Merge pull request #129 from 3b1b/uncertainty

Uncertainty

active_projects/fourier.py

@@ -32,6 +32,7 @@ from topics.graph_scene import *
 
 USE_ALMOST_FOURIER_BY_DEFAULT = True
 NUM_SAMPLES_FOR_FFT = 1000
+DEFAULT_COMPLEX_TO_REAL_FUNC = lambda z : z.real
 
 
 def get_fourier_graph(
@@ -53,7 +54,7 @@ def get_fourier_graph(
     graph = VMobject()
     graph.set_points_smoothly([
         axes.coords_to_point(
-            x, 200.0*complex_to_real_func(y)/n_samples,
+            x, complex_to_real_func(y)/n_samples,
         )
         for x, y in zip(frequencies, fft_output[:n_samples//2])
     ])
@@ -62,18 +63,17 @@ def get_fourier_graph(
 
 def get_fourier_transform(
     func, t_min, t_max, 
-    complex_to_real_func = lambda z : z.real,
+    complex_to_real_func = DEFAULT_COMPLEX_TO_REAL_FUNC,
     use_almost_fourier = USE_ALMOST_FOURIER_BY_DEFAULT,
+    **kwargs ##Just eats these
     ):
     scalar = 1./(t_max - t_min) if use_almost_fourier else 1.0
     def fourier_transform(f):
-        return scalar*scipy.integrate.quad(
-            lambda t : complex_to_real_func(
-                # f(t) e^{-TAU*i*f*t}
-                func(t)*np.exp(complex(0, -TAU*f*t))
-            ),
+        z = scalar*scipy.integrate.quad(
+            lambda t : func(t)*np.exp(complex(0, -TAU*f*t)),
             t_min, t_max
         )[0]
+        return complex_to_real_func(z)
     return fourier_transform
 
 ##
@@ -939,11 +939,28 @@ class FourierMachineScene(Scene):
         if not hasattr(self, "frequency_axes"):
             self.get_frequency_axes()
         func = time_graph.underlying_function
-        t_min = self.time_axes.x_min
-        t_max = self.time_axes.x_max
+        t_axis = self.time_axes.x_axis
+        t_min = t_axis.point_to_number(time_graph.points[0])
+        t_max = t_axis.point_to_number(time_graph.points[-1])
+        f_max = self.frequency_axes.x_max
+        # result = get_fourier_graph(
+        #     self.frequency_axes, func, t_min, t_max,
+        #     **kwargs
+        # )
+        # too_far_right_point_indices = [
+        #     i
+        #     for i, point in enumerate(result.points)
+        #     if self.frequency_axes.x_axis.point_to_number(point) > f_max
+        # ]
+        # if too_far_right_point_indices:
+        #     i = min(too_far_right_point_indices)
+        #     prop = float(i)/len(result.points)
+        #     result.pointwise_become_partial(result, 0, prop)
+        # return result
         return self.frequency_axes.get_graph(
             get_fourier_transform(func, t_min, t_max, **kwargs),
             color = self.center_of_mass_color,
+            **kwargs
         )
 
     def get_polarized_mobject(self, mobject, freq = 1.0):
@@ -999,7 +1016,8 @@ class FourierMachineScene(Scene):
         vector = Vector(UP, color = WHITE)
         graph_copy = graph.copy()
         x_axis = self.time_axes.x_axis
-        x_min, x_max = x_axis.x_min, x_axis.x_max
+        x_min = x_axis.point_to_number(graph.points[0])
+        x_max = x_axis.point_to_number(graph.points[-1])
         def update_vector(vector, alpha):
             x = interpolate(x_min, x_max, alpha)
             vector.put_start_and_end_on(
@@ -1016,7 +1034,13 @@ class FourierMachineScene(Scene):
         origin = self.circle_plane.coords_to_point(0, 0)
         graph_copy = polarized_graph.copy()
         def update_vector(vector, alpha):
-            point = graph_copy.point_from_proportion(alpha)
+            # Not sure why this is needed, but without smoothing 
+            # out the alpha like this, the vector would occasionally
+            # jump around
+            point = center_of_mass([
+                graph_copy.point_from_proportion(alpha+d)
+                for d in np.linspace(-0.001, 0.001, 5)
+            ])
             vector.put_start_and_end_on_with_projection(origin, point)
             return vector
         return UpdateFromAlphaFunc(vector, update_vector, **config)
@@ -1299,6 +1323,7 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
     CONFIG = {
         "initial_winding_frequency" : 3.0,
         "center_of_mass_color" : RED,
+        "center_of_mass_multiple" : 1,
     }
     def construct(self):
         self.remove(self.pi_creature)
@@ -1581,10 +1606,11 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
 
