A nice small commit capturing one atomic change, as usual

animation/transform.py

@@ -123,6 +123,7 @@ class FadeIn(Transform):
         mobject.fade(1)
         if isinstance(mobject, VMobject):
             mobject.set_stroke(width = 0)
+            mobject.set_fill(opacity = 0)
         Transform.__init__(self, mobject, target, **kwargs)
 
 

eola/chapter7.py

@@ -780,7 +780,7 @@ class Symbolic2To1DTransform(Scene):
 class RecommendChapter3(Scene):
     def construct(self):
         title = TextMobject("""
-            Definite watch Chapter 3
+            Definitely watch Chapter 3
             if you haven't already
         """)
         title.to_edge(UP)
@@ -2316,7 +2316,56 @@ class NextVideo(Scene):
         self.play(ShowCreation(rect))
         self.dither()
 
-
+class CrossAndDualWords(Scene):
+    def construct(self):
+        from eola.chapter5 import get_det_text
+        
+        v_tex, u_tex, w_tex = [
+            "\\vec{\\textbf{%s}}"%s
+            for s in "vuw"
+        ]
+        vector_word = TextMobject("Vector:")
+        transform_word = TextMobject("Dual transform:")
+
+        cross = TexMobject(
+            v_tex, "=", u_tex, "\\times", w_tex
+        )
+        for tex, color in zip([v_tex, u_tex, w_tex], [V_COLOR, U_COLOR, W_COLOR]):
+            cross.highlight_by_tex(tex, color)
+        input_array_tex = matrix_to_tex_string(["x", "y", "z"])
+        func = TexMobject("L\\left(%s\\right) = "%input_array_tex)
+        matrix = Matrix(np.array([
+            ["x", "y", "z"],
+            ["u_1", "u_2", "u_3"],
+            ["w_1", "w_2", "w_3"],
+        ]).T)
+        matrix.highlight_columns(WHITE, U_COLOR, W_COLOR)
+        det_text = get_det_text(matrix)
+        det_text.add(matrix)
+        dot_with_cross = TexMobject(
+            "%s \\cdot ("%input_array_tex,
+            u_tex, "\\times", w_tex, ")"
+        )
+        dot_with_cross.highlight_by_tex(u_tex, U_COLOR)
+        dot_with_cross.highlight_by_tex(w_tex, W_COLOR)
+        transform = Group(func, det_text)
+        transform.arrange_submobjects()
+
+        Group(transform, dot_with_cross).scale(0.7)
+        vector_word.to_corner(UP+LEFT)
+        transform_word.next_to(vector_word, DOWN, buff = MED_BUFF, aligned_edge = LEFT)
+        cross.next_to(vector_word, buff = MED_BUFF)
+        transform.next_to(transform_word, DOWN, buff = MED_BUFF, aligned_edge = LEFT)
+        dot_with_cross.next_to(func, RIGHT)
+
+        self.add(vector_word)
+        self.play(Write(cross))
+        self.dither()
+        self.play(FadeIn(transform_word))
+        self.play(Write(transform))
+        self.dither()
+        self.play(Transform(det_text, dot_with_cross))
+        self.dither()
 
 
 

eola/chapter8.py

@@ -22,66 +22,454 @@ from eola.two_d_space import *
 from eola.chapter5 import get_det_text
 
 
-V_COLOR = RED
 U_COLOR = ORANGE
+V_COLOR = YELLOW
 W_COLOR = MAROON_B
 
 class OpeningQuote(Scene):
     def construct(self):
         words = TextMobject(
-            "To ask the",
-            "right question\\\\",
-            "is harder than to answer it." 
+            "From [Grothendieck], I have also learned not"
+            "to take glory in the ", 
+            "difficulty of a proof:", 
+            "difficulty means we have not understood."
+            "The idea is to be able to",
+            "paint a landscape",
+            "in which the proof is obvious.",
+            arg_separator = " "
         )
+        words.highlight_by_tex("difficulty of a proof:", RED)
+        words.highlight_by_tex("paint a landscape", GREEN)
+        words.scale_to_fit_width(2*SPACE_WIDTH - 2)
         words.to_edge(UP)
-        words[1].highlight(BLUE)
-        author = TextMobject("-Georg Cantor")
+        author = TextMobject("-Pierre Deligne")
         author.highlight(YELLOW)
         author.next_to(words, DOWN, buff = 0.5)
 
         self.play(FadeIn(words))
-        self.dither(2)
+        self.dither(4)
         self.play(Write(author, run_time = 3))
         self.dither()
 
