More vectorizations conversions

animation/simple_animations.py

@@ -32,13 +32,24 @@ class Rotating(Animation):
 
 
 class ShowPartial(Animation):
+    CONFIG = {
+        "one_submobject_at_a_time" : False
+    }
     def update_mobject(self, alpha):
         pairs = zip(
             self.starting_mobject.submobject_family(),
             self.mobject.submobject_family()
         )
-        for start, mob in pairs:
+        for i, (start, mob) in enumerate(pairs):
-            mob.become_partial(start, *self.get_bounds(alpha))
+            if self.one_submobject_at_a_time:
+                lower = float(i)/len(pairs)
+                upper = float(i+1)/len(pairs)
+                sub_alpha = (alpha-lower)/(upper-lower)
+                sub_alpha = max(0, sub_alpha)
+                sub_alpha = min(1, sub_alpha)
+            else:
+                sub_alpha = alpha
+            mob.become_partial(start, *self.get_bounds(sub_alpha))
 
     def get_bounds(self, alpha):
         raise Exception("Not Implemented")
@@ -48,6 +59,12 @@ class ShowCreation(ShowPartial):
     def get_bounds(self, alpha):
         return (0, alpha)
 
+class ShowCreationPerSubmobject(ShowCreation):
+    CONFIG = {
+        "one_submobject_at_a_time" : True,
+        "run_time" : 3
+    }
+
 class ShowPassingFlash(ShowPartial):
     CONFIG = {
         "time_width" : 0.1

helpers.py

@@ -11,7 +11,6 @@ from scipy import linalg
 
 from constants import *
 
-
 def get_smooth_handle_points(points):
     num_handles = len(points) - 1
     dim = points.shape[1]    

mobject/svg_mobject.py

@@ -184,6 +184,7 @@ class VMobjectFromSVGPathstring(VMobject):
             if not is_closed(points):
                 #Both handles and new anchor are the start
                 new_points = points[[0, 0, 0]]
+            self.mark_paths_closed = True
         self.growing_path.add_control_points(new_points)
 
     def string_to_points(self, coord_string):

mobject/vectorized_mobject.py

@@ -11,7 +11,7 @@ class VMobject(Mobject):
         #Indicates that it will not be displayed, but
         #that it should count in parent mobject's path
         "is_subpath"       : False,
-        "close_new_points" : True,
+        "close_new_points" : False,
         "mark_paths_closed" : False,
     }
     def __init__(self, *args, **kwargs):

topics/functions.py

@@ -1,56 +1,51 @@
 from scipy import integrate
 
-from mobject import Mobject, Mobject1D, Mobject
+from mobject.vectorized_mobject import VMobject
 
 from helpers import *
 
-class FunctionGraph(Mobject1D):
+class FunctionGraph(VMobject):
     CONFIG = {
-        "color" : BLUE,
+        "color" : BLUE_D,
-        "x_min" : -10,
+        "x_min" : -SPACE_WIDTH,
-        "x_max" : 10,
+        "x_max" : SPACE_WIDTH,
-        "spatial_radius" : SPACE_WIDTH,
+        "space_unit_to_num" : 1,
+        "epsilon" : 0.5,
     }
     def __init__(self, function, **kwargs):
         self.function = function
-        Mobject1D.__init__(self, **kwargs)
+        VMobject.__init__(self, **kwargs)
 
     def generate_points(self):
-        numerical_radius = (self.x_max - self.x_min)/2
+        self.set_anchor_points([
-        numerical_center = (self.x_max + self.x_min)/2
+            x*RIGHT + self.function(x)*UP
-        ratio = numerical_radius / self.spatial_radius
+            for pre_x in np.arange(self.x_min, self.x_max, self.epsilon)
-        epsilon = self.epsilon * ratio
+            for x in [self.space_unit_to_num*pre_x]
-        self.add_points([
+        ], mode = "smooth")
-            np.array([(x-numerical_center)/ratio, self.function(x), 0])
-            for x in np.arange(self.x_min, self.x_max, self.epsilon)
-        ])
 
