def test_lineintegral():
c = Curve([E**t + 1, E**t - 1], (t, 0, ln(2)))
assert line_integrate(x + y, c, [x, y]) == 3*sqrt(2)
def construct(self):
# PART A)
GREY_BLACK = "#a9a9a9"
SILVER = "#C0C0C0"
dot_color = interpolate_color(SILVER, BLACK,0.1)
silver_coord= [0,-2,0]
silver_size= 0.15
split_width=.1
sq = Rectangle(height=6, width=2).set_color(BLACK)
silv = Square(silver_size*2, fill_color=SILVER, stroke_color=SILVER, fill_opacity=1).move_to(silver_coord)
silv.title = Tex("Silberquelle", color=BLACK).scale(0.5).next_to(silv,DOWN, buff=SMALL_BUFF)
self.add(silv,silv.title)
silver_holder = VGroup(Line([-1,-2,0],[0-silver_size,-2,0],color=BLACK),
Line([0+silver_size,-2,0],[1,-2,0], color=BLACK))
sq = VGroup(sq, Line(sq.get_top(), sq.get_top()+SMALL_BUFF*DOWN*0.6,color=BLACK))
self.add(sq)
self.add(silver_holder)
self.add(silv)
slitA = VGroup(Line([-1,-0.5,0],[0-split_width,-0.5,0]),Line([0+split_width,-0.5,0],[1,-0.5,0])).set_color(BLACK)
slitB = VGroup(Line([-1, 0.5,0],[0-split_width, 0.5,0]),Line([0+split_width, 0.5,0],[1, 0.5,0])).set_color(BLACK)
self.add(slitA, slitB)
self.bring_to_front(silv)
dashedl=DashedLine(silver_coord, 0.5*UP).set_color(dot_color)
self.add(dashedl)
# PART B)
# cold
# T1 = MathTex(r"\text{T}_{\text{kalt}} = 20^\circ \text{C}").set_color(BLACK)
# self.add(T1.scale(0.7).next_to(sq,LEFT).shift(2*DOWN))
# r1 = 3.8
# r2= 4.5
# r3 =5.5
# speed1=0.7/config.frame_rate*30
# speed2=1/config.frame_rate*30
# speed3=1.5/config.frame_rate*30
#hot
T2 = MathTex(r"\text{T}_{\text{heiß}} = 500^\circ \text{C}").set_color(BLACK)
self.add(T2.scale(0.7).next_to(sq,LEFT).shift(2*DOWN))
r1 = 8
r2= 10.5
r3 =15
speed1=0.7/config.frame_rate*30*2
speed2=1/config.frame_rate*30*2
speed3=1.5/config.frame_rate*30*2
# start_here 1
radius = r1
t_min = 0
t_max1 = np.arcsin(2.5/ radius)
def f1(x):
radius = r1
return [radius * np.cos(x) - radius,0.5+ radius * np.sin(x), 0]
lenf1 = float(Curve([radius * cos(t) - radius, 0.5+radius * sin(t)], (t, t_min, t_max1)).length)
print(lenf1)
param_func1 = ParametricFunction(f1, t_min, t_max1 , stroke_color=dot_color, stroke_opacity=0.3 )
dot1 = Dot(fill_color=dot_color).scale(0.5)
dot1.time = 0
def func_updater1(mobj, dt):
if mobj.timex % 30 == 0:
mobj.submobjects.append(dot1.copy())
for ob in mobj.submobjects:
ob.time += 0.01*t_max1/lenf1*speed1
ob.move_to(f1(ob.time))
if ob.time >= t_max1:
ob.set_opacity(0)
mobj.timex += 1
param_func1.timex = 0
param_func1.add_updater(func_updater1)
self.add(param_func1)
# # start_here2
radius = r2
t_min = 0
t_max2 = np.arcsin(2.5/radius)
def f2(x):
radius = r2
return [radius * np.cos(x) - radius, 0.5+radius * np.sin(x), 0]
param_func2 = ParametricFunction(f2, t_min, t_max2 , stroke_color=dot_color, stroke_opacity=0.3)
lenf2 = float(Curve([radius * cos(t) - radius, 0.5 + radius * sin(t)], (t, t_min, t_max2)).length)
dot2 = Dot(fill_color=dot_color).scale(0.5)
dot2.time = 0
def func_updater2(mobj, dt):
if mobj.timex % 10 == 0:
mobj.submobjects.append(dot2.copy())
for ob in mobj.submobjects:
ob.time += 0.01*t_max2/lenf2*speed2
ob.move_to(f2(ob.time))
if ob.time >= t_max2:
ob.set_opacity(0)
mobj.timex += 1
param_func2.timex = 0
param_func2.add_updater(func_updater2)
self.add(param_func2)
# # start_here3
radius = r3
t_min = 0
t_max3 = np.arcsin(2.5/radius)
def f3(x):