-class CrossAndDualWords(Scene):
+class DoTheSameForCross(TeacherStudentsScene):
     def construct(self):
-        v_tex, u_tex, w_tex = [
-            "\\vec{\\textbf{%s}}"%s
-            for s in "vuw"
+        words = TextMobject("Let's do the same \\\\ for", "cross products")
+        words.highlight_by_tex("cross products", YELLOW)
+        self.teacher_says(words, pi_creature_target_mode = "surprised")
+        self.random_blink(2)
+        self.change_student_modes("pondering")
+        self.random_blink()
+
+class ListSteps(RandolphScene):
+    CONFIG = {
+        "randy_corner" : DOWN+RIGHT
+    }
+    def construct(self):
+        title = TextMobject("Two parts")
+        title.highlight(YELLOW)
+        title.to_edge(UP)
+        h_line = Line(LEFT, RIGHT).scale(SPACE_WIDTH)
+        h_line.next_to(title, DOWN)
+
+        step_1 = TextMobject("1. Standard introduction")
+        step_2 = TextMobject("2. Deeper understanding with ", "linear transformations")
+        step_2.highlight_by_tex("linear transformations", BLUE)
+        steps = Group(step_1, step_2)
+        steps.arrange_submobjects(DOWN, aligned_edge = LEFT, buff = LARGE_BUFF)
+        steps.next_to(self.randy, UP)
+        steps.to_edge(LEFT)
+
+        self.play(
+            FadeIn(step_1),
+            self.randy.change_mode, "happy"
+        )
+        self.dither()
+        self.play(
+            Write(step_2),
+            self.randy.change_mode, "pondering"
+        )
+        self.dither()
+
+class ContrastDotAndCross(Scene):
+    def construct(self):
+        self.add_t_chart()
+        self.add_dot_products()
+        self.add_cross_product()
+        self.add_2d_cross_product()
+        self.emphasize_output_type()
+
+    def add_t_chart(self):
+        for word, vect, color in ("Dot", LEFT, BLUE_C), ("Cross", RIGHT, YELLOW):
+            title = TextMobject("%s product"%word)
+            title.shift(vect*SPACE_WIDTH/2)
+            title.to_edge(UP)
+            title.highlight(color)
+            self.add(title)
+        v_line = Line(UP, DOWN).scale(SPACE_HEIGHT)
+        l_h_line = Line(LEFT, ORIGIN).scale(SPACE_WIDTH)
+        r_h_line = Line(ORIGIN, RIGHT).scale(SPACE_WIDTH)
+        r_h_line.next_to(title, DOWN)
+        l_h_line.next_to(r_h_line, LEFT, buff = 0)
+        self.add(v_line, l_h_line, r_h_line)
+        self.l_h_line, self.r_h_line = l_h_line, r_h_line
+
+    def add_dot_products(self, max_width = SPACE_WIDTH-1, dims = [2, 5]):
+        colors = [X_COLOR, Y_COLOR, Z_COLOR, MAROON_B, TEAL]
+        last_mob = self.l_h_line
+        for dim in dims:
+            arrays = [
+                [random.randint(0, 9) for in_count in range(dim)]
+                for out_count in range(2)
             ]
-        vector_word = TextMobject("Vector:")
-        transform_word = TextMobject("Dual transform:")
-
-        cross = TexMobject(
-            v_tex, "=", u_tex, "\\times", w_tex
+            m1, m2 = map(Matrix, arrays)
+            for matrix in m1, m2:
+                for entry, color in zip(matrix.get_entries(), colors):
+                    entry.highlight(color)
+            syms = map(TexMobject, ["="] + ["+"]*(dim-1))
+            result = Group(*it.chain(*zip(
+                syms,
+                [
+                    Group(
+                        e1, TexMobject("\\cdot"), e2
+                    ).arrange_submobjects()
+                    for e1, e2 in zip(*[m.copy().get_entries() for m in m1, m2])
+                ]
+            )))
+            result.arrange_submobjects(RIGHT)
+            dot_prod = Group(
+                m1, TexMobject("\\cdot"), m2, result
             )
-        for tex, color in zip([v_tex, u_tex, w_tex], [V_COLOR, U_COLOR, W_COLOR]):
-            cross.highlight_by_tex(tex, color)
-        input_array_tex = matrix_to_tex_string(["x", "y", "z"])