 
-class ParametricFunction(Mobject1D):
+class ParametricFunction(VMobject):
     CONFIG = {
-        "start" : 0,
+        "t_min" : 0,
-        "end"   : 1,
+        "t_max" : 1,
+        "epsilon" : 0.1,
     }
     def __init__(self, function, **kwargs):
         self.function = function
-        Mobject1D.__init__(self, **kwargs)
+        VMobject.__init__(self, **kwargs)
 
     def generate_points(self):
-        integral = integrate.quad(
+        self.set_anchor_points([
-            lambda t : np.linalg.norm(self.function(t)),
+            self.function(t)
-            self.start, self.end
+            for t in np.arange(self.t_min, self.t_max, self.epsilon)
-        )
+        ], mode = "smooth")
-        length = np.linalg.norm(integral)
-        epsilon = self.epsilon / length        
-        t_range = np.arange(self.start, self.end, epsilon)
-        self.add_points([self.function(t) for t in t_range])
 
 
-class Axes(Mobject):
+class Axes(VMobject):
-    def __init__(self, **kwargs):
+    def generate_points(self):
-        x_axis = NumberLine(**kwargs)
+        self.x_axis = NumberLine(**kwargs)
-        y_axis = NumberLine(**kwargs).rotate(np.pi/2, OUT)
+        self.y_axis = NumberLine(**kwargs).rotate(np.pi/2)
-        Mobject.__init__(self, x_axis, y_axis)
+        self.add(self.x_axis, self.y_axis)
 
 
         

topics/geometry.py

@@ -1,13 +1,12 @@
 from helpers import *
 
-from mobject import Mobject, Mobject1D, Point
+from mobject import Mobject
 from mobject.vectorized_mobject import VMobject
 
 class Arc(VMobject):
     CONFIG = {
         "radius"           : 1.0,
         "start_angle"      : 0,
-        "close_new_points" : False,
         "num_anchors"      : 8,
         "anchors_span_full_range" : True
     }
@@ -59,7 +58,6 @@ class Dot(Circle): #Use 1D density, even though 2D
 class Line(VMobject):
     CONFIG = {
         "buff" : 0,
-        "close_new_points" : False,
     }
     def __init__(self, start, end, **kwargs):
         digest_config(self, kwargs)
@@ -171,7 +169,8 @@ class CubicBezier(VMobject):
 class Polygon(VMobject):
     CONFIG = {
         "color" : GREEN_D,
-        "mark_paths_closed" : True
+        "mark_paths_closed" : True,
+        "close_new_points" : True,
     }
     def __init__(self, *vertices, **kwargs):
         assert len(vertices) > 1
@@ -190,7 +189,8 @@ class Rectangle(VMobject):
         "color"  : YELLOW,
         "height" : 2.0,
         "width"  : 4.0,
-        "mark_paths_closed" : True
+        "mark_paths_closed" : True,
+        "close_new_points" : True,
     }
     def generate_points(self):
         y, x = self.height/2, self.width/2

topics/number_line.py

@@ -1,74 +1,61 @@
 from helpers import *
 
 from mobject import Mobject1D
+from mobject.vectorized_mobject import VMobject
 from mobject.tex_mobject import TexMobject
+from topics.geometry import Line, Arrow
 from scene import Scene
 
-class NumberLine(Mobject1D):
+class NumberLine(VMobject):
     CONFIG = {
         "color" : BLUE,
-        "numerical_radius"             : SPACE_WIDTH,
+        "x_min" : -SPACE_WIDTH,
-        "number_at_center"             : 0,
+        "x_max" : SPACE_WIDTH,
-        "unit_length_to_spatial_width" : 1,
+        "space_unit_to_num" : 1,
         "tick_size" : 0.1,
         "tick_frequency" : 0.5,
-        "leftmost_tick"                : None,
+        "leftmost_tick" : None, #Defaults to ceil(x_min)
         "numbers_with_elongated_ticks" : [0],
         "longer_tick_multiple" : 2,
+        "number_at_center" : 0,
     }
     def __init__(self, **kwargs):
         digest_config(self, kwargs)
         if self.leftmost_tick is None:
-            self.leftmost_tick = -int(self.numerical_radius-self.number_at_center)
+            self.leftmost_tick = np.ceil(self.x_min)
-        self.left_num  = self.number_at_center - self.numerical_radius
+        VMobject.__init__(self, **kwargs)
-        self.right_num = self.number_at_center + self.numerical_radius
-        Mobject1D.__init__(self, **kwargs)
 
