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