     def get_pol_graph_center_of_mass(self):
         pg = self.graph.polarized_mobject
-        result = center_of_mass([
-            pg.point_from_proportion(alpha)
-            for alpha in np.linspace(0, 1, 1000)
-        ])
+        result = center_of_mass(pg.get_anchors())
+        if self.center_of_mass_multiple != 1:
+            mult = self.center_of_mass_multiple
+            origin = self.circle_plane.coords_to_point(0, 0)
+            result = mult*(result - origin) + origin
         return result
 
     def generate_fourier_dot_transform(self, fourier_graph):
@@ -1626,7 +1652,7 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
 
     def change_frequency(self, new_freq, **kwargs):
         kwargs["run_time"] = kwargs.get("run_time", 3)
-        kwargs["rate_func"] = kwargs.get(
+        rate_func = kwargs.pop(
             "rate_func", bezier([0, 0, 1, 1])
         )
         added_anims = kwargs.get("added_anims", [])
@@ -1645,6 +1671,8 @@ class DrawFrequencyPlot(WrapCosineGraphAroundCircle, PiCreatureScene):
             anims.append(self.fourier_graph_dot_anim)
         if hasattr(self, "fourier_graph_drawing_update_anim"):
             anims.append(self.fourier_graph_drawing_update_anim)
+        for anim in anims:
+            anim.rate_func = rate_func
         anims += added_anims
         self.play(*anims, **kwargs)
 

camera/camera.py

@@ -30,7 +30,7 @@ class Camera(object):
         "max_allowable_norm" : 2*SPACE_WIDTH,
         "image_mode" : "RGBA",
         "n_rgb_coords" : 4,
-        "background_alpha" : 0, #Out of color_max_val
+        "background_alpha" : 0, #Out of rgb_max_val
         "pixel_array_dtype" : 'uint8',
         "use_z_coordinate_for_display_order" : False,
         # z_buff_func is only used if the flag above is set to True.
@@ -40,7 +40,7 @@ class Camera(object):
 
     def __init__(self, background = None, **kwargs):
         digest_config(self, kwargs, locals())
-        self.color_max_val = np.iinfo(self.pixel_array_dtype).max
+        self.rgb_max_val = np.iinfo(self.pixel_array_dtype).max
         self.init_background()
         self.resize_space_shape()
         self.reset()
@@ -92,7 +92,7 @@ class Camera(object):
         retval = np.array(pixel_array)
         if convert_from_floats:
             retval = np.apply_along_axis(
-                lambda f : (f * self.color_max_val).astype(self.pixel_array_dtype),
+                lambda f : (f * self.rgb_max_val).astype(self.pixel_array_dtype),
                 2,
                 retval)
         return retval
@@ -177,29 +177,30 @@ class Camera(object):
 
     def capture_mobjects(self, mobjects, **kwargs):
         mobjects = self.get_mobjects_to_display(mobjects, **kwargs)
-        vmobjects = []
-        for mobject in mobjects:
-            if isinstance(mobject, VMobject):
-                 vmobjects.append(mobject)
-            elif len(vmobjects) > 0:
-                self.display_multiple_vectorized_mobjects(vmobjects)
-                vmobjects = []
-                
-            if isinstance(mobject, PMobject):
-                self.display_point_cloud(
-                    mobject.points, mobject.rgbas, 
-                    self.adjusted_thickness(mobject.stroke_width)
-                )
-            elif isinstance(mobject, ImageMobject):
-                self.display_image_mobject(mobject)
-            elif isinstance(mobject, Mobject):
-                pass #Remainder of loop will handle submobjects
-            else:
-                raise Exception(
-                    "Unknown mobject type: " + mobject.__class__.__name__
-                )
-            #TODO, more?  Call out if it's unknown?
-        self.display_multiple_vectorized_mobjects(vmobjects)
+
+        # Organize this list into batches of the same type, and 
+        # apply corresponding function to those batches
+        type_func_pairs = [
+            (VMobject, self.display_multiple_vectorized_mobjects),
+            (PMobject,  self.display_multiple_point_cloud_mobjects),
+            (ImageMobject,  self.display_multiple_image_mobjects),
+            (Mobject, lambda batch : batch), #Do nothing
+        ]
+        def get_mobject_type(mobject):
+            for mobject_type, func in type_func_pairs:
+                if isinstance(mobject, mobject_type):
+                    return mobject_type
+            raise Exception(
+                "Trying to display something which is not of type Mobject"
+            )
+        batch_type_pairs = batch_by_property(mobjects, get_mobject_type)
+
+        #Display in these batches
+        for batch, batch_type in batch_type_pairs:
+            #check what the type is, and call the appropriate function
+            for mobject_type, func in type_func_pairs:
+                if batch_type == mobject_type:
+                    func(batch)
 
