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GraphScene refactor that will definitively mess up existing chapter1 and chapter2 GraphScene animations

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This commit is contained in:
Grant Sanderson 2017-01-24 16:21:35 -08:00
parent ebd825a3a2
commit 7dbbcf82ff
3 changed files with 137 additions and 62 deletions
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2
eoc/chapter1.py
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@ -26,6 +26,8 @@ from mobject.tex_mobject import *
from eoc.graph_scene import GraphScene
#### Warning, scenes here not updated based on most recent GraphScene changes #######
class CircleScene(PiCreatureScene):
CONFIG = {
"radius" : 1.5,

4
eoc/chapter2.py
View file

@ -31,6 +31,10 @@ DISTANCE_COLOR = BLUE
TIME_COLOR = YELLOW
VELOCITY_COLOR = GREEN
#### Warning, scenes here not updated based on most recent GraphScene changes #######
class Car(SVGMobject):
CONFIG = {
"file_name" : "Car",

193
eoc/graph_scene.py
View file

@ -4,7 +4,8 @@ from scene import Scene
# from topics.geometry import
from mobject.tex_mobject import TexMobject, TextMobject
from mobject.vectorized_mobject import VGroup, VectorizedPoint
from animation.simple_animations import Write, ShowCreation
from animation.simple_animations import Write, ShowCreation, UpdateFromAlphaFunc
from animation.transform import Transform
from topics.number_line import NumberLine
from topics.functions import ParametricFunction
from topics.geometry import Rectangle, DashedLine, Line
@ -17,22 +18,23 @@ class GraphScene(Scene):
"x_tick_frequency" : 1,
"x_leftmost_tick" : None, #Change if different from x_min
"x_labeled_nums" : range(1, 10),
"x_axis_label" : "x",
"x_axis_label" : "$x$",
"y_min" : -1,
"y_max" : 10,
"y_axis_height" : 6,
"y_tick_frequency" : 1,
"y_bottom_tick" : None, #Change if different from y_min
"y_labeled_nums" : range(1, 10),
"y_axis_label" : "y",
"y_axis_label" : "$y$",
"axes_color" : GREY,
"graph_origin" : 2.5*DOWN + 4*LEFT,
"y_axis_numbers_nudge" : 0.4*UP+0.5*LEFT,
"num_graph_anchor_points" : 25,
"default_graph_colors" : [BLUE, GREEN, YELLOW],
"default_derivative_color" : RED,
"default_derivative_color" : GREEN,
"default_input_color" : YELLOW,
}
def setup_axes(self, animate = True):
def setup_axes(self, animate = False):
x_num_range = float(self.x_max - self.x_min)
self.space_unit_to_x = self.x_axis_width/x_num_range
x_axis = NumberLine(
@ -88,11 +90,7 @@ class GraphScene(Scene):
result += self.y_axis.number_to_point(y)[1]*UP
return result
def graph_function(self, func,
color = None,
animate = False,
is_main_graph = True,
):
def get_graph(self, func, color = None):
if color is None:
color = self.default_graph_colors.next()
@ -106,77 +104,69 @@ class GraphScene(Scene):
num_anchor_points = self.num_graph_anchor_points,
)
graph.underlying_function = func
if is_main_graph:
self.graph = graph
self.func = func
if animate:
self.play(ShowCreation(graph))
self.add(graph)
return graph
def input_to_graph_point(self, x, graph = None):
if graph is None:
assert(hasattr(self, "graph"))
graph = self.graph
def input_to_graph_point(self, x, graph):
return self.coords_to_point(x, graph.underlying_function(x))
def angle_of_tangent(self, x, graph = None, dx = 0.01):
def angle_of_tangent(self, x, graph, dx = 0.01):
vect = self.input_to_graph_point(x + dx, graph) - self.input_to_graph_point(x, graph)
return angle_of_vector(vect)
def slope_of_tangent(self, *args):
return np.tan(self.angle_of_tangent(*args))
def slope_of_tangent(self, *args, **kwargs):
return np.tan(self.angle_of_tangent(*args, **kwargs))
def get_derivative_graph(self, graph = None, dx = 0.01, color = None):
def get_derivative_graph(self, graph, dx = 0.01, color = None):
if color is None:
color = self.default_derivative_color
derivative_graph = self.graph_function(
return self.get_graph(
lambda x : self.slope_of_tangent(x, graph, dx) / self.space_unit_to_y,
color = color,
animate = False,
is_main_graph = False
)
self.remove(derivative_graph)
return derivative_graph