-        func = TexMobject("f\\left(%s\\right) = "%input_array_tex)
+            dot_prod.arrange_submobjects(RIGHT)
+            if dot_prod.get_width() > max_width:
+                dot_prod.scale_to_fit_width(max_width)
+            dot_prod.next_to(last_mob, DOWN, buff = MED_BUFF)
+            last_mob = dot_prod
+            dot_prod.to_edge(LEFT)
+            self.play(Write(dot_prod))
+
+    def add_cross_product(self):
+        colors = [X_COLOR, Y_COLOR, Z_COLOR]
+
+        arrays = [
+            [random.randint(0, 9) for in_count in range(3)]
+            for out_count in range(2)
+        ]
+        matrices = map(Matrix, arrays)
+        for matrix in matrices:
+            for entry, color in zip(matrix.get_entries(), colors):
+                entry.highlight(color)
+        m1, m2 = matrices
+        cross_product = Group(m1, TexMobject("\\times"), m2)
+        cross_product.arrange_submobjects()
+
+        index_to_cross_enty = {}
+        syms = Group()
+        movement_sets = []
+        for a, b, c in it.permutations(range(3)):
+            e1, e2 = m1.get_entries()[b], m2.get_entries()[c]
+            for e in e1, e2:
+                e.target = e.copy()
+            movement_sets.append([e1, e1.target, e2, e2.target])
+            dot = TexMobject("\\cdot")
+            syms.add(dot)
+            cross_entry = Group(e1.target, dot, e2.target)
+            cross_entry.arrange_submobjects()
+            if a not in index_to_cross_enty:
+                index_to_cross_enty[a] = []
+            index_to_cross_enty[a].append(cross_entry)
+        result_entries = []
+        for a in range(3):
+            prod1, prod2 = index_to_cross_enty[a]
+            if a == 1:
+                prod1, prod2 = prod2, prod1
+            prod2.arrange_submobjects(LEFT)
+            minus = TexMobject("-")
+            syms.add(minus)
+            entry = Group(prod1, minus, prod2)
+            entry.arrange_submobjects(RIGHT)
+            result_entries.append(entry)
+
+        result = Matrix(result_entries)
+        full_cross_product = Group(
+            cross_product, TexMobject("="), result
+        )
+        full_cross_product.arrange_submobjects()
+        full_cross_product.scale(0.75)
+        full_cross_product.next_to(self.r_h_line, DOWN, buff = MED_BUFF/2)
+        full_cross_product.remove(result)
+        self.play(
+            Write(full_cross_product),
+            Write(syms)
+        )
+        movements = []
+        for e1, e1_target, e2, e2_target in movement_sets:
+            movements += [
+                e1.copy().move_to, e1_target,
+                e2.copy().move_to, e2_target,
+            ]
+        self.play(
+            Write(result.get_brackets()),
+            *movements,
+            run_time = 2
+        )
+        self.dither()
+
+        brace = Brace(cross_product)
+        brace_text = brace.get_text("Only 3d")
+        self.play(
+            GrowFromCenter(brace),
+            Write(brace_text)
+        )
+
+        self.cross_result = result
+        self.only_3d_text = brace_text
+
+    def add_2d_cross_product(self):
+        h_line = DashedLine(ORIGIN, SPACE_WIDTH*RIGHT)
+        h_line.next_to(self.only_3d_text, DOWN, buff = MED_BUFF/2)
+        h_line.to_edge(RIGHT, buff = 0)
+        arrays = np.random.randint(0, 9, (2, 2))
+        m1, m2 = matrices = map(Matrix, arrays)
+        for m in matrices:
+            for e, color in zip(m.get_entries(), [X_COLOR, Y_COLOR]):
+                e.highlight(color)
+        cross_product = Group(m1, TexMobject("\\times"), m2)
+        cross_product.arrange_submobjects()
+        (x1, x2), (x3, x4) = tuple(m1.get_entries()), tuple(m2.get_entries())
+        entries = [x1, x2, x3, x4]
+        for entry in entries:
+            entry.target = entry.copy()