     ## Methods associated with svg rendering
 
@@ -215,12 +216,12 @@ class Camera(object):
     def display_multiple_vectorized_mobjects(self, vmobjects):
         if len(vmobjects) == 0:
             return
-        batches = batch_by_property(
+        batch_file_pairs = batch_by_property(
             vmobjects, 
             lambda vm : vm.get_background_image_file()
         )
-        for batch in batches:
-            if batch[0].get_background_image_file():
+        for batch, file_name in batch_file_pairs:
+            if file_name:
                 self.display_multiple_background_colored_vmobject(batch)
             else:
                 self.display_multiple_non_background_colored_vmobjects(batch)
@@ -252,7 +253,7 @@ class Camera(object):
             stroke_hex = rgb_to_hex(stroke_rgb)
             pen = aggdraw.Pen(stroke_hex, stroke_width)
 
-        fill_opacity = int(self.color_max_val*vmobject.get_fill_opacity())
+        fill_opacity = int(self.rgb_max_val*vmobject.get_fill_opacity())
         if fill_opacity == 0:
             fill = None
         else:
@@ -305,13 +306,19 @@ class Camera(object):
     def display_multiple_background_colored_vmobject(self, cvmobjects):
         displayer = self.get_background_colored_vmobject_displayer()
         cvmobject_pixel_array = displayer.display(*cvmobjects)
-        self.pixel_array[:,:] = np.maximum(
-            self.pixel_array, cvmobject_pixel_array
-        )
+        self.overlay_rgba_array(cvmobject_pixel_array)
         return self
 
     ## Methods for other rendering
 
+    def display_multiple_point_cloud_mobjects(self, pmobjects):
+        for pmobject in pmobjects:
+            self.display_point_cloud(
+                pmobject.points,
+                pmobject.rgbas,
+                self.adjusted_thickness(pmobject.stroke_width)
+            )
+
     def display_point_cloud(self, points, rgbas, thickness):
         if len(points) == 0:
             return
@@ -322,7 +329,7 @@ class Camera(object):
         )
         rgba_len = self.pixel_array.shape[2]
 
-        rgbas = (self.color_max_val*rgbas).astype(self.pixel_array_dtype)
+        rgbas = (self.rgb_max_val*rgbas).astype(self.pixel_array_dtype)
         target_len = len(pixel_coords)
         factor = target_len/len(rgbas)
         rgbas = np.array([rgbas]*factor).reshape((target_len, rgba_len))
@@ -342,6 +349,10 @@ class Camera(object):
         new_pa[indices] = rgbas
         self.pixel_array = new_pa.reshape((ph, pw, rgba_len))
 
+    def display_multiple_image_mobjects(self, image_mobjects):
+        for image_mobject in image_mobjects:
+            self.display_image_mobject(image_mobject)
+
     def display_image_mobject(self, image_mobject):
         corner_coords = self.points_to_pixel_coords(image_mobject.points)
         ul_coords, ur_coords, dl_coords = corner_coords
@@ -410,17 +421,23 @@ class Camera(object):
         self.overlay_rgba_array(image)
 