     def generate_points(self):
-        spatial_radius = self.numerical_radius*self.unit_length_to_spatial_width
+        self.main_line = Line(self.x_min*RIGHT, self.x_max*RIGHT)
-        self.add_points([
+        self.add(self.main_line)
-            (b*x, 0, 0)
+        for x in self.get_tick_numbers():
-            for x in np.arange(0, spatial_radius, self.epsilon)
+            self.add_tick(x, self.tick_size)
-            for b in [-1, 1]
+        for x in self.numbers_with_elongated_ticks:
-        ])
+            self.add_tick(x, self.longer_tick_multiple*self.tick_size)
-        self.index_of_left  = np.argmin(self.points[:,0])
+        self.stretch(self.space_unit_to_num, 0)
-        self.index_of_right = np.argmax(self.points[:,0])
+        self.shift(-self.number_to_point(self.number_at_center))
-        spatial_tick_frequency = self.tick_frequency*self.unit_length_to_spatial_width
+
-        self.add_points([
+    def add_tick(self, x, size):
-            (x, y, 0)
+        self.add(Line(
-            for num in self.get_tick_numbers()
+            x*RIGHT+size*DOWN,
-            for y in np.arange(-self.tick_size, self.tick_size, self.epsilon)
+            x*RIGHT+size*UP,
-            for x in [self.number_to_point(num)[0]]
+        ))
-        ])
+        return self
-        for number in self.numbers_with_elongated_ticks:
-            self.elongate_tick_at(number, self.longer_tick_multiple)
-        self.number_of_points_without_numbers = self.get_num_points()
 
     def get_tick_numbers(self):
-        return np.arange(self.leftmost_tick, self.right_num, self.tick_frequency)
+        return np.arange(self.leftmost_tick, self.x_max, self.tick_frequency)
-
-    def elongate_tick_at(self, number, multiple = 2):
-        x = self.number_to_point(number)[0]
-        self.add_points([
-            [x, y, 0]
-            for y in np.arange(
-                -multiple*self.tick_size, 
-                multiple*self.tick_size,
-                self.epsilon
-            )
-        ])
-        return self
 
     def number_to_point(self, number):
         return interpolate(
-            self.get_left(),
+            self.main_line.get_left(),
-            self.get_right(),
+            self.main_line.get_right(),
-            float(number-self.left_num)/(self.right_num - self.left_num)
+            float(number-self.x_min)/(self.x_max - self.x_min)
         )
 
     def point_to_number(self, point):
-        new_point = point-self.get_center()
+        dist_from_left = (point[0]-self.main_line.get_left()[0])
-        return self.number_at_center + new_point[0]/self.unit_length_to_spatial_width
+        num_dist_from_left = num_dist_from_left/self.space_unit_to_num
+        return self.x_min + dist_from_left
 
     def default_numbers_to_display(self):
         return self.get_tick_numbers()[::2]
@@ -83,11 +70,11 @@ class NumberLine(Mobject1D):
         result = []
         for number in numbers:
             mob = TexMobject(str(int(number)))
-            vert_scale = 2*self.tick_size/mob.get_height()
+            mob.scale_to_fit_height(2*self.tick_size)
-            hori_scale = self.tick_frequency*self.unit_length_to_spatial_width/mob.get_width()
+            mob.shift(
-            mob.scale(min(vert_scale, hori_scale))
+                self.number_to_point(number),
-            mob.shift(self.number_to_point(number))
+                self.get_vertical_number_offset(**kwargs)
-            mob.shift(self.get_vertical_number_offset(**kwargs))
+            )
             result.append(mob)
         return result
 
