From c913bd19ad172a5c76b68ba0713baae48cd0b6b2 Mon Sep 17 00:00:00 2001 From: Peter Istvan <istipisti00@gmail.com> Date: Fri, 26 Jun 2020 21:47:57 +0300 Subject: [PATCH] =?UTF-8?q?V=C3=A9gleges?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/__pycache__/fizika.cpython-36.pyc | Bin 893 -> 1789 bytes src/__pycache__/hiperbola.cpython-36.pyc | Bin 0 -> 1832 bytes src/__pycache__/kirajzol.cpython-36.pyc | Bin 738 -> 0 bytes src/__pycache__/rajz.cpython-36.pyc | Bin 0 -> 1768 bytes src/fizika.py | 57 +- src/hiperbola.py | 31 + src/kirajzol.py | 23 - src/plot.svg | 4193 ++++++++++++---------- src/rajz.py | 36 + src/teszt.py | 139 +- 10 files changed, 2387 insertions(+), 2092 deletions(-) create mode 100644 src/__pycache__/hiperbola.cpython-36.pyc delete mode 100644 src/__pycache__/kirajzol.cpython-36.pyc create mode 100644 src/__pycache__/rajz.cpython-36.pyc create mode 100644 src/hiperbola.py delete mode 100644 src/kirajzol.py create mode 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rHely): rVektor = [rHely[0] - rToltes[0], rHely[1] - rToltes[1]] rHossz = (rVektor[0] ** 2 + rVektor[1] ** 2) ** 0.5 return [K * qToltes * rVektor[0] / rHossz ** 3, K * qToltes * rVektor[1] / rHossz ** 3] -# A (0, 0) és (0, 1) végpontú adott töltéssűrűségű pálca által generált térerősség rHely helyzetvektorú pontban -# A felbontás(>=1) megadja, hogy a pálcát hány pontszerű darabra bontja fel a numerikus közelítés +# A (PALCA_X, PALCA_YMIN) és (PALCA_X, PALCA_YMAX) végpontú adott töltéssűrűségű pálca elektromos tere rHely-en +# A felbontás megadja, hogy a pálcát hány pontszerű darabra bontja fel a numerikus integrálás def tererosseg2D(rHely, toltessuruseg, felbontas): E = [0, 0] if rHely[0] == PALCA_X and PALCA_YMAX >= rHely[1] >= PALCA_YMIN: @@ -21,6 +34,38 @@ def tererosseg2D(rHely, toltessuruseg, felbontas): else: for k in range(0, felbontas): palca_hossz = PALCA_YMAX - PALCA_YMIN - dE = tererosseg2Dtoltes([0, k * palca_hossz / felbontas], toltessuruseg * palca_hossz / felbontas, rHely) + dE = tererosseg2Dtoltes([PALCA_X, PALCA_YMIN + k * palca_hossz / felbontas], toltessuruseg * palca_hossz / felbontas, rHely) E[0], E[1] = E[0] + dE[0], E[1] + dE[1] return E + + +# Az rHely-en a pálca által generált térerősség irányvektora (normált vektora) +# A t független valós paraméter, a mező statikussága miatt nem játszik szerepet +# Az f(t, vektor) alakot a SciPy csomag követeli meg az iránymező kezdőfeltételes integrálásakor +def irany(t, rHely): + vek = tererosseg2D(rHely, LMBD, PALCA_FELBONTAS) + if vek == [0, 0]: + return [0, 0] + else: + hossz = (vek[0]**2 + vek[1]**2)**0.5 + return [vek[0]/hossz, vek[1]/hossz] + + +# Visszatéríti az irany(t, rHely) által megadott iránymező megfelelő erővonalát mint pontok irányított sorozatát +# Az adott kezdőpontot mint kezdőfeltételt a scipy.integrate.ode.integrate() függvény veszi át +def erovonal(kezdopont, dt): + # Ha negatív a töltéssűrűség, az integrálás iránya "időben visszafele" lesz + if LMBD < 0: + dt = -dt + ev = [kezdopont] + megoldo = ode(irany) + megoldo.set_integrator('vode') + megoldo.set_initial_value(kezdopont, 0) + while megoldo.successful(): + megoldo.integrate(megoldo.t + dt) + ev.append([megoldo.y[0], megoldo.y[1]]) + if megoldo.y[0] > XMAX or megoldo.y[0] < XMIN or megoldo.y[1] > YMAX or megoldo.y[1] < YMIN: + break + if LMBD < 0: + ev.reverse() + return ev diff --git a/src/hiperbola.py b/src/hiperbola.py new file mode 100644 index 0000000..2d3d177 --- /dev/null +++ b/src/hiperbola.py @@ -0,0 +1,31 @@ +import src.fizika as fiz +import numpy as np + + +def