Finished formal derivative definition animations of eoc7

eoc/chapter7.py

@@ -104,36 +104,52 @@ class ThisVideo(TeacherStudentsScene):
         self.change_student_modes(*["happy"]*3)
         self.dither(2)
 
-class ApproachWordToLim(PiCreatureScene):
+class LimitJustMeansApproach(PiCreatureScene):
     CONFIG = {
-        "dx_color" : GREEN
+        "dx_color" : GREEN,
+        "max_num_zeros" : 7,
     }
     def construct(self):
         limit_expression = self.get_limit_expression()
-        limit_expression.next_to(
-            self.pi_creature, LEFT, aligned_edge = UP
-        )
+        limit_expression.shift(2*LEFT)
+        limit_expression.to_edge(UP)
 
         evaluated_expressions = self.get_evaluated_expressions()
-        evaluated_expressions.to_edge(UP)
+        evaluated_expressions.next_to(limit_expression, DOWN, buff = LARGE_BUFF)
         brace = Brace(evaluated_expressions[0][-1], DOWN)
         question = TextMobject("What does this ``approach''?")
         question.next_to(brace, DOWN)
 
-        expression = evaluated_expressions[0]
-        self.add(expression, brace, question)
-        self.change_mode("raise_right_hand")
-        for next_expression in evaluated_expressions[1:]:
-            next_expression.move_to(expression, RIGHT)
-            self.play(Transform(expression, next_expression))
-            self.dither(0.5)
-        self.play(
-            Write(limit_expression),
-            self.pi_creature.change_mode, "pondering"
+        point = VectorizedPoint(limit_expression.get_right())
+        expression = VGroup(
+            limit_expression[1].copy(), 
+            point, point.copy()
         )
-        self.play(Indicate(limit_expression[0]))
+        self.add(limit_expression)
+        self.change_mode("raise_right_hand")
+        for next_expression in evaluated_expressions:
+            next_expression.move_to(evaluated_expressions[0], RIGHT)
+            self.play(
+                Transform(
+                    expression, next_expression,
+                    submobject_mode = "lagged_start",
+                    lag_factor = 1.2,
+                ),
+                self.pi_creature.look_at, next_expression[-1]
+            )
+            if brace not in self.get_mobjects():
+                self.play(
+                    GrowFromCenter(brace),
+                    Write(question)
+                )
+            self.dither(0.5)
         self.dither(2)
 
+    def create_pi_creature(self):
+        self.pi_creature = Mortimer().flip()
+        self.pi_creature.to_corner(DOWN+LEFT)
+        return self.pi_creature
+
     def get_limit_expression(self):
         lim = TexMobject("\\lim_", "{dx", " \\to 0}")
         lim.highlight_by_tex("dx", self.dx_color)
@@ -144,7 +160,7 @@ class ApproachWordToLim(PiCreatureScene):
 
     def get_evaluated_expressions(self):
         result = VGroup()
-        for num_zeros in range(1, 6):
+        for num_zeros in range(1, self.max_num_zeros+1):
             dx_str = "0." + "0"*num_zeros + "1"
             expression = self.get_expression(dx_str)            
             dx = float(dx_str)
@@ -165,7 +181,7 @@ class ApproachWordToLim(PiCreatureScene):
 class RefreshOnDerivativeDefinition(GraphScene):
     CONFIG = {
         "start_x" : 2,
-        "dx" : 0.7,
+        "start_dx" : 0.7,
         "df_color" : YELLOW,
         "dx_color" : GREEN,
         "secant_line_color" : MAROON_B,
@@ -183,11 +199,12 @@ class RefreshOnDerivativeDefinition(GraphScene):
                 line_class = DashedLine,
                 color = RED
             )
-            for nudge in 0, self.dx
+            for nudge in 0, self.start_dx
         ]
+        nudged_x_v_line.save_state()
         ss_group = self.get_secant_slope_group(
             self.start_x, graph,
-            dx = self.dx,
+            dx = self.start_dx,
             dx_label = "dx",
             df_label = "df",
             df_line_color = self.df_color,
@@ -204,6 +221,7 @@ class RefreshOnDerivativeDefinition(GraphScene):
         dx = derivative.get_part_by_tex("dx")
         input_x = derivative.get_part_by_tex(str(self.start_x))
         derivative.move_to(self.coords_to_point(7, 4))
+        derivative.save_state()
         deriv_brace = Brace(derivative)
         dx_to_0 = TexMobject("dx", "\\to 0")
         dx_to_0.highlight_by_tex("dx", self.dx_color)
@@ -278,7 +296,7 @@ class RefreshOnDerivativeDefinition(GraphScene):
 
