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sum_diff_phase.py
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sum_diff_phase.py
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from manimlib.imports import *
class PhaseChange(Scene):
def construct(self):
self.draw_axis()
self.draw_grid()
self.draw_wave()
self.wait()
def get_axis(self, max_y=1):
g = VGroup()
min_x = -6
max_x = 6
def xy(x, y):
return np.array([x, y, 0])
def tex(str, color=WHITE):
return TexMobject(str,color=color).scale(0.6)
def get_line(s,e):
return Line(s,e , color=BLUE, stroke_width=5)
x_axis = get_line(xy(min_x,0), xy(max_x,0))
g.add(x_axis)
x_labels = [tex("0.5", color=BLUE), tex("1", color=BLUE)]
# i: 0 1
# x: 0 6
for i in range(len(x_labels)):
x_labels[i].next_to(xy(6*i,0), DOWN)
g.add(x_labels[i])
# max_y: 1 -> 0.5 ~ -0.5
# 2 -> 1 ~ -1
y_axis = get_line(xy(min_x, max_y/2),xy(min_x,-max_y/2) )
g.add(y_axis)
y_labels = []
for i in range(max_y, -max_y-1, -1):
y_labels.append(tex(str(i)))
#i: 0 1 2 or 0 1 2 3 4
#y: 0.5 0 -0.5 1 0.5 0 -0.5 -1
for i in range(len(y_labels)):
y_labels[i].next_to(xy(-6, -0.5*(i-max_y)), LEFT)
g.add(y_labels[i])
self.min_x = min_x
self.max_x = max_x
return g
def draw_grid(self):
def get_s_line(x1, y1, x2, y2): # small grid
return Line(np.array([x1, y1, 0]), np.array([x2, y2, 0]), stroke_color=BLUE_D, stroke_width=1,
stroke_opacity=0.7)
y1, y2 = 2.5, -2.5
sv_lines = [get_s_line(x, y1, x, y2) for x in np.arange(self.min_x , self.max_x+1, 1)]
self.add(*sv_lines)
def draw_axis(self):
def tex(str):
return TexMobject(str, ).scale(0.8)
eq1 = tex(r"y_1=\sin 2\pi \cdot 2 \cdot t")
eq2 = tex(r"y_1=\sin (2\pi \cdot 2 \cdot t - \phi), \phi = ")
eq3 = tex(r"y = y_1 + y_2")
phi_num = Integer(0, color=RED)
axis1 = self.get_axis(1)
axis1.shift(UP*2)
eq1.next_to(axis1,UP,aligned_edge=LEFT, buff=0).shift(RIGHT*0.8+DOWN*0.1)
axis2 = self.get_axis(1)
axis2.shift(UP*0.5)
eq2.next_to(axis2, UP, aligned_edge=LEFT, buff=0).shift(RIGHT * 0.8+DOWN*0.1)
phi_num.next_to(eq2, RIGHT)
axis3 = self.get_axis(2)
axis3.shift(DOWN*1.5)
eq3.next_to(axis3, UP, aligned_edge=LEFT, buff=0).shift(RIGHT * 0.8+DOWN*0.1)
self.add(axis1, axis2, axis3)
self.add(eq1, eq2, phi_num, eq3)
self.phi_num = phi_num
def draw_wave(self):
vt = ValueTracker(0)
def get_wave(A=1, f=2, phi=0): # phi: degree
# x: -6 ... 0 ... 6
# t: 0 .. 0.5 .. 1
# t = x/12 + 0.5
return FunctionGraph(
lambda x: A/2*np.sin(2 * PI * f * (x / 12 + 0.5) - phi * PI / 180),
# lambda t : np.sin(t),
x_min=self.min_x,
x_max=self.max_x,
)
def get_sum_cal(A=1,f=2):
phi = vt.get_value()
return FunctionGraph(
lambda x: (A / 2 * np.sin(2 * PI * f * (x / 12 + 0.5))) +
(A / 2 * np.sin(2 * PI * f * (x / 12 + 0.5)-(phi * PI / 180))),
# lambda t : np.sin(t),
x_min=self.min_x,
x_max=self.max_x,
)
wave1 = get_wave(1, 2, 0).shift(UP * 2)
wave2 = get_wave(1, 2, 0).shift(UP * 0.5)
wave3 = get_sum_cal(1, 2).shift(DOWN * 1.5)
self.add(wave1, wave2, wave3)
#ani
def update_wave2(mob):
new_wave = get_wave(phi=vt.get_value()).shift(UP * 0.5)
mob.become(new_wave)
def update_wave3(mob):
new_wave = get_sum_cal(1, 2).shift(DOWN * 1.5)
mob.become(new_wave)
def update_phi(mob):
mob.set_value(vt.get_value())
wave2.add_updater(update_wave2)
wave3.add_updater(update_wave3)
self.phi_num.add_updater(update_phi)
self.play(vt.set_value, 360, rate_func=linear, run_time=10)
self.wait()