+        eq, dot1, minus, dot2 = syms = map(TexMobject, 
+            ["=", "\\cdot", "-", "\\cdot"]
+        )
+        result = Group(
+            eq, x1.target, dot1, x4.target,
+            minus, x3.target, dot2, x2.target,
+        )
+        result.arrange_submobjects(RIGHT)
+        full_cross_product = Group(cross_product, result)
+        full_cross_product.arrange_submobjects(RIGHT)
+        full_cross_product.next_to(h_line, DOWN, buff = MED_BUFF/2)
+
+        self.play(ShowCreation(h_line))
+        self.play(Write(cross_product))
+        self.play(
+            Write(Group(*syms)),
+            *[
+                Transform(entry.copy(), entry.target)
+                for entry in entries
+            ]
+        )
+        self.dither()
+        self.two_d_result = Group(*result[1:])
+
+    def emphasize_output_type(self):
+        three_d_brace = Brace(self.cross_result)
+        two_d_brace = Brace(self.two_d_result)
+        vector = three_d_brace.get_text("Vector")
+        number = two_d_brace.get_text("Number")
+
+        self.play(
+            GrowFromCenter(three_d_brace),
+            Write(vector)
+        )
+        self.dither()
+        self.play(
+            GrowFromCenter(two_d_brace),
+            Write(number)
+        )
+        self.dither()
+
+class PrereqDeterminant(Scene):
+    def construct(self):
+        title = TextMobject("""
+            Prerequisite: Understanding determinants
+        """)
+        title.scale_to_fit_width(2*SPACE_WIDTH - 2)
+        title.to_edge(UP)
+        rect = Rectangle(width = 16, height = 9, color = BLUE)
+        rect.scale_to_fit_height(6)
+        rect.next_to(title, DOWN)
+
+        self.add(title)
+        self.play(ShowCreation(rect))
+        self.dither()  
+
+class Define2dCrossProduct(LinearTransformationScene):
+    CONFIG = {
+        "show_basis_vectors" : False,
+        "v_coords" : [3, 1],
+        "w_coords" : [2, -1],
+    }
+    def construct(self):
+        self.initial_definition()
+        self.show_transformation()
+        self.transform_square()
+        self.show_orientation_rule()
+
+
+    def initial_definition(self):
+        self.plane.save_state()
+        self.plane.fade()
+        v = self.add_vector(self.v_coords, color = V_COLOR)
+        w = self.add_vector(self.w_coords, color = W_COLOR)
+        self.moving_vectors.remove(v)
+        self.moving_vectors.remove(w)
+        for vect, name in (v, "v"), (w, "w"):
+            color = vect.get_color()
+            vect.label = self.label_vector(vect, name, color = color)
+            vect.coord_array = self.write_vector_coordinates(
+                vect, color = color
+            )
+            vect.coords = vect.coord_array.get_entries()
+        movers = [v.label, w.label, v.coords, w.coords]
+        for mover in movers:
+            mover.target = mover.copy()
+        times = TexMobject("\\times")
+        cross_product = Group(
+            v.label.target, times, w.label.target
+        )
+
+        cross_product.arrange_submobjects()
         matrix = Matrix(np.array([
-            ["x", "y", "z"],
-            ["u_1", "u_2", "u_3"],
-            ["w_1", "w_2", "w_3"],
+            list(v.coords.target),
+            list(w.coords.target)
         ]).T)
-        matrix.highlight_columns(WHITE, U_COLOR, W_COLOR)
         det_text = get_det_text(matrix)
-        det_text.add(matrix)
-        equals_dot = TexMobject(
-            "= %s \\cdot"%input_array_tex, v_tex
+        full_det = Group(det_text, matrix)
+        equals = TexMobject("=")
+        equation = Group(cross_product, equals, full_det)
+        equation.arrange_submobjects()
+        equation.to_corner(UP+LEFT)
+
+        matrix_background = BackgroundRectangle(matrix)
+        cross_background = BackgroundRectangle(cross_product)        
