mirror of
https://github.com/3b1b/manim.git
synced 2025-08-05 16:49:03 +00:00
Fixed interpolation problem in ExplainTrigFunctionDistances
This commit is contained in:
Grant Sanderson
parent
b1eb9a135b
commit
44216ffe0d
1 changed files with 129 additions and 73 deletions
202
tattoo.py
202
tattoo.py
|
|
@ -111,7 +111,6 @@ class TrigRepresentationsScene(Scene):
|
||||||
end_point = (1./np.sin(self.theta_value))*self.unit_length*UP
|
end_point = (1./np.sin(self.theta_value))*self.unit_length*UP
|
||||||
return Line(start_point, end_point, color = color)
|
return Line(start_point, end_point, color = color)
|
||||||
|
|
||||||
|
|
||||||
class IntroduceCSC(TrigRepresentationsScene):
|
class IntroduceCSC(TrigRepresentationsScene):
|
||||||
def construct(self):
|
def construct(self):
|
||||||
self.clear()
|
self.clear()
|
||||||
|
|
@ -261,20 +260,25 @@ class ExplainTrigFunctionDistances(TrigRepresentationsScene, PiCreatureScene):
|
||||||
self.dither()
|
self.dither()
|
||||||
self.change_mode("well")
|
self.change_mode("well")
|
||||||
|
|
||||||
original_theta_value = self.theta_value
|
mover = VGroup(
|
||||||
self.theta_value = self.alt_theta_val
|
sin_group,
|
||||||
sin_group.target = self.get_line_brace_text("sin")
|
cos_group,
|
||||||
cos_group.target = self.get_line_brace_text("cos")
|
self.theta_group,
|
||||||
self.theta_group.target = self.get_theta_group()
|
|
||||||
self.play(
|
|
||||||
*map(MoveToTarget,
|
|
||||||
[sin_group, cos_group, self.theta_group]
|
|
||||||
),
|
|
||||||
path_arc = self.theta_value - original_theta_value,
|
|
||||||
rate_func = there_and_back,
|
|
||||||
run_time = 5
|
|
||||||
)
|
)
|
||||||
self.theta_value = original_theta_value
|
thetas = np.linspace(self.theta_value, self.alt_theta_val, 10)
|
||||||
|
targets = []
|
||||||
|
for theta in list(thetas) + list(reversed(thetas)):
|
||||||
|
self.theta_value = theta
|
||||||
|
targets.append(VGroup(
|
||||||
|
self.get_line_brace_text("sin"),
|
||||||
|
self.get_line_brace_text("cos"),
|
||||||
|
self.get_theta_group()
|
||||||
|
))
|
||||||
|
self.play(Succession(*[
|
||||||
|
Transform(mover, target)
|
||||||
|
for target in targets
|
||||||
|
], run_time = 5, rate_func = smooth))
|
||||||
|
|
||||||
self.change_mode("happy")
|
self.change_mode("happy")
|
||||||
self.dither()
|
self.dither()
|
||||||
self.sin_group, self.cos_group = sin_group, cos_group
|
self.sin_group, self.cos_group = sin_group, cos_group
|
||||||
|
|
@ -330,20 +334,25 @@ class ExplainTrigFunctionDistances(TrigRepresentationsScene, PiCreatureScene):
|
||||||
small_lines.add(small_line)
|
small_lines.add(small_line)
|
||||||
self.play(FadeOut(line), Animation(small_lines))
|
self.play(FadeOut(line), Animation(small_lines))
|
||||||
|
|
||||||
original_theta_value = self.theta_value
|
mover = VGroup(
|
||||||
self.theta_value = self.alt_theta_val
