range, size=(4, )) + + # append the random coordinate to the list storing the coordinates + self.list_coords.append(self.temp_coord) + + # increment the generated star counter + self.num_of_stars += n + print("\tDone") + print("\tGenerated " + str(n) + " Stars\n") + +\end{lstlisting} + +\subsubsection{Print out all the star coordinates} + +\begin{lstlisting} + + # print out all the coordinates in list_coords + def print_stars(self): + print(">>> Listing the coordinates of all stars:") + # print the coordinates of every star + for value in self.list_coords: + print(value) + + print("\tDone\n") + +\end{lstlisting} + +\subsubsection{Calculate the forces acting inbetween two stars} + +\begin{lstlisting} + + # calculate the forces acting between two stars on a specified axis + # star1 = coordinates of the first star + # star2 = coordinates of the second star + # axes = "x", "y" or "z" (CASE SENSITIVE!) + def calc_forces(self, star1, star2, axes): + if axes == "x": + mass = star1[3] * star2[3] + distance = math.sqrt(math.pow(star1[0] - star2[0], 2)) + elif axes == "y": + mass = star1[3] * star2[3] + distance = math.sqrt(math.pow(star1[1] - star2[1], 2)) + elif axes == "z": + mass = star1[3] * star2[3] + distance = math.sqrt(math.pow(star1[2] - star2[2], 2)) + + # stop division by zero + if distance == 0: + pass + else: + # return the acting force + return self.G * mass / math.pow(distance, 2) + +\end{lstlisting} + +\subsubsection{Calculate all the forces acting in the galaxy} + +\begin{lstlisting} + + # calculate all the forces acting in the current galaxy + def calc_all_forces(self): + print(">>> Calculating all the forces acting inbetween the stars:") + + if (self.num_of_stars <= 5): + # print some information above the columns + print(">>> Printing the forces acting inbetween every star") + print("{:-<60}".format("")) + print("\t| {:<3}| {:<3}| ".format("a", "b")) + print("\t+{:-<4}+{:-<4}+{:-<60} ".format("", "", "")) + + else: + print("\t[W] Too many stars to print out!") + print("{:-<60}".format("")) + + # for every star + for i in range(0, self.num_of_stars): + + # initialize + self.force = 0 + + # every other star: + for j in range(0, self.num_of_stars): + + # don't calculate the force between a star and and itself + if i != j and i < j: + self.arr_force = np.array((0, 0, 0)) + + # calculate the force between the two stars + force_x = self.calc_forces(self.list_coords[i], + self.list_coords[j], "x") + force_y = self.calc_forces(self.list_coords[i], + self.list_coords[j], "y") + force_z = self.calc_forces(self.list_coords[i], + self.list_coords[j], "z") + + # print("overall force: ", end="") + self.arr_force = np.array((force_x, force_y, force_z)) + + if (self.num_of_stars <= 5): + print("\t| {:<3}| {:<3}| {:<60}".format( + str(i), str(j), str(self.arr_force))) + """ + force_x = 42 + force_y = 36 + force_z = 24 + + (0, 0, 0) --> (42, 36, 24) + """ + + # append the variable to the list storing all the forces + self.list_force_star.append(self.arr_force) + + print("{:-<60}".format("")) + print("\tDone\n") + +\end{lstlisting} + +\subsubsection{Print the individual forces acting on one star} + +\begin{lstlisting} + + # print the individual forces acting on a star + def print_individual_forces(self, n=None, print_confirm=False): + print(">>> Printing the individual forces acting on every star") + + if self.num_of_stars > 10: + print("\t[W] Too many stars to print out!") + print("{:-<60}".format("")) + + for i in range(0, 3): + print("\t" + str(i) + " " + str(self.list_force_star[i])) + + print("\n\t...\n") + + for i in range( + int(len(self.list_force_star) - 3), + len(self.list_force_star)): + print("\t" + str(i) + " " + str(self.list_force_star[i])) + print("{:-<60}".format("")) + + else: + print("{:-<60}".format("")) + if n is None: + # for value in self.list_force_star: + for i in range(0, len(self.list_force_star)): + print("\t" + str(i) + " " + str(self.list_force_star[i])) + else: + print(self.list_force_star[n]) + + print("{:-<60}".format("")) + print("\tDone\n") + +\end{lstlisting} + +\subsubsection{Find out if a star is inside one sphere} + +\begin{lstlisting} + + # star [x, y, z, mass] + # sphere [x, y, z, radius] + def is_star_in_sphere(self, star, sphere): + + # define the sphere values + self.sphere_x = sphere[0] + self.sphere_y = sphere[1] + self.sphere_z = sphere[2] + self.sphere_r = sphere[3] + + # define the star coordinates + self.star_x = star[0] + self.star_y = star[1] + self.star_z = star[2] + + # find out the distance between the point and the