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 100644 src/rajz.py

diff --git a/src/__pycache__/fizika.cpython-36.pyc b/src/__pycache__/fizika.cpython-36.pyc
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diff --git a/src/fizika.py b/src/fizika.py
index c4f055c..901ccc3 100644
--- a/src/fizika.py
+++ b/src/fizika.py
@@ -1,19 +1,32 @@
+from scipy.integrate import ode as ode
+
 # Coulomb-állandó
 K = 8.98e9
-
+# Pálca paraméterei
 PALCA_X = 0.0
-PALCA_YMIN = 0.0
-PALCA_YMAX = 1.0
+PALCA_YMIN = -0.5
+PALCA_YMAX = 0.5
+LMBD = 1
+PALCA_FELBONTAS = 10000
+# Az iránymező integrálásának "idő-lépésköze"
+# Az erővonalon a referenciapontok sűrűségét befolyásolja
+T_LEPES = 0.005
+# A vizsgált sík határai
+XMIN = PALCA_X - 0.5
+XMAX = PALCA_X + 0.5
+YMIN = PALCA_YMIN - 0.5
+YMAX = PALCA_YMAX + 0.5
 
 
+# rToltés helyen található ponttöltés elektromos tere rHely-en
 def tererosseg2Dtoltes(rToltes, qToltes, 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 = np.sin
-
-def deriv_z(z, phi):
-    u, udot = z
-    return [udot, -u + sqrt(u)]
-
-phi = np.linspace(0, 7.0*pi, 2000)
-zinit = [1.49907, 0]
-z = integrate.odeint(deriv_z, zinit, phi)
-u, udot = z.T
-# plt.plot(phi, u)
-fig, ax = plt.subplots()
-ax.plot(1/u*cos(phi), 1/u*sin(phi))
-ax.set_aspect('equal')
-plt.grid(True)
-plt.show()
\ No newline at end of file
diff --git a/src/plot.svg b/src/plot.svg
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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()
-- 
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