@@ -100,102 +87,110 @@ class NumberLine(Mobject1D):
 
 class UnitInterval(NumberLine):
     CONFIG = {
-        "numerical_radius"             : 0.5,
+        "x_min" : 0,
-        "unit_length_to_spatial_width" : 2*(SPACE_WIDTH-1),
+        "x_max" : 1,
+        "space_unit_to_num" : 6,
         "tick_frequency" : 0.1,
-        "leftmost_tick"                : 0,
-        "number_at_center"             : 0.5,                 
         "numbers_with_elongated_ticks" : [0, 1],
+        "number_at_center" : 0.5,
     }
 
 
-class NumberPlane(Mobject1D):
+class NumberPlane(VMobject):
     CONFIG = {
-        "color"                    : BLUE,
+        "color" : BLUE_D,
+        "secondary_color" : BLUE_E,
+        "axes_color" : WHITE,
         "x_radius": SPACE_WIDTH,
         "y_radius": SPACE_HEIGHT,
-        "x_unit_to_spatial_width"  : 1,
+        "space_unit_to_x_unit" : 1,
-        "y_unit_to_spatial_height" : 1,
+        "space_unit_to_y_unit" : 1,
         "x_line_frequency" : 1,
-        "x_faded_line_frequency"   : 0.5,
         "y_line_frequency" : 1,
-        "y_faded_line_frequency"   : 0.5,
+        "secondary_line_ratio" : 1,
-        "fade_factor"              : 0.3,
+        "written_coordinate_height" : 0.5,
-        "number_scale_factor"      : 0.25,
+        "written_coordinate_nudge" : 0.1*(DOWN+RIGHT),
-        "num_pair_at_center"       : np.array((0, 0)),
+        "num_pair_at_center" : (0, 0),
     }
     
     def generate_points(self):
-        #TODO, clean this
+        self.axes = VMobject()
-        color = self.color
+        self.main_lines = VMobject()
-        faded = Color(rgb = self.fade_factor*np.array(color.get_rgb()))
+        self.secondary_lines = VMobject()
-
+        tuples = [
-        freq_color_tuples = [
+            (
-            (self.x_line_frequency, self.y_line_frequency, color),
+                self.x_radius, 
-            (self.x_faded_line_frequency, self.y_faded_line_frequency, faded),
+                self.x_line_frequency, 
+                self.y_radius*DOWN, 
+                self.y_radius*UP,
+                RIGHT
+            ),
+            (
+                self.y_radius, 
+                self.y_line_frequency, 
+                self.x_radius*LEFT, 
+                self.x_radius*RIGHT,
+                UP,
+            ),
         ]
-        x_vals = []
+        for radius, freq, start, end, unit in tuples:
-        y_vals = []
+            main_range = np.arange(0, radius, freq)
-        for x_freq, y_freq, color in freq_color_tuples:
+            step = freq/float(freq + self.secondary_line_ratio)
-            if not x_freq or not y_freq:
+            for v in np.arange(0, radius, step):
-                continue
+                line1 = Line(start+v*unit, end+v*unit)
-            x_vals = np.array(filter(lambda x : x not in x_vals, np.arange(
+                line2 = Line(start-v*unit, end-v*unit)                
-                0, self.x_radius,
+                if v == 0:
-                self.x_unit_to_spatial_width*x_freq
+                    self.axes.add(line1)
-            )))
+                elif v in main_range:
-            y_vals = np.array(filter(lambda y : y not in y_vals, np.arange(
+                    self.main_lines.add(line1, line2)
-                0, self.y_radius,
+                else:
-                self.y_unit_to_spatial_height*y_freq
+                    self.secondary_lines.add(line1, line2)
-            )))
+        self.add(self.axes, self.main_lines, self.secondary_lines)
-            x_cont_vals = np.arange(
+        self.stretch(self.space_unit_to_x_unit, 0)
-                0, self.x_radius,
+        self.stretch(self.space_unit_to_y_unit, 1)
-                self.epsilon/self.x_unit_to_spatial_width
-            )
-            y_cont_vals = np.arange(
-                0, self.y_radius,
-                self.epsilon/self.y_unit_to_spatial_height
-            )
-            for x_sgn, y_sgn in it.product([-1, 1], [-1, 1]):
-                self.add_points(
-                    list(it.product(x_sgn*x_vals, y_sgn*y_cont_vals, [0])) + \
-                    list(it.product(x_sgn*x_cont_vals, y_sgn*y_vals, [0])),
-                    color = color
-                )
-        self.shift(self.get_center_point())
-
 