center of the sphere + # if the distance is bigger than the radius of the sphere, the point is + # not inside the sphere. Elsewise, the point is inside the sphere + + x = math.pow(self.sphere_x - self.star_x, 2) + y = math.pow(self.sphere_y - self.star_y, 2) + z = math.pow(self.sphere_z - self.star_z, 2) + r = math.sqrt(x + y + z) + + if r > self.sphere_r: + return False + else: + return True + + # self.sphere_x_neg = self.sphere_x - self.sphere_r + # self.sphere_x_pos = self.sphere_x + self.sphere_r + # + # self.sphere_y_neg = self.sphere_y - self.sphere_r + # self.sphere_y_pos = self.sphere_y + self.sphere_r + # + # self.sphere_z_neg = self.sphere_z - self.sphere_r + # self.sphere_z_pos = self.sphere_z + self.sphere_r + # + # # find out if the star is inside the sphere + # if self.sphere_x_neg < self.star_x < self.sphere_x_pos: + # if self.sphere_y_neg < self.star_y < self.sphere_y_pos: + # if self.sphere_z_neg < self.star_z < self.sphere_z_pos: + # return True + # else: + # return False + # else: + # return False + # else: + # return False + +\end{lstlisting} + +\subsubsection{Find out which star in in which spheres} + +\begin{lstlisting} + + # find out which stars in in which spheres + def is_star_in_sphere_all(self): + + # print(self.sphrer_rs) + + print(">>> is_star_in_sphere_all") + + # initialize a temporary counter in order to index the spheres + tmp_counter = 0 + + # cycle through all the stars + for sphere in self.sphere_coords: + # print("sphere: " + str(sphere)) + + tmp_list = [] + for star in self.list_coords: + # parse the needed values from the sphere list + + # if the star is inside the sphere + if (self.is_star_in_sphere(star, sphere) is True): + # print("\nstar: " + str(star)) + + star_x = [] + + for value in star: + # print(value, end=" ") + # print("") + star_x.append(value) + + # print("star_x :" + str(star_x)) + + tmp_list.append(star_x) + + # print("") + # print("tmp_list: " + str(tmp_list)) + # print("END") + + self.sphere_coords[sphere] = tmp_list + + print("") + # print(self.sphere_coords) + + # cycle through the dictionary storing which star is in which cell + for value in self.sphere_coords: + stars_in_sphere = self.sphere_coords[value] + + # calculate the individual forces in the sphere + self.calc_forces_sphere(stars_in_sphere) + + # for value in stars_in_sphere: + # print(value) + +\end{lstlisting} + +\subsubsection{Generate the sphere positions} + +\begin{lstlisting} + + # function generating the positions of the sphere cells + def gen_sphere_positions(self, sampling_rate): + + print(">>> Generating the sphere positions") + + # initialize a dictionary linking the sphere coordinates to the + # coordiantes of the stars in the sphere + self.sphere_coords = {} + + # calculate the distance between the midpoints of the spheres + sphere_distance = int(round(self.galaxy_range / sampling_rate, 0)) + + # define the sphere_radius + tmp_var = math.pow(sphere_distance, 2) + sphere_radius = math.sqrt(tmp_var + tmp_var + tmp_var) + + # define a sphere counter for "labeling" the spheres + tmp_counter = 0 + + # cycle through all potential points + for i in range(-self.galaxy_range, self.galaxy_range, sphere_distance): + for j in range(-self.galaxy_range, self.galaxy_range, + sphere_distance): + for k in range(-self.galaxy_range, self.galaxy_range, + sphere_distance): + + # generate a temporary array combining all values + # temp_arr = np.array((i, j, k, sphere_radius, tmp_counter)) + tmp_arr = (i, j, k, sphere_radius, tmp_counter) + + # append the array to the list storing the sphere infos + # self.list_sphere_coords.append(temp_arr) + + # print("temp_arr: " + str(temp_arr)) + self.sphere_coords[tmp_arr[0:4]] = [] + + # increment the sphere counter + tmp_counter += 1 + + # print(self.sphere_coords) + print("\tDone\n") + +\end{lstlisting} + +\subsubsection{Calculate the forces acting inside the sphere} + +\begin{lstlisting} + + def calc_forces_sphere(self, stars_in_sphere): + print("stars_in_sphere: ", end="") + print(stars_in_sphere) + # for value in stars_in_sphere: + # self.calc_all_forces(stars_in_sphere) + # print(value) + +\end{lstlisting} + +\subsubsection{calculate the forces acting in every sphere} + +\begin{lstlisting} + + def calc_forces_sphere_all(): + # for i in range(0, len(num_of_spheres)): + # for star in sphere[i]: + # for star_2 in len(0, num_of_stars_in_sphere[i]) + # a = calc_force(star, star[j]) + + pass + + def gen_print_forces_after_t(t): + pass + + # def all_stars_in_sphere(self, star, se) + +\end{lstlisting} + +\subsection{GAN} |