         self.animate_secant_slope_group_change(
             ss_group,
-            target_dx = self.dx,
+            target_dx = self.start_dx,
             run_time = 2
         )
         self.play(ShowCreation(nudged_x_v_line))
@@ -323,6 +341,437 @@ class RefreshOnDerivativeDefinition(GraphScene):
         )
         self.dither(2)
 
+        #Record attributes for DiscussLowercaseDs below
+        digest_locals(self)
+
+class RantOpenAndClose(Scene):
+    def construct(self):
+        pass
+
+class DiscussLowercaseDs(RefreshOnDerivativeDefinition, PiCreatureScene, ZoomedScene):
+    CONFIG = {
+        "zoomed_canvas_corner" : UP+LEFT
+    }
+    def construct(self):
+        self.skip_superclass_anims()
+        self.replace_dx_terms()
+        self.compare_rhs_and_lhs()
+        self.h_is_finite()
+
+    def skip_superclass_anims(self):
+        self.remove(self.pi_creature)        
+        self.force_skipping()
+        RefreshOnDerivativeDefinition.construct(self)
+        self.revert_to_original_skipping_status()
+        self.animate_secant_slope_group_change(
+            self.ss_group, target_dx = self.start_dx,
+            added_anims = [
+                self.nudged_x_v_line.restore,
+                Animation(self.ss_group.df_line)
+            ],
+            run_time = 1
+        )
+        everything = self.get_top_level_mobjects()
+        everything.remove(self.derivative)
+        self.play(*[
+            ApplyMethod(mob.shift, 2.5*LEFT)
+            for mob in everything
+        ] + [
+            FadeIn(self.pi_creature)
+        ])
+
+    def replace_dx_terms(self):
+        dx_list = [self.dx_to_0[0]]
+        dx_list += self.new_deriv.get_parts_by_tex("dx")
+        mover = dx_list[0]
+        mover_scale_val = 1.5
+        mover.initial_right = mover.get_right()
+
+        self.play(
+            mover.scale, mover_scale_val,
+            mover.next_to, self.pi_creature.get_corner(UP+LEFT), 
+                UP, MED_SMALL_BUFF,
+            self.pi_creature.change_mode, "sassy",
+            path_arc = np.pi/2,
+        )
+        self.blink()
+        self.dither()
+        for tex in "\\Delta x", "h":
+            dx_list_replacement = [
+                TexMobject(
+                    tex
+                ).highlight(self.dx_color).move_to(dx, DOWN)
+                for dx in dx_list
+            ]
+            self.play(
+                Transform(
+                    VGroup(*dx_list),
+                    VGroup(*dx_list_replacement),
+                ),
+                self.pi_creature.change_mode, "raise_right_hand"
+            )
+            self.dither()
+        self.play(
+            mover.scale, 0.9,
+            mover.move_to, mover.initial_right, RIGHT,
+            self.pi_creature.change_mode, "happy",
+        )
+        self.play(
+            self.dx_to_0.next_to, self.lim, DOWN, SMALL_BUFF,
+        )
+        self.dither()
+
+    def compare_rhs_and_lhs(self):
+        self.derivative.restore()
+        lhs = self.derivative
+        equals = TexMobject("=")
+        rhs = VGroup(self.lim, self.dx_to_0, self.new_deriv)
+        rhs.generate_target()
+        rhs.target.next_to(self.pi_creature, UP, MED_LARGE_BUFF)
+        rhs.target.to_edge(RIGHT)
+        equals.next_to(rhs.target, LEFT)
+        lhs.next_to(equals, LEFT)
+
+        d_circles = VGroup(*[
+            Circle(color = BLUE_B).replace(
+                lhs.get_part_by_tex(tex)[0],
+                stretch = True,
+            ).scale_in_place(1.5).rotate_in_place(-np.pi/12)
+            for tex in "df", "dx"
+        ])
+        d_words = TextMobject("""
+            Limit idea is
+            built in
+        """)
+        d_words.next_to(d_circles, DOWN)