|
tan_group,
|
||||||
tan_group.target = self.get_line_brace_text("tan")
|
cot_group,
|
||||||
cot_group.target = self.get_line_brace_text("cot")
|
self.theta_group,
|
||||||
self.theta_group.target = self.get_theta_group()
|
|
||||||
self.play(
|
|
||||||
*map(MoveToTarget,
|
|
||||||
[tan_group, cot_group, self.theta_group]
|
|
||||||
),
|
|
||||||
path_arc = self.theta_value - original_theta_value,
|
|
||||||
rate_func = there_and_back,
|
|
||||||
run_time = 5
|
|
||||||
)
|
)
|
||||||
self.theta_value = original_theta_value
|
thetas = np.linspace(self.theta_value, self.alt_theta_val, 10)
|
||||||
|
targets = []
|
||||||
|
for theta in list(thetas) + list(reversed(thetas)):
|
||||||
|
self.theta_value = theta
|
||||||
|
targets.append(VGroup(
|
||||||
|
self.get_line_brace_text("tan"),
|
||||||
|
self.get_line_brace_text("cot"),
|
||||||
|
self.get_theta_group()
|
||||||
|
))
|
||||||
|
self.play(Succession(*[
|
||||||
|
Transform(mover, target)
|
||||||
|
for target in targets
|
||||||
|
], run_time = 5, rate_func = smooth))
|
||||||
|
|
||||||
self.change_mode("happy")
|
self.change_mode("happy")
|
||||||
self.dither(2)
|
self.dither(2)
|
||||||
|
|
||||||
|
|
@ -399,27 +408,34 @@ class ExplainTrigFunctionDistances(TrigRepresentationsScene, PiCreatureScene):
|
||||||
)
|
)
|
||||||
self.dither()
|
self.dither()
|
||||||
|
|
||||||
|
mover = VGroup(
|
||||||
original_theta_value = self.theta_value
|
sec_group,
|
||||||
self.theta_value = self.alt_theta_val
|
csc_group,
|
||||||
sec_group.target = self.get_line_brace_text("sec")
|
self.theta_group,
|
||||||
csc_group.target = self.get_line_brace_text("csc")
|
self.tangent_line,
|
||||||
for group in sec_group, csc_group:
|
|
||||||
line = group.target[0]
|
|
||||||
group.target.add(
|
|
||||||
Dot(line.get_end(), color = line.get_color())
|
|
||||||
)
|
|
||||||
self.theta_group.target = self.get_theta_group()
|
|
||||||
self.tangent_line.target = self.get_tangent_line()
|
|
||||||
self.play(
|
|
||||||
*map(MoveToTarget,
|
|
||||||
[sec_group, csc_group, self.tangent_line, self.theta_group]
|
|
||||||
),
|
|
||||||
path_arc = self.theta_value - original_theta_value,
|
|
||||||
rate_func = there_and_back,
|
|
||||||
run_time = 5
|
|
||||||
)
|
)
|
||||||
self.theta_value = original_theta_value
|
thetas = np.linspace(self.theta_value, self.alt_theta_val, 10)
|
||||||
|
targets = []
|
||||||
|
for theta in list(thetas) + list(reversed(thetas)):
|
||||||
|
self.theta_value = theta
|
||||||
|
new_sec_group = self.get_line_brace_text("sec")
|
||||||
|
new_csc_group = self.get_line_brace_text("csc")
|
||||||
|
for group in new_sec_group, new_csc_group:
|
||||||
|
line = group[0]
|
||||||
|
group.add(
|
||||||
|
Dot(line.get_end(), color = line.get_color())
|
||||||
|
)
|
||||||
|
targets.append(VGroup(
|
||||||
|
new_sec_group,