def label_graph(self, graph, label = "f(x)",
proportion = 0.7,
direction = LEFT,
buff = MED_BUFF,
color = None,
animate = True
):
def get_graph_label(
self,
graph,
label = "f(x)",
x_val = None,
direction = RIGHT,
buff = MED_BUFF,
color = None,
):
label = TexMobject(label)
color = color or graph.get_color()
label.highlight(color)
if x_val is None:
x_range = np.linspace(self.x_min, self.x_max, 20)
for left_x, right_x in zip(x_range, x_range[1:]):
right_point = self.input_to_graph_point(right_x, graph)
if right_point[1] > SPACE_HEIGHT:
break
x_val = left_x
label.next_to(
graph.point_from_proportion(proportion),
self.input_to_graph_point(x_val, graph),
direction,
buff = buff
)
if animate:
self.play(Write(label))
self.add(label)
label.shift_onto_screen()
return label
def get_riemann_rectangles(self,
x_min = None,
x_max = None,
dx = 0.1,
stroke_width = 1,
start_color = BLUE,
end_color = GREEN):
assert(hasattr(self, "func"))
def get_riemann_rectangles(
self,
graph,
x_min = None,
x_max = None,
dx = 0.1,
stroke_width = 1,
start_color = BLUE,
end_color = GREEN):
x_min = x_min if x_min is not None else self.x_min
x_max = x_max if x_max is not None else self.x_max
rectangles = VGroup()
for x in np.arange(x_min, x_max, dx):
points = VGroup(*map(VectorizedPoint, [
self.coords_to_point(x, 0),
self.coords_to_point(x+dx, self.func(x+dx)),
self.input_to_graph_point(x+dx, graph)
]))
rect = Rectangle()
rect.replace(points, stretch = True)
@ -186,15 +176,12 @@ class GraphScene(Scene):
rectangles.set_stroke(BLACK, width = stroke_width)
return rectangles
def get_vertical_line_to_graph(self,
x,
graph = None,
line_class = Line,
line_kwargs = None,
):
if graph is None:
assert(hasattr(self, "graph"))
graph = self.graph
def get_vertical_line_to_graph(
self,
x, graph,
line_class = Line,
line_kwargs = None,
):
if line_kwargs is None:
line_kwargs = {}
if "color" not in line_kwargs:
@ -205,7 +192,89 @@ class GraphScene(Scene):
**line_kwargs
)
def get_secant_slope_group(
self,
x, graph,
dx = None,
dx_line_color = None,
df_line_color = None,
slope_line_color = None,
dx_label = None,
df_label = None,
include_secant_line = True,
secant_line_color = None,
secant_line_length = 10,
):
kwargs = locals()
kwargs.pop("self")
group = VGroup()
group.kwargs = kwargs
dx = dx or float(self.x_max - self.x_min)/10
dx_line_color = dx_line_color or self.default_input_color
df_line_color = df_line_color or graph.get_color()
p1 = self.input_to_graph_point(x, graph)
p2 = self.input_to_graph_point(x+dx, graph)
interim_point = p2[0]*RIGHT + p1[1]*UP
group.dx_line = Line(
p1, interim_point,
color = dx_line_color
)
group.df_line = Line(
interim_point, p2,
color = df_line_color
)
if dx_label is not None:
group.dx_label = TexMobject(dx_label)
if group.dx_label.get_width() > group.dx_line.get_width():
group.dx_label.scale_to_fit_width(group.dx_line.get_width())
group.dx_label.next_to(group.dx_line, DOWN, SMALL_BUFF)
group.dx_label.highlight(group.dx_line.get_color())
if df_label is not None:
group.df_label = TexMobject(df_label)
if group.df_label.get_height() > group.df_line.get_height():
group.df_label.scale_to_fit_height(group.df_line.get_height())
group.df_label.next_to(group.df_line, RIGHT, SMALL_BUFF)
group.df_label.highlight(group.df_line.get_color())
if include_secant_line:
secant_line_color = secant_line_color or self.default_derivative_color
group.secant_line = Line(p1, p2, color = secant_line_color)
group.secant_line.scale_in_place(
secant_line_length/group.secant_line.get_length()
)
group.digest_mobject_attrs()
return group
def animate_secant_slope_group_dx_change(
self, secant_slope_group, target_dx,
run_time = 3,
**anim_kwargs
):
start_dx = secant_slope_group.kwargs["dx"]
def update_func(group, alpha):
dx = interpolate(start_dx, target_dx, alpha)
kwargs = dict(secant_slope_group.kwargs)
kwargs["dx"] = dx
new_group = self.get_secant_slope_group(**kwargs)
Transform(group, new_group).update(1)
return group
self.play(UpdateFromAlphaFunc(
secant_slope_group, update_func,
run_time = run_time,
**anim_kwargs
))