+        d_words.highlight(d_circles[0].get_color())
+
+        lhs_rect, rhs_rect = rects = [
+            Rectangle(color = GREEN_B).replace(
+                mob, stretch = True
+            )
+            for mob in lhs, rhs.target
+        ]
+        for rect in rects:
+            rect.stretch_to_fit_width(rect.get_width()+2*MED_SMALL_BUFF)
+            rect.stretch_to_fit_height(rect.get_height()+2*MED_SMALL_BUFF)
+        formal_definition_words = TextMobject("""
+            Formal derivative definition 
+        """)
+        formal_definition_words.scale_to_fit_width(rhs_rect.get_width())
+        formal_definition_words.next_to(rhs_rect, UP)
+        formal_definition_words.highlight(rhs_rect.get_color())
+        formal_definition_words.add_background_rectangle()
+
+        df = VGroup(lhs.get_part_by_tex("df"))
+        df_target = VGroup(*self.new_deriv.get_parts_by_tex("f"))
+
+        self.play(
+            MoveToTarget(rhs),
+            Write(lhs),
+            Write(equals),
+        )
+        self.play(
+            ShowCreation(d_circles, run_time = 2),
+            self.pi_creature.change_mode, "pondering"
+        )
+        self.play(Write(d_words))
+        self.animate_secant_slope_group_change(
+            self.ss_group, target_dx = 0.01,
+            added_anims = [
+                Transform(
+                    self.nudged_x_v_line, self.start_x_v_line,
+                    run_time = 3
+                )
+            ]
+        )
+        self.change_mode("thinking")
+        self.dither(2)
+        self.play(
+            ShowCreation(lhs_rect),
+            FadeOut(d_circles),
+            FadeOut(d_words),
+        )
+        self.dither(2)
+        self.play(
+            ReplacementTransform(lhs_rect, rhs_rect),
+            self.pi_creature.change_mode, "raise_right_hand"
+        )
+        self.dither(2)
+        self.play(ReplacementTransform(
+            df.copy(), df_target, 
+            path_arc = -np.pi/2,
+            run_time = 2
+        ))
+        self.dither(2)
+        self.play(Indicate(
+            VGroup(*rhs[:2]),
+            run_time = 2
+        ))
+        self.dither()
+
+        self.play(Write(formal_definition_words))
+        self.play(
+            self.pi_creature.change_mode, "happy",
+            self.pi_creature.look_at, formal_definition_words
+        )
+        self.dither(2)
+
+        lhs.add_background_rectangle()
+        self.add(rhs_rect, rhs)
+        self.definition_group = VGroup(
+            lhs, equals, rhs_rect, rhs, formal_definition_words
+        )
+        self.lhs, self.rhs, self.rhs_rect = lhs, rhs, rhs_rect
+
+    def h_is_finite(self):
+        self.play(
+            FadeOut(self.graph_label),
+            self.definition_group.center,
+            self.definition_group.to_corner, UP+RIGHT,
+            self.pi_creature.change_mode, "sassy",
+            self.pi_creature.look_at, 4*UP
+        )
+        self.dither()
+
+
+        words = TextMobject("No ``infinitely small''")
+        words.next_to(
+            self.definition_group, DOWN,
+            buff = LARGE_BUFF, 
+        ) 
+        arrow = Arrow(words.get_top(), self.rhs_rect.get_bottom())
+        arrow.highlight(WHITE)
+
+        h_group = VGroup(
+            self.rhs[1].get_part_by_tex("dx"),
+            *self.rhs[2].get_parts_by_tex("dx")
+        )
+        moving_h = h_group[0]
+        moving_h.original_center = moving_h.get_center()
+        dx_group = VGroup()
+        for h in h_group:
+            dx = TexMobject("dx")
+            dx.highlight(h.get_color())
+            dx.replace(h, dim_to_match = 1)
+            dx_group.add(dx)
+        moving_dx = dx_group[0]       
+