     def overlay_rgba_array(self, arr):
-        # """ Overlays arr onto self.pixel_array with relevant alphas"""
-        bg, fg = fdiv(self.pixel_array, self.color_max_val), fdiv(arr, self.color_max_val)
-        bga, fga = [arr[:,:,3:] for arr in bg, fg]
-        alpha_sum = fga + (1-fga)*bga
-        with np.errstate(divide = 'ignore', invalid='ignore'):
-            bg[:,:,:3] = reduce(op.add, [
-                np.divide(fg[:,:,:3]*fga, alpha_sum),
-                np.divide(bg[:,:,:3]*(1-fga)*bga, alpha_sum),
-            ])
-        bg[:,:,3:] = 1 - (1 - bga)*(1 - fga)
-        self.pixel_array = (self.color_max_val*bg).astype(self.pixel_array_dtype)
+        fg = arr
+        bg = self.pixel_array
+        # rgba_max_val = self.rgb_max_val
+        src_rgb, src_a, dst_rgb, dst_a = [
+            a.astype(np.float32)/self.rgb_max_val
+            for a in fg[...,:3], fg[...,3], bg[...,:3], bg[...,3]
+        ]
+
+        out_a = src_a + dst_a*(1.0-src_a)
+        out_rgb = fdiv(
+            src_rgb*src_a[..., None] + \
+            dst_rgb*dst_a[..., None]*(1.0-src_a[..., None]),
+            out_a[..., None]
+        )
+
+        self.pixel_array[..., :3] = out_rgb*self.rgb_max_val
+        self.pixel_array[..., 3] = out_a*self.rgb_max_val
 
     def align_points_to_camera(self, points):
         ## This is where projection should live
@@ -537,8 +554,7 @@ class BackgroundColoredVMobjectDisplayer(object):
         mode = "RGBA" if pixel_array.shape[2] == 4 else "RGB"
         return self.resize_background_array(background_array, width, height, mode)
 
-    def get_background_array(self, cvmobject):
-        file_name = cvmobject.get_background_image_file()
+    def get_background_array(self, file_name):
         if file_name in self.file_name_to_pixel_array_map:
             return self.file_name_to_pixel_array_map[file_name]
         full_path = get_full_raster_image_path(file_name)
@@ -553,12 +569,12 @@ class BackgroundColoredVMobjectDisplayer(object):
         return array
 
     def display(self, *cvmobjects):
-        batches = batch_by_property(
+        batch_image_file_pairs = batch_by_property(
             cvmobjects, lambda cv : cv.get_background_image_file()
         )
         curr_array = None
-        for batch in batches:
-            background_array = self.get_background_array(batch[0])
+        for batch, image_file in batch_image_file_pairs:
+            background_array = self.get_background_array(image_file)
             for cvmobject in batch:
                 self.camera.display_vectorized(cvmobject, self.canvas)
             self.canvas.flush()

helpers.py

@@ -227,22 +227,30 @@ def adjacent_pairs(objects):
     return zip(objects, list(objects[1:])+[objects[0]])
 
 def batch_by_property(items, property_func):
-    batches = []
-    def add_batch(batch):
+    """
+    Takes in a list, and returns a list of tuples, (batch, prop)
+    such that all items in a batch have the same output when
+    put into property_func, and such that chaining all these
+    batches together would give the original list.
+    """
+    batch_prop_pairs = []
+    def add_batch_prop_pair(batch):
         if len(batch) > 0:
-            batches.append(batch)
+            batch_prop_pairs.append(
+                (batch, property_func(batch[0]))
+            )
     curr_batch = []
     curr_prop = None
     for item in items:
         prop = property_func(item)
         if prop != curr_prop:
-            add_batch(curr_batch)
+            add_batch_prop_pair(curr_batch)
             curr_prop = prop
             curr_batch = [item]
         else:
             curr_batch.append(item)
-    add_batch(curr_batch)
-    return batches
+    add_batch_prop_pair(curr_batch)
+    return batch_prop_pairs
 
 def complex_to_R3(complex_num):
     return np.array((complex_num.real, complex_num.imag, 0))

mobject/tex_mobject.py

@@ -141,9 +141,15 @@ class TexMobject(SVGMobject):
         self.submobjects = new_submobjects
         return self
 