+    def init_colors(self):
+        VMobject.init_colors(self)
+        self.axes.set_stroke(self.axes_color)
+        # self.main_lines.set_stroke(self.color)
+        self.secondary_lines.set_stroke(self.secondary_color, 1)
+        return self
 
     def get_center_point(self):
         return self.num_pair_to_point(self.num_pair_at_center)
 
     def num_pair_to_point(self, pair):
-        pair = pair + self.num_pair_at_center
+        pair = np.array(pair) + self.num_pair_at_center
         result = self.get_center()
-        result[0] += pair[0]*self.x_unit_to_spatial_width
+        result[0] += pair[0]*self.space_unit_to_x_unit
-        result[1] += pair[1]*self.y_unit_to_spatial_height
+        result[1] += pair[1]*self.space_unit_to_y_unit
         return result
 
     def point_to_num_pair(self, point):
         new_point = point-self.get_center()
         center_x, center_y = self.num_pair_at_center
-        x = center_x + point[0]/self.x_unit_to_spatial_width
+        x = center_x + point[0]/self.space_unit_to_x_unit
-        y = center_y + point[1]/self.y_unit_to_spatial_height
+        y = center_y + point[1]/self.space_unit_to_y_unit
         return x, y
 
     def get_coordinate_labels(self, x_vals = None, y_vals = None):
         result = []
-        nudge = 0.1*(DOWN+RIGHT)
         if x_vals == None and y_vals == None:
             x_vals = range(-int(self.x_radius), int(self.x_radius))
             y_vals = range(-int(self.y_radius), int(self.y_radius))
-        for index, vals in zip([0, 1], [x_vals, y_vals]):
+        for index, vals in enumerate([x_vals, y_vals]):
             num_pair = [0, 0]
             for val in vals:
                 num_pair[index] = val
                 point = self.num_pair_to_point(num_pair)
                 num = TexMobject(str(val))
-                num.scale(self.number_scale_factor)
+                num.scale_to_fit_height(
-                num.shift(point-num.get_corner(UP+LEFT)+nudge)
+                    self.written_coordinate_height
+                )
+                num.shift(
+                    point-num.get_corner(UP+LEFT),
+                    self.written_coordinate_nudge
+                )
                 result.append(num)
         return result
 
@@ -204,134 +199,15 @@ class NumberPlane(Mobject1D):
         return self
 
     def get_vector(self, coords, **kwargs):
-        if len(coords) == 2:
+        point = coords[0]*RIGHT + coords[1]*UP
-            coords = tuple(list(coords) + [0])
         arrow = Arrow(ORIGIN, coords, **kwargs)
-        arrow.remove_tip()
-        arrow.align_data(Line(ORIGIN, SPACE_WIDTH*LEFT))
-        arrow.add_tip()
         return arrow
 