+        self.play(Write(words), ShowCreation(arrow))
+        self.dither(2)
+
+        self.play(
+            moving_h.next_to, self.pi_creature.get_corner(UP+RIGHT), UP,
+            self.pi_creature.change_mode, "raise_left_hand",
+        )
+        self.dither()
+        moving_dx.move_to(moving_h)
+        h_group.save_state()
+        self.play(Transform(
+            h_group, dx_group, 
+            path_arc = np.pi,
+        ))
+        self.dither(2)
+        self.play(h_group.restore, path_arc = np.pi)
+        self.play(
+            moving_h.move_to, moving_h.original_center,
+            self.pi_creature.change_mode, "plain"
+        )
+        self.dither()
+
+        self.activate_zooming()
+        lil_rect = self.little_rectangle
+        lil_rect.move_to(self.ss_group)
+        lil_rect.scale_in_place(3)
+        lil_rect.save_state()
+        self.dither()
+        self.add(self.rhs)
+        self.play(
+            lil_rect.scale_to_fit_width,
+            self.ss_group.dx_line.get_width()*4,
+            run_time = 4
+        )
+        self.dither()
+        dx = self.ss_group.dx_label
+        dx.save_state()
+        h = TexMobject("h")
+        h.highlight(dx.get_color())
+        h.replace(dx, dim_to_match = 1)
+        self.play(Transform(dx, h, path_arc = np.pi))
+        self.play(Indicate(dx))
+        self.dither()
+        self.play(dx.restore, path_arc = np.pi)
+        self.play(lil_rect.restore, run_time = 4)
+        self.dither()
+        self.disactivate_zooming()
+
+class OtherViewsOfDx(TeacherStudentsScene):
+    def construct(self):
+        definition = TexMobject(
+            "{df", "\\over \\,", "dx}", "(", "2", ")", "=",
+            "\\lim", "_{h", "\\to", "0}", 
+            "{f", "(", "2", "+", "h", ")", "-", "f", "(", "2", ")",
+            "\\over \\,", "h}"
+        )
+        tex_to_color = {
+            "df" : YELLOW,
+            "f" : YELLOW,
+            "dx" : GREEN,
+            "h" : GREEN,
+            "2" : RED
+        }
+        for tex, color in tex_to_color.items():
+            definition.highlight_by_tex(tex, color)
+        definition.scale(0.8)
+        definition.to_corner(UP+LEFT)
+        dx_group = VGroup(*definition.get_parts_by_tex("dx"))
+        h_group = VGroup(*definition.get_parts_by_tex("h"))
+        self.add(definition)
+
+        statements = [
+            TextMobject(*args)
+            for args in [
+                ("Why the new \\\\ variable", "$h$", "?"),
+                ("$dx$", "is more $\\dots$ contentious.")
+            ]
+        ]
+        for statement in statements:
+            statement.h, statement.dx = [
+                VGroup(*statement.get_parts_by_tex(
+                    tex, substring = False
+                )).highlight(GREEN)
+                for tex in "$h$", "$dx$"
+            ]
+
+
+        self.force_skipping()
+        self.student_says(
+            statements[0],
+            student_index = 1,
+            target_mode = "confused"
+        )
+        self.play(ReplacementTransform(
+            statements[0].h.copy(), h_group,
+            run_time = 2,
+            submobject_mode = "lagged_start",
+            lag_factor = 1.5,
+        ))
+        self.dither()
+        self.revert_to_original_skipping_status()##
+        self.teacher_says(
+            statements[1],
+            target_mode = "hesitant",
+        )
+        self.play(ReplacementTransform(
+            statements[1].dx.copy(), dx_group, 
+            run_time = 2
+        ))
+        self.dither()
+
+
+
+class GraphLimitExpression(GraphScene):
+    CONFIG = {
+        "start_x" : 2,
+        "h_color" : GREEN,
+        "f_color" : YELLOW,
+        "start_x_color" : RED,
+        "graph_origin" : 3*DOWN,