fokuszpont_tavolsagkulonbseg(x, y, f1x, f1y, f2x, f2y): + d1 = ((x - f1x)**2 + (y - f1y)**2)**0.5 + d2 = ((x - f2x)**2 + (y - f2y)**2)**0.5 + return abs(d1 - d2) + + +def hiperbola(): + print("Erővonal vizsgálata...") + print("----------------------") + KP_X = fiz.PALCA_X + 0.01 + KP_Y = (fiz.PALCA_YMAX * 3 + fiz.PALCA_YMIN)/4 + KP = [KP_X, KP_Y] + print("A vizsgált erővonal kezdőpontja: " + str(KP)) + ev = fiz.erovonal(KP, 0.0005) + F1 = [fiz.PALCA_X, fiz.PALCA_YMIN] + F2 = [fiz.PALCA_X, fiz.PALCA_YMAX] + print("A feltételezett fókuszpontok: " + str(F1) + " és " + str(F2)) + diffs = [fokuszpont_tavolsagkulonbseg(P[0], P[1], F1[0], F1[1], F2[0], F2[1]) for P in ev] + atlag = np.mean(diffs) + print("Az erővonal pontjaiban a fókuszpontoktól való távolságkülönbség átlaga: " + str(atlag) + " m") + ivhossz = 0 + for i in range(0, len(ev)-1): + ivhossz += ((ev[i][0] - ev[i+1][0])**2 + (ev[i][1] - ev[i+1][1])**2)**0.5 + max_elt = max(abs(val - atlag) for val in diffs) + print("Az átlagtól való maximális eltérés: " + str(max_elt) + " egy " + str(ivhossz) + " m hosszú görbe szakaszon") + if max_elt < 0.0001: + print("Az erővonal hiperbola") diff --git a/src/kirajzol.py b/src/kirajzol.py deleted file mode 100644 index f4c8247..0000000 --- a/src/kirajzol.py +++ /dev/null @@ -1,23 +0,0 @@ -import scipy.integrate as integrate -import matplotlib.pyplot as plt -import numpy as np - -pi = np.pi -sqrt = np.sqrt -cos = np.cos -sin 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style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/> @@ -2366,7 +2685,7 @@ L 414.72 41.472 </g> </g> <defs> - <clipPath id="p41e5f7c203"> + <clipPath id="p43906bf0a4"> <rect height="266.112" width="357.12" x="57.6" y="41.472"/> </clipPath> </defs> diff --git a/src/rajz.py b/src/rajz.py new file mode 100644 index 0000000..c807c0b --- /dev/null +++ b/src/rajz.py @@ -0,0 +1,36 @@ +import matplotlib.pyplot as plt +import src.fizika as fiz +from src.fizika import PALCA_X, PALCA_YMIN, PALCA_YMAX + +VONALSURUSEG = 10 +PALCA_VASTAGSAG = 0.02 + + +def erovonal_rajzol(kezdopont, dt): + ev = fiz.erovonal(kezdopont, dt) + ev_x = [ev[i][0] for i in range(0, len(ev))] + ev_y = [ev[i][1] for i in range(0, len(ev))] + plt.plot(ev_x, ev_y, color='blue', linewidth=0.001) + hossz = len(ev) + idx = int((hossz - 1)/2) + kov = idx + 1 + plt.arrow(ev_x[idx], ev_y[idx], (ev_x[kov] - ev_x[idx])/2, (ev_y[kov] - ev_y[idx])/2, color='blue', width=0.01, head_width=0.03) + + +def palca_rajzol(): + plt.plot([PALCA_X, PALCA_X], [fiz.PALCA_YMIN, PALCA_YMAX], color='red', linewidth=2) + + +def rajzol(): + dx = PALCA_VASTAGSAG/2 + dt = fiz.T_LEPES + palca_rajzol() + lepeskoz = (PALCA_YMAX - PALCA_YMIN)/VONALSURUSEG + kezdopontok = [[PALCA_X, PALCA_YMIN - dx], [PALCA_X, PALCA_YMAX + dx]] + for k in range(0, VONALSURUSEG): + kezdopontok.append([PALCA_X + dx, PALCA_YMIN + (2*k + 1)/2*lepeskoz]) + kezdopontok.append([PALCA_X - dx, PALCA_YMIN + (2*k + 1)/2*lepeskoz]) + for kp in kezdopontok: + erovonal_rajzol(kp, dt) + plt.savefig("plot.svg") + print("Kirajzolás kész") diff --git a/src/teszt.py b/src/teszt.py index 35043ae..fa23d7e 100644 --- a/src/teszt.py +++ b/src/teszt.py @@ -1,126 +1,13 @@ -import matplotlib -import matplotlib.pyplot as plt -import src.fizika as fiz -from src.fizika import tererosseg2D -from scipy.integrate import ode as ode - -toltessuruseg = 1 -felbontas = 1000 -vonalsuruseg = 10 - -XMIN = fiz.PALCA_X - 0.5 -XMAX = fiz.PALCA_X + 0.5 -YMIN = fiz.PALCA_YMIN - 0.5 -YMAX = fiz.PALCA_YMAX + 0.5 - - -def irany(t, rHely): - vek = tererosseg2D(rHely, toltessuruseg, felbontas) - if vek == [0, 0]: - return [0, 0] - else: - hossz = (vek[0]**2 + vek[1]**2)**0.5 - return [vek[0]/hossz, vek[1]/hossz] - - -def iranymezo(): - XDENSITY = 20 - YDENSITY = 20 - - XRANGE = (XMAX - XMIN)/XDENSITY - YRANGE = (YMAX - YMIN)/YDENSITY - - for i in range(0, XDENSITY): - for j in range(0, YDENSITY): - xcoord = XMIN + XRANGE * i - ycoord = YMIN + YRANGE * j - if xcoord != fiz.PALCA_X or (xcoord == fiz.PALCA_X and fiz.PALCA_YMAX < ycoord or ycoord < fiz.PALCA_YMIN): - # print(str([xcoord, ycoord])) - plt.quiver(xcoord, ycoord, irany(0, [xcoord, ycoord])[0], irany(0, [xcoord, ycoord])[1], width=0.01) - - -def erovonal(kezdopont, dt): - if toltessuruseg < 0: - dt = -dt - ev = [kezdopont] - r = ode(irany) - r.set_integrator('vode') - r.set_initial_value(kezdopont, 0) - while r.successful(): - r.integrate(r.t + dt) - ev.append([r.y[0], r.y[1]]) - if r.y[0] > XMAX or r.y[0] < XMIN or r.y[1] > YMAX or r.y[1] < YMIN: - break - return ev - - -def erovonal_rajzolas(kezdopont, dt): - ev = erovonal(kezdopont, dt) - ev_x = [ev[i][0] for i in range(0, len(ev))] - ev_y = [ev[i][1] for i in range(0, len(ev))] - plt.plot(ev_x, ev_y, color='black') - hossz = len(ev) - idx = int((hossz - 1)/2) - if toltessuruseg < 0: - kov = idx - 1 - else: - kov = idx + 1 - plt.arrow(ev_x[idx], ev_y[idx], (ev_x[kov] - ev_x[idx])/2, (ev_y[kov] - ev_y[idx])/2, color='black', head_width=0.02)#, head_length=0.02) - - -def tererovonalak(): - dx = 0.01 - dt = 0.008 - # pálca belsejéből induló erővonalak - for k in range(1, vonalsuruseg): - # jobbra induló erővonal - erovonal_rajzolas([0.0 + dx, k/vonalsuruseg], dt) - # balra induló erővonal - erovonal_rajzolas([0.0 - dx, k/vonalsuruseg], dt) - - print("Palca megvan") - - # pálca [0, 1] végéből induló erővonalak - erovonal_rajzolas([fiz.PALCA_X + dx, fiz.PALCA_YMAX], dt) - erovonal_rajzolas([fiz.PALCA_X - dx, fiz.PALCA_YMAX], dt) - erovonal_rajzolas([fiz.PALCA_X, fiz.PALCA_YMAX + dx], dt) - - print("[0, 1] megvan") - - # pálca [0, 0] végéből induló erővonalak - erovonal_rajzolas([fiz.PALCA_X + dx, fiz.PALCA_YMIN], dt) - erovonal_rajzolas([fiz.PALCA_X - dx, fiz.PALCA_YMIN], dt) - erovonal_rajzolas([fiz.PALCA_X, fiz.PALCA_YMIN - dx], dt) - - print("[0, 1] megvan") - - -def fokuszpont_tavolsagosszeg(x, y, f1x, f1y, f2x, f2y): - d1 = ((x - f1x)**2 + (y - f1y)**2)**0.5 - d2 = ((x - f2x)**2 + (y - f2y)**2)**0.5 - return abs(d1 - d2) - - -def hiperbola(): - ivhossz = 0.0 - P_X = fiz.PALCA_X + 0.01 - P_Y = (fiz.PALCA_YMAX * 3 + fiz.PALCA_YMIN)/4 - ev = erovonal([P_X, P_Y], 0.0005) - for p in ev: - print(str(fokuszpont_tavolsagosszeg(p[0], p[1], fiz.PALCA_X, fiz.PALCA_YMIN, fiz.PALCA_X, fiz.PALCA_YMAX))) - - for i in range(0, len(ev)-1): - ivhossz += ((ev[i][0] - ev[i+1][0])**2 + (ev[i][1] - ev[i+1][1])**2)**0.5 - - print("Ivhossz = " + str(ivhossz)) - - -# iranymezo() - -toltessuruseg = float(input("lambda = ")) -tererovonalak() - -plt.savefig("plot.svg") - -hiperbola() -print("Hiperbola megvan") +from src.fizika import PALCA_X, PALCA_YMIN, PALCA_YMAX, XMIN, XMAX, YMIN, YMAX, LMBD +import src.rajz as rjz +import src.hiperbola as hip + +print("Szigetelő pálca erővonalainak kirajzolása...") +print("--------------------------------------------") +print("Pálca végpontjainak koordinátái: " + str([PALCA_X, PALCA_YMIN]) + " " + str([PALCA_X, PALCA_YMAX])) +print("Pálca töltéssűrűsége: " + str(LMBD) + " C/m") +print("Vizsgált terület határai: ") +print("\tx: " + str(XMIN) + "..." + str(XMAX) + " y: " + str(YMIN) + "..." + str(YMAX)) + +rjz.rajzol() +hip.hiperbola() -- GitLab