+
+        disclaimer = TextMobject("$^*$ See ``Note on conventions'' in description")
+        disclaimer.scale(0.7)
+        disclaimer.highlight(RED)
+        disclaimer.next_to(
+            det_text.get_corner(UP+RIGHT), RIGHT, buff = 0
         )
-        equals_dot.highlight_by_tex(v_tex, V_COLOR)
-        transform = Group(func, det_text)
-        transform.arrange_submobjects()
+        disclaimer.add_background_rectangle()
+
+        self.play(
+            FadeIn(cross_background),
+            Transform(v.label.copy(), v.label.target),
+            Transform(w.label.copy(), w.label.target),
+            Write(times),
+        )
+        self.dither()
+        self.play(Transform(v.coords.copy(), v.coords.target))
+        self.play(Transform(w.coords.copy(), w.coords.target))
+        self.play(
+            ShowCreation(matrix_background),            
+            Write(matrix.get_brackets()), 
+            Animation(matrix.get_entries()),
+            run_time = 1
+        )
+        matrix.add_to_back(matrix_background)
+        self.dither()
+        self.play(
+            Write(equals),
+            Write(det_text),
+            Animation(matrix),
+        )
+        self.dither()
+        self.play(FadeIn(disclaimer))
+        self.dither()
+        self.play(FadeOut(disclaimer))
+        self.dither()
+
+        self.matrix = matrix
+        self.det_text = det_text
+
+    def show_transformation(self):
+        matrix = self.matrix
+        everything = self.get_mobjects()
+        everything.remove(self.plane)
+        everything.remove(self.background_plane)
+        everything.remove(matrix)
+        self.play(
+            *map(FadeOut, everything) + [
+            Animation(self.background_plane),
+            self.plane.restore,            
+            Animation(matrix),
+        ])
+        side_brace = Brace(matrix, RIGHT)
+        transform_words = side_brace.get_text("Linear transformation")
+        transform_words.add_background_rectangle()
+
+        col1, col2 = [
+            Group(*matrix.get_mob_matrix()[:,i])
+            for i in 0, 1
+        ]
+
+        both_words = []
+        for char, color, col in ("i", X_COLOR, col1), ("j", Y_COLOR, col2):
+            words = TextMobject("Where $\\hat\\%smath$ lands"%char)
+            words.highlight(color)
+            words.add_background_rectangle()
+            words.next_to(col, DOWN, buff = LARGE_BUFF)
+            words.arrow = Arrow(words.get_top(), col.get_bottom(), color = color)
+            both_words.append(words)
+        i_words, j_words = both_words
+
+        self.play(
+            GrowFromCenter(side_brace),
+            Write(transform_words)
+        )
+        self.play(
+            Write(i_words),
+            ShowCreation(i_words.arrow),
+            col1.highlight, X_COLOR
+        )
+        self.dither()
+        self.play(
+            Transform(i_words, j_words),
+            Transform(i_words.arrow, j_words.arrow),
+            col2.highlight, Y_COLOR
+        )
+        self.dither()
+        self.play(*map(FadeOut, [i_words, i_words.arrow]))
+
+        i_hat, j_hat = self.get_basis_vectors()
+        basis_labels = self.get_basis_vector_labels()
+        self.play(
+            ShowCreation(i_hat),
+            ShowCreation(j_hat),
+            Write(basis_labels)
+        )
+        self.dither()
+        self.play(FadeOut(basis_labels))
+        self.add_vector(i_hat)
+        self.add_vector(j_hat)
+        self.play(*map(FadeOut, [side_brace, transform_words]))
+        self.add_foreground_mobject(matrix)
+        self.apply_transposed_matrix([self.v_coords, self.w_coords])
+        self.dither()
+
+
+    def transform_square(self):
+        pass
+
+    def show_orientation_rule(self):
+        pass
+
+
+
+
+
+
+
+
+
+
+
+
+
 