+        "x_min" : -5,
+        "x_max" : 5,
+        "x_axis_label" : "$h$",
+        "x_labeled_nums" : range(-5, 6),
+        "y_min" : 0,
+        "y_max" : 20,
+        "y_tick_frequency" : 1,
+        "y_labeled_nums" : range(5, 25, 5),
+        "y_axis_label" : "",
+    }
+    def construct(self):
+        self.force_skipping()
+
+        def func(h):
+            return 3*(2**2) + 3*2*h + h**2
+
+        self.setup_axes()
+        self.introduce_limit_term()
+        self.show_graph()
+        self.emphasize_non_definedness_at_0()
+        self.point_out_limit_point()
+        self.show_epsilon_delta_intuition()
+        self.limits_as_a_language()
+
+    def introduce_limit_term(self):
+        abstract_limit = TexMobject(
+            "\\lim", "_{h", "\\to 0}", "=",
+            "{f", "(", str(self.start_x), "+", "h", ")", 
+            "-", "f", "(", str(self.start_x), ")",
+            "\\over \\,", "h}",
+            arg_separator = "",
+        )
+        cube_limit = TexMobject(
+            "\\lim", "_{h", "\\to 0}", "=",
+            "{(", str(self.start_x), "+", "h", ")", "^3",
+            "-", "(", str(self.start_x), ")", "^3",
+            "\\over \\,", "h}",
+            arg_separator = "",
+        )
+        tex_to_color = {
+            "h" : self.h_color,
+            "f" : self.f_color,
+            "3" : self.f_color,
+            str(self.start_x) : self.start_x_color
+        }
+        for expression in abstract_limit, cube_limit:
+            for tex, color in tex_to_color.items():
+                expression.highlight_by_tex(tex, color)
+            expression.next_to(ORIGIN, RIGHT, LARGE_BUFF)
+            expression.to_edge(UP)
+
+        brace = Brace(VGroup(*abstract_limit[4:]), DOWN)
+        graph_this = brace.get_text("Graph this")
+
+        self.revert_to_original_skipping_status()
+        self.add(abstract_limit)
+        self.play(
+            GrowFromCenter(brace),
+            Write(graph_this)
+        )
+        self.dither()
+        self.play(*[
+            ReplacementTransform(
+                VGroup(*abstract_limit.get_parts_by_tex(tex)),
+                VGroup(*cube_limit.get_parts_by_tex(
+                    tex if tex is not "f" else "3"
+                )),
+                run_time = 2,
+            )
+            for tex in [
+                "lim", "h", "to", "=", "f", "(", 
+                str(self.start_x), "+", ")", "-", "over"
+            ]
+        ])
+        self.dither()
+        for part in cube_limit.get_parts_by_tex("2"):
+            self.play(Indicate(part))
+        self.dither(2)
+
+    def show_graph(self):
+        pass
+
+    def emphasize_non_definedness_at_0(self):
+        pass
+
+    def point_out_limit_point(self):
+        pass
+
+    def show_epsilon_delta_intuition(self):
+        pass
+
+    def limits_as_a_language(self):
+        pass
+
+
 
 
 

scene/zoomed_scene.py

@@ -129,7 +129,6 @@ class ZoomedScene(Scene):
         )
         if self.zoom_activated and self.little_rectangle in moving_mobjects:
             # When the camera is moving, so is everything,
-            mobjects = self.get_mobjects()
             return self.get_mobjects(), []
         else:
             return moving_mobjects, static_mobjects

topics/characters.py

@@ -413,10 +413,10 @@ class PiCreatureScene(Scene):
                 *content,
                 bubble_class = bubble_class,
                 bubble_kwargs = bubble_kwargs,
-                target_mode = target_mode
+                target_mode = target_mode,
+                **kwargs
             ),
-            *added_anims,
-            **kwargs
+            *added_anims
         )
 
     def pi_creature_says(self, pi_creature, *content, **kwargs):