|
||||||
|
new_csc_group,
|
||||||
|
self.get_theta_group(),
|
||||||
|
self.get_tangent_line(),
|
||||||
|
))
|
||||||
|
self.play(Succession(*[
|
||||||
|
Transform(mover, target)
|
||||||
|
for target in targets
|
||||||
|
], run_time = 5, rate_func = smooth))
|
||||||
|
|
||||||
self.change_mode("confused")
|
self.change_mode("confused")
|
||||||
self.dither(2)
|
self.dither(2)
|
||||||
|
|
||||||
|
|
@ -444,11 +460,13 @@ class ExplainTrigFunctionDistances(TrigRepresentationsScene, PiCreatureScene):
|
||||||
|
|
||||||
tri1 = Polygon(
|
tri1 = Polygon(
|
||||||
ORIGIN, radial_line.get_end(), sin_line.get_end(),
|
ORIGIN, radial_line.get_end(), sin_line.get_end(),
|
||||||
color = GREEN
|
color = GREEN,
|
||||||
|
stroke_width = 8,
|
||||||
)
|
)
|
||||||
tri2 = Polygon(
|
tri2 = Polygon(
|
||||||
csc_line.get_end(), ORIGIN, radial_line.get_end(),
|
csc_line.get_end(), ORIGIN, radial_line.get_end(),
|
||||||
color = GREEN
|
color = GREEN,
|
||||||
|
stroke_width = 8,
|
||||||
)
|
)
|
||||||
|
|
||||||
opp_over_hyp = TexMobject(
|
opp_over_hyp = TexMobject(
|
||||||
|
|
@ -476,6 +494,10 @@ class ExplainTrigFunctionDistances(TrigRepresentationsScene, PiCreatureScene):
|
||||||
tri1.save_state()
|
tri1.save_state()
|
||||||
self.play(Transform(tri1, tri2, path_arc = np.pi/2))
|
self.play(Transform(tri1, tri2, path_arc = np.pi/2))
|
||||||
self.play(Write(arc_theta))
|
self.play(Write(arc_theta))
|
||||||
|
self.play(ApplyMethod(
|
||||||
|
tri1.rotate_in_place, np.pi/12,
|
||||||
|
rate_func = wiggle
|
||||||
|
))
|
||||||
self.dither(2)
|
self.dither(2)
|
||||||
|
|
||||||
self.play(Write(opp_over_hyp))
|
self.play(Write(opp_over_hyp))
|
||||||
|
|
@ -539,43 +561,52 @@ class ExplainTrigFunctionDistances(TrigRepresentationsScene, PiCreatureScene):
|
||||||
)
|
)
|
||||||
self.dither()
|
self.dither()
|
||||||
self.play(
|
self.play(
|
||||||
dem2.move_to, frac2[-2],
|
dem2.move_to, frac2[2],
|
||||||
VGroup(*frac2[-2:]).highlight, BLACK
|
VGroup(*frac2[1:3]).highlight, BLACK
|
||||||
)
|
)
|
||||||
|
self.dither()
|
||||||
|
|
||||||
def summarize_full_group(self):
|
def summarize_full_group(self):
|
||||||
scale_factor = 1.5
|
scale_factor = 1.5
|
||||||
theta_subgroup = VGroup(self.theta_group[0], self.theta_group[-1])
|
theta_subgroup = VGroup(self.theta_group[0], self.theta_group[-1])
|
||||||
self.play(
|
self.play(*it.chain(*[
|
||||||
self.circle.scale, scale_factor,
|
[mob.scale, scale_factor]
|
||||||
self.axes.scale, scale_factor,
|
for mob in [
|
||||||
theta_subgroup.scale, scale_factor,
|
self.circle, self.axes,
|
||||||
)
|
theta_subgroup, self.tangent_line
|
||||||
|
]
|
||||||
|
]))
|
||||||
self.unit_length *= scale_factor
|
self.unit_length *= scale_factor
|
||||||
|
|
||||||
to_fade = VGroup()
|
to_fade = VGroup()
|
||||||
for func_name in ["sin", "tan", "sec", "cos", "cot", "csc"]:
|
for func_name in ["sin", "tan", "sec", "cos", "cot", "csc"]:
|
||||||
line, brace, text = self.get_line_brace_text(func_name)
|
line, brace, text = self.get_line_brace_text(func_name)
|
||||||
angle = line.get_angle()
|
|
||||||
if np.cos(angle) < 0:
|
|
||||||
angle += np.pi
|
|
||||||
if func_name is "sin":
|
|
||||||
target = line.get_center()+0.2*LEFT+0.1*DOWN
|
|
||||||
else:
|
|
||||||
target = VGroup(brace, line).get_center_of_mass()
|
|
||||||
if func_name in ["sin", "cos"]:
|
if func_name in ["sin", "cos"]:
|
||||||
|
angle = line.get_angle()
|
||||||
|
if np.cos(angle) < 0:
|
||||||
|
angle += np.pi
|
||||||
|
if func_name is "sin":
|
||||||
|
target = line.get_center()+0.2*LEFT+0.1*DOWN
|
||||||
|
else:
|
||||||
|
target = VGroup(brace, line).get_center_of_mass()
|
||||||
text.scale(0.75)
|
text.scale(0.75)
|
||||||
text.rotate(angle)
|
text.rotate(angle)
|
||||||
text.move_to(target)
|
text.move_to(target)
|
||||||
line.set_stroke(width = 6)
|
line.set_stroke(width = 6)
|
||||||
self.play(
|
self.play(
|
||||||
ShowCreation(line),
|
ShowCreation(line),
|
||||||
Write(text, run_time = 1)
|
Write(text, run_time = 1)
|
||||||
)
|
)
|
||||||
|
else:
|
||||||
|
self.play(
|
||||||
|
ShowCreation(line),
|
||||||
|
GrowFromCenter(brace),
|
||||||
|
Write(text, run_time = 1)
|
||||||
|
)
|
||||||
|
if func_name in ["sec", "csc", "cot"]:
|
||||||
|
to_fade.add(*self.get_mobjects_from_last_animation())
|
||||||
if func_name is "sec":
|
if func_name is "sec":
|
||||||
self.dither()
|
self.dither()
|
||||||
if func_name in ["sec", "csc", "cot"]:
|
|
||||||
to_fade.add(line, text)
|
|
||||||
self.dither()
|
self.dither()
|
||||||
self.change_mode("surprised")
|
self.change_mode("surprised")
|
||||||
self.dither(2)
|
self.dither(2)
|
||||||
|
|
@ -610,7 +641,32 @@ class ExplainTrigFunctionDistances(TrigRepresentationsScene, PiCreatureScene):
|
||||||
color = GREY
|
color = GREY
|
||||||
)
|
)
|
||||||
|
|
||||||
|
class RenameAllInTermsOfSine(Scene):
|
||||||
|
def construct(self):
|
||||||
|
texs = [
|
||||||
|
"\\sin(\\theta)",
|
||||||
|
"\\cos(\\theta)",
|
||||||
|
"\\tan(\\theta)",
|
||||||
|
"\\csc(\\theta)",
|
||||||
|
"\\sec(\\theta)",
|
||||||
|
"\\cot(\\theta)",
|
||||||
|
]
|
||||||
|
shift_vals = [
|
||||||
|
2*LEFT+3*UP,
|
||||||
|
2*LEFT+UP,
|
||||||
|
2*LEFT+DOWN,
|
||||||
|
2*RIGHT+3*UP,
|
||||||
|
2*RIGHT+UP,
|
||||||
|
2*RIGHT+DOWN,
|
||||||
|
]
|
||||||
|
equivs = [
|
||||||
|
"",
|
||||||
|
"\\sin(90^\\circ - \\theta)",
|
||||||
|
"\\frac{\\sin(\\theta)}{\\sin(90^\\circ - \\theta)}",
|
||||||
|
"\\frac{1}{\\sin(\\theta)}",
|
||||||
|
"\\frac{1}{\\sin(90^\\circ - \\theta)}",
|
||||||
|
"\\frac{\\sin(90^\\circ - \\theta)}{\\sin(\\theta)}",
|
||||||
|
]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
|
||||||
Loading…
Add table
Reference in a new issue