-
+    def prepare_for_nonlinear_transform(self):
-class XYZAxes(Mobject1D):
+        for mob in self.submobject_family():
-    CONFIG = {
+            if mob.get_num_points() > 0:
-        "color"          : TEAL,
+                mob.insert_n_anchor_points(20)
-        "radius"         : SPACE_HEIGHT,
+                mob.change_anchor_mode("smooth")
-        "tick_frequency" : 1,
-    }
-    def generate_points(self):
-        self.x_axis = NumberLine(
-            numerical_radius = self.radius,
-            tick_frequency = self.tick_frequency
-        )
-        self.y_axis = self.x_axis.copy().rotate(np.pi/2, OUT)
-        self.z_axis = self.x_axis.copy().rotate(np.pi/2, DOWN)
-        self.digest_mobject_attrs()
-
-
-
-class SpaceGrid(Mobject1D):
-    CONFIG = {
-        "color"                  : GREEN,
-        "radius"                 : SPACE_HEIGHT,
-        "unit_to_spatial_length" : 1,
-        "line_frequency"         : 2,
-    }
-    def generate_points(self):
-        line_range = range(-int(self.radius), int(self.radius)+1, self.line_frequency)
-        for i in range(3):
-            perm = np.arange(i, i+3) % 3
-            for a, b in it.product(line_range, line_range):
-                start = np.array([a, b, -self.radius])[perm]
-                end   = np.array([a, b, self.radius])[perm]
-                self.add_line(start, end)
-        self.pose_at_angle()
-
-
-
-class NumberLineScene(Scene):
-    def construct(self, **number_line_config):
-        self.number_line = NumberLine(**number_line_config)
-        self.displayed_numbers = self.number_line.default_numbers_to_display()
-        self.number_mobs = self.number_line.get_number_mobjects(*self.displayed_numbers)
-        self.add(self.number_line, *self.number_mobs)
-
-    def zoom_in_on(self, number, zoom_factor, run_time = 2.0):
-        unit_length_to_spatial_width = self.number_line.unit_length_to_spatial_width*zoom_factor
-        radius = SPACE_WIDTH/unit_length_to_spatial_width
-        tick_frequency = 10**(np.floor(np.log10(radius)))
-        left_tick = tick_frequency*(np.ceil((number-radius)/tick_frequency))
-        new_number_line = NumberLine(
-            numerical_radius = radius,
-            unit_length_to_spatial_width = unit_length_to_spatial_width,
-            tick_frequency = tick_frequency,
-            leftmost_tick = left_tick,
-            number_at_center = number
-        )
-        new_displayed_numbers = new_number_line.default_numbers_to_display()
-        new_number_mobs = new_number_line.get_number_mobjects(*new_displayed_numbers)        
-
-        transforms = []
-        additional_mobjects = []
-        squished_new_line = new_number_line.copy()
-        squished_new_line.scale(1.0/zoom_factor)
-        squished_new_line.shift(self.number_line.number_to_point(number))
-        squished_new_line.points[:,1] = self.number_line.number_to_point(0)[1]
-        transforms.append(Transform(squished_new_line, new_number_line))
-        for mob, num in zip(new_number_mobs, new_displayed_numbers):
-            point = Point(self.number_line.number_to_point(num))
-            point.shift(new_number_line.get_vertical_number_offset())
-            transforms.append(Transform(point, mob))
-        for mob in self.mobjects:
-            if mob == self.number_line:
-                new_mob = mob.copy()
-                new_mob.shift(-self.number_line.number_to_point(number))
-                new_mob.stretch(zoom_factor, 0)
-                transforms.append(Transform(mob, new_mob))
-                continue
-            mob_center = mob.get_center()
-            number_under_center = self.number_line.point_to_number(mob_center)
-            new_point = new_number_line.number_to_point(number_under_center)
-            new_point += mob_center[1]*UP
-            if mob in self.number_mobs:
-                transforms.append(Transform(mob, Point(new_point)))
-            else:
-                transforms.append(ApplyMethod(mob.shift, new_point - mob_center))
-                additional_mobjects.append(mob)
-        line_to_hide_pixelation = Line(
-            self.number_line.get_left(),
-            self.number_line.get_right(),
-            color = self.number_line.get_color()
-        )
-        self.add(line_to_hide_pixelation)
-        self.play(*transforms, run_time = run_time)
-        self.clear()
-        self.number_line = new_number_line
-        self.displayed_numbers = new_displayed_numbers
-        self.number_mobs = new_number_mobs
-        self.add(self.number_line, *self.number_mobs)
-        self.add(*additional_mobjects)
-
-    def show_multiplication(self, num, **kwargs):
-        if "path_func" not in kwargs:
-            if num > 0:
-                kwargs["path_func"] = straight_path
-            else:
-                kwargs["path_func"] = counterclockwise_path()
-        self.play(*[
-            ApplyMethod(self.number_line.stretch, num, 0, **kwargs)
-        ]+[
-            ApplyMethod(mob.shift, (num-1)*mob.get_center()[0]*RIGHT, **kwargs)
-            for mob in self.number_mobs
-        ])
-
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-
-
-
-
-
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