-    def get_parts_by_tex(self, tex, substring = True):
+    def get_parts_by_tex(self, tex, substring = True, case_sensitive = True):
         def test(tex1, tex2):
-            return tex1 == tex2 or (substring and tex1 in tex2)
+            if not case_sensitive:
+                tex1 = tex1.lower()
+                tex2 = tex2.lower()
+            if substring:
+                return tex1 in tex2
+            else:
+                return tex1 == tex2
 
         tex_submobjects = filter(
             lambda m : isinstance(m, TexMobject),

mobject/vectorized_mobject.py

@@ -122,7 +122,7 @@ class VMobject(Mobject):
         return self
 
     def get_fill_rgb(self):
-        return self.fill_rgb
+        return np.clip(self.fill_rgb, 0, 1)
 
     def get_fill_color(self):
         try:
@@ -135,7 +135,7 @@ class VMobject(Mobject):
         return np.clip(self.fill_opacity, 0, 1)
 
     def get_stroke_rgb(self):
-        return self.stroke_rgb
+        return np.clip(self.stroke_rgb, 0, 1)
 
     def get_stroke_color(self):
         try:

old_projects/eoc/chapter2.py

@@ -35,90 +35,6 @@ VELOCITY_COLOR = GREEN
 #### Warning, scenes here not updated based on most recent GraphScene changes #######
 
 
-class Car(SVGMobject):
-    CONFIG = {
-        "file_name" : "Car", 
-        "height" : 1,
-        "color" : "#BBBBBB",
-    }
-    def __init__(self, **kwargs):
-        SVGMobject.__init__(self, **kwargs)
-        self.scale_to_fit_height(self.height)
-        self.set_stroke(color = WHITE, width = 0)
-        self.set_fill(self.color, opacity = 1)
-
-        randy = Randolph(mode = "happy")
-        randy.scale_to_fit_height(0.6*self.get_height())
-        randy.stretch(0.8, 0)
-        randy.look(RIGHT)
-        randy.move_to(self)
-        randy.shift(0.07*self.height*(RIGHT+UP))
-        self.randy = randy
-        self.add_to_back(randy)
-
-        orientation_line = Line(self.get_left(), self.get_right())
-        orientation_line.set_stroke(width = 0)
-        self.add(orientation_line)
-        self.orientation_line = orientation_line
-
-        self.add_treds_to_tires()
-
-    def move_to(self, point_or_mobject):
-        vect = rotate_vector(
-            UP+LEFT, self.orientation_line.get_angle()
-        )
-        self.next_to(point_or_mobject, vect, buff = 0)
-        return self
-
-    def get_front_line(self):
-        return DashedLine(
-            self.get_corner(UP+RIGHT), 
-            self.get_corner(DOWN+RIGHT),
-            color = DISTANCE_COLOR,
-            dashed_segment_length = 0.05,
-        )
-
-    def add_treds_to_tires(self):
-        for tire in self.get_tires():
-            radius = tire.get_width()/2
-            center = tire.get_center()
-            tred = Line(
-                0.9*radius*RIGHT, 1.4*radius*RIGHT,
-                stroke_width = 2,
-                color = BLACK
-            )
-            tred.rotate_in_place(np.pi/4)
-            for theta in np.arange(0, 2*np.pi, np.pi/4):
-                new_tred = tred.copy()
-                new_tred.rotate(theta)
-                new_tred.shift(center)
-                tire.add(new_tred)
-        return self
-
-    def get_tires(self):
-        return VGroup(self[1][1], self[1][3])
-
-class MoveCar(ApplyMethod):
-    CONFIG = {
-        "moving_forward" : True,
-    }
-    def __init__(self, car, target_point, **kwargs):
-        ApplyMethod.__init__(self, car.move_to, target_point, **kwargs)
-        displacement = self.target_mobject.get_right()-self.starting_mobject.get_right()
-        distance = np.linalg.norm(displacement)
-        if not self.moving_forward:
-            distance *= -1
-        tire_radius = car.get_tires()[0].get_width()/2
-        self.total_tire_radians = -distance/tire_radius
-
-    def update_mobject(self, alpha):
-        ApplyMethod.update_mobject(self, alpha)
-        if alpha == 0:
-            return
-        radians = alpha*self.total_tire_radians
-        for tire in self.mobject.get_tires():
-            tire.rotate_in_place(radians)
-
 class IncrementNumber(Succession):
     CONFIG = {
         "start_num" : 0,

topics/number_line.py

@@ -219,7 +219,29 @@ class Axes(VGroup):
         return graph
 
     def input_to_graph_point(self, x, graph):
-        return self.coords_to_point(x, graph.underlying_function(x))
+        if hasattr(graph, "underlying_function"):
+            return self.coords_to_point(x, graph.underlying_function(x))
+        else:
+            #binary search
+            lh, rh = 0, 1
+            while abs(lh - rh) > 0.001:
+                mh = np.mean([lh, rh])
+                hands = [lh, mh, rh]
+                points = map(graph.point_from_proportion, hands)
+                lx, mx, rx = map(self.x_axis.point_to_number, points)
+                if lx <= x and rx >= x:
+                    if mx > x:
+                        rh = mh
+                    else:
+                        lh = mh
+                elif lx <= x and rx <= x:
+                    return points[2]
+                elif lx >= x and rx >= x:
+                    return points[0]
+                elif lx > x and rx < x:
+                    lh, rh = rh, lh
+            return points[1]
+
 