-        vector_word.next_to(transform_word, UP, buff = LARGE_BUFF, aligned_edge = LEFT)
-        cross.next_to(vector_word, buff = MED_BUFF)
-        transform.next_to(transform_word, buff = MED_BUFF)
-        equals_dot.next_to(det_text, DOWN, aligned_edge = LEFT)
 
-        self.add_mobjects_among(locals().values())
-        self.show_frame()
 
 
 

eola/two_d_space.py

@@ -2,7 +2,7 @@ import numpy as np
 
 from scene import Scene
 from mobject import Mobject
-from mobject.vectorized_mobject import VMobject
+from mobject.vectorized_mobject import VMobject, Group
 from mobject.tex_mobject import TexMobject, TextMobject
 from animation import Animation    
 from animation.transform import ApplyPointwiseFunction, Transform, \
@@ -75,7 +75,7 @@ class VectorScene(Scene):
 
     def get_basis_vector_labels(self, **kwargs):
         i_hat, j_hat = self.get_basis_vectors()
-        return [
+        return Group(*[
             self.get_vector_label(
                 vect, label, color = color, 
                 label_scale_factor = 1,
@@ -85,7 +85,7 @@ class VectorScene(Scene):
                 (i_hat, "\\hat{\\imath}", X_COLOR),
                 (j_hat, "\\hat{\\jmath}", Y_COLOR),
             ]
-        ]
+        ])
 
     def get_vector_label(self, vector, label, 
                          direction = "left", 

extract_scene.py

@@ -80,6 +80,7 @@ def get_configuration(sys_argv):
    actions = ["write", "preview", "save_image"]
    if not any([config[key] for key in actions]):
       config["write"] = True   
+   config["skip_animations"] = config["save_image"] and not config["write"]
 
    if len(args) == 0:
       print HELP_MESSAGE
@@ -197,7 +198,8 @@ def main():
    )
    config["movie_prefix"] = config["file"].replace(".py", "")
    scene_kwargs = {
-      "camera_config" : config["camera_config"]
+      "camera_config" : config["camera_config"],
+      "skip_animations" : config["skip_animations"],
    }
    for SceneClass in get_scene_classes(scene_names_to_classes, config):
       for args in get_scene_args(SceneClass, config):

scene/scene.py

@@ -23,6 +23,7 @@ class Scene(object):
         "camera_config"   : {},
         "frame_duration"  : DEFAULT_FRAME_DURATION,
         "construct_args"  : [],
+        "skip_animations" : False,
     }
     def __init__(self, **kwargs):
         digest_config(self, kwargs)
@@ -214,6 +215,9 @@ class Scene(object):
     def play(self, *args, **kwargs):
         if len(args) == 0:
             raise Exception("Called Scene.play with no animations")
+        if self.skip_animations:
+            kwargs["run_time"] = 0
+
         animations = self.compile_play_args_to_animation_list(*args)
         self.num_plays += 1
 
@@ -274,6 +278,8 @@ class Scene(object):
         return self
 
     def dither(self, duration = DEFAULT_DITHER_TIME):
+        if self.skip_animations:
+            return self
         self.update_frame()
         self.frames += [self.get_frame()]*int(duration / self.frame_duration)
         return self

topics/characters.py

@@ -296,11 +296,14 @@ class ThoughtBubble(Bubble):
 
 class RandolphScene(Scene):
     CONFIG = {
-        "randy_mode" : "plain"
+        "randy_kwargs" : {},
+        "randy_corner" : DOWN+LEFT
     }
     def setup(self):
-        self.randy = Randolph(mode = self.randy_mode)
-        self.randy.to_corner()
+        self.randy = Randolph(**self.randy_kwargs)
+        self.randy.to_corner(self.randy_corner)
+        if self.randy_corner[0] > 0:
+            self.randy.flip()
         self.add(self.randy)
 
     def dither(self, time = 1, blink = True):

topics/geometry.py

@@ -313,28 +313,16 @@ class BackgroundRectangle(Rectangle):
         "fill_opacity" : 0.75,
     }
     def __init__(self, mobject, **kwargs):
-        self.lock_style = False
         Rectangle.__init__(self, **kwargs)
-        self.lock_style = True
         self.replace(mobject, stretch = True)
         self.original_fill_opacity = self.fill_opacity
 
     def pointwise_become_partial(self, mobject, a, b):
-        self.lock_style = False
         self.set_fill(opacity = b*self.original_fill_opacity)
-        self.lock_style = True
         return self
 
-    def fade_to(self, *args, **kwargs):
-        self.lock_style = False
-        Rectangle.fade_to(self, *args, **kwargs)
-        self.lock_style = True
-        return self
-
-    def set_style_data(self, *args, **kwargs):
-        if self.lock_style:
-            return self #Do nothing
-        return Rectangle.set_style_data(self, *args, **kwargs)
+    def get_fill_color(self):
+        return Color(self.color)
 
 
 class Grid(VMobject):