radius = r3
return [radius * np.cos(x) - radius, 0.5+radius * np.sin(x), 0]
param_func3 = ParametricFunction(f3, t_min, t_max3 , stroke_color=dot_color, stroke_opacity=0.3)
lenf3 = float(Curve([radius * cos(t) - radius, 0.5 + radius * sin(t)], (t, t_min, t_max3)).length)
dot3 = Dot(fill_color=dot_color).scale(0.5)
dot3.time = 0
def func_updater3(mobj, dt):
rem= False
if mobj.timex % 30 == 0:
mobj.submobjects.append(dot3.copy())
for ob in mobj.submobjects:
ob.time += 0.01*t_max3/lenf3*speed3
ob.move_to(f3(ob.time))
if ob.time >= t_max3:
ob.set_opacity(0)
mobj.timex += 1
param_func3.timex = 0
param_func3.add_updater(func_updater3)
self.add(param_func3)
self.camera_frame.move_to(3*RIGHT)
rot_anchor=5*RIGHT+2*DOWN
self.add(Dot(color= RED, point=rot_anchor))
self.add(CurvedArrow(rot_anchor+UR, rot_anchor+UL, color=BLACK).scale(0.3, about_point= rot_anchor).flip())
kinetiker= VGroup(sq,silv,silver_holder,slitA,slitB,dashedl).copy().scale(0.3).shift(rot_anchor+1.5*UP)
self.add(kinetiker)
self.tttime=0
text1= Text("Sicht von mitrotierender Kamera").set_color(BLACK).scale(0.4).next_to(sq, DOWN)
text2= Text("Sicht von außen").set_color(BLACK).scale(0.4).next_to(text1,RIGHT).set_x(5)
bg=BackgroundRectangle(text2).set_fill(WHITE).set_opacity(0.7)
self.add(text1)
self.add(bg,text2)
self.bring_to_front(sq)
self.roof = Dot().move_to(kinetiker.get_top())
self.floor= Dot().move_to(kinetiker.submobjects[4].get_center())
def update_mobj(mobj,dt):
self.roof.rotate(-0.1*1/config.frame_rate, about_point=rot_anchor)
self.floor.rotate(-0.1*1/config.frame_rate, about_point=rot_anchor)
mobj.rotate(-0.1*1/config.frame_rate, about_point=rot_anchor)
self.tttime += 0.1
kinetiker.add_updater(update_mobj)
x1 = Dot(fill_color=SILVER).scale(0.7)
self.activate_zooming(animate=False)
zoomed_camera = self.zoomed_camera
zoomed_display = self.zoomed_display
frame = zoomed_camera.frame
zoomed_display_frame = zoomed_display.display_frame
frame.move_to(sq.get_top()+SMALL_BUFF*DOWN*3)
frame.set_color(PURPLE)
zoomed_display_frame.set_color(RED)
zoomed_display.next_to(sq.get_top()+SMALL_BUFF*DOWN*3,RIGHT).set_x(rot_anchor[0])
self.add(frame,zoomed_display)
# for i in range(0,20): #for cold
l = VMobject()
lxx = VMobject()
self.add(l, lxx)
self.bring_to_back(lxx)
self.bring_to_back(l)
self.partial_floor_val= ORIGIN
lxx.add_updater(lambda x: x.become(Line(self.partial_floor_val, x1.get_center()).set_color(interpolate_color(SILVER,WHITE,0.2))))
for i in range(0,40): #for hot 40
self.partial_floor_val = self.floor.get_center()
l.become(Line(self.floor.get_center(), self.roof.get_center(), color= interpolate_color(SILVER,WHITE,0.7)))
self.play(MoveAlongPath(x1,Line(self.floor.get_center(), self.roof.get_center(), color= BLACK),rate_func= linear, run_time=0.5)) # run_time1 for cold
x = x.replace("*", "·")
print(x)
'''
# integrate
i = integrate(sin(x), (x))
p(i)
i = integrate(sin(x), (x, 0, pi/2))
p(i)
i = integrate(z, (x), (y), (z))
p(i)
# plotting some func
d = integrate(x, (x), (y))
plot3d(d, (x, -10, 10), (y, -10, 10))
c = integrate(x, (x))
plot(c, (x, 10, 20))
'''
'''
///////////////////////////////////
'''
from sympy import Curve, line_integrate, E, ln
x, y, t = symbols("x y t")
C = Curve([E**t + 1, E**t - 1], (t, 0, ln(2)))
i = line_integrate(x + y, C, [x, y])
p(i)