 class ThreeDAxes(Axes):
     CONFIG = {

topics/objects.py

@@ -486,6 +486,104 @@ class ThoughtBubble(Bubble):
         self.submobjects[-1].set_fill(GREEN_SCREEN, opacity = 1)
         return self
 
+class Car(SVGMobject):
+    CONFIG = {
+        "file_name" : "Car", 
+        "height" : 1,
+        "color" : LIGHT_GREY,
+        "light_colors" : [BLACK, BLACK],
+    }
+    def __init__(self, **kwargs):
+        SVGMobject.__init__(self, **kwargs)
+        self.scale_to_fit_height(self.height)
+        self.set_stroke(color = WHITE, width = 0)
+        self.set_fill(self.color, opacity = 1)
+
+        from topics.characters import Randolph
+        randy = Randolph(mode = "happy")
+        randy.scale_to_fit_height(0.6*self.get_height())
+        randy.stretch(0.8, 0)
+        randy.look(RIGHT)
+        randy.move_to(self)
+        randy.shift(0.07*self.height*(RIGHT+UP))
+        self.randy = self.pi_creature = randy
+        self.add_to_back(randy)
+
+        orientation_line = Line(self.get_left(), self.get_right())
+        orientation_line.set_stroke(width = 0)
+        self.add(orientation_line)
+        self.orientation_line = orientation_line
+
+        for light, color in zip(self.get_lights(), self.light_colors):
+            light.set_fill(color, 1)
+            light.is_subpath = False
+
+        self.add_treds_to_tires()
+
+    def move_to(self, point_or_mobject):
+        vect = rotate_vector(
+            UP+LEFT, self.orientation_line.get_angle()
+        )
+        self.next_to(point_or_mobject, vect, buff = 0)
+        return self
+
+    def get_front_line(self):
+        return DashedLine(
+            self.get_corner(UP+RIGHT), 
+            self.get_corner(DOWN+RIGHT),
+            color = DISTANCE_COLOR,
+            dashed_segment_length = 0.05,
+        )
+
+    def add_treds_to_tires(self):
+        for tire in self.get_tires():
+            radius = tire.get_width()/2
+            center = tire.get_center()
+            tred = Line(
+                0.9*radius*RIGHT, 1.4*radius*RIGHT,
+                stroke_width = 2,
+                color = BLACK
+            )
+            tred.rotate_in_place(np.pi/4)
+            for theta in np.arange(0, 2*np.pi, np.pi/4):
+                new_tred = tred.copy()
+                new_tred.rotate(theta, about_point = ORIGIN)
+                new_tred.shift(center)
+                tire.add(new_tred)
+        return self
+
+    def get_tires(self):
+        return VGroup(self[1][1], self[1][3])
+
+    def get_lights(self):
+        return VGroup(self.get_front_light(), self.get_rear_light())
+
+    def get_front_light(self):
+        return self[1][5]
+
+    def get_rear_light(self):
+        return self[1][8]
+
+class MoveCar(ApplyMethod):
+    CONFIG = {
+        "moving_forward" : True,
+    }
+    def __init__(self, car, target_point, **kwargs):
+        ApplyMethod.__init__(self, car.move_to, target_point, **kwargs)
+        displacement = self.target_mobject.get_right()-self.starting_mobject.get_right()
+        distance = np.linalg.norm(displacement)
+        if not self.moving_forward:
+            distance *= -1
+        tire_radius = car.get_tires()[0].get_width()/2
+        self.total_tire_radians = -distance/tire_radius
+
+    def update_mobject(self, alpha):
+        ApplyMethod.update_mobject(self, alpha)
+        if alpha == 0:
+            return
+        radians = alpha*self.total_tire_radians
+        for tire in self.mobject.get_tires():
+            tire.rotate_in_place(radians)
 
 #TODO: Where should this live?
 class Broadcast(LaggedStart):