def get_riemann_rectangles(
self,
graph,
x_min=None,
x_max=None,
dx=0.1,
input_sample_type="left",
stroke_width=1,
stroke_color=BLACK,
fill_opacity=1,
start_color=None,
end_color=None,
show_signed_area=True,
width_scale_factor=1.001
):
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
if start_color is None:
start_color = self.default_riemann_start_color
if end_color is None:
end_color = self.default_riemann_end_color
rectangles = VGroup()
x_range = np.arange(x_min, x_max, dx)
colors = color_gradient([start_color, end_color], len(x_range))
for x, color in zip(x_range, colors):
if input_sample_type == "left":
sample_input = x
elif input_sample_type == "right":
sample_input = x + dx
elif input_sample_type == "center":
sample_input = x + 0.5 * dx
else:
raise Exception("Invalid input sample type")
graph_point = self.input_to_graph_point(sample_input, graph)
points = VGroup(*list(map(VectorizedPoint, [
self.coords_to_point(x, 0),
self.coords_to_point(x + width_scale_factor * dx, 0),
graph_point
])))
rect = Rectangle()
rect.replace(points, stretch=True)
if graph_point[1] < self.graph_origin[1] and show_signed_area:
fill_color = invert_color(color)
else:
fill_color = color
rect.set_fill(fill_color, opacity=fill_opacity)
rect.set_stroke(stroke_color, width=stroke_width)
rectangles.add(rect)
return rectangles
def get_riemann_rectangles(
self,
graph,
x_min=None,
x_max=None,
dx=0.1,
input_sample_type="left",
stroke_width=1,
stroke_color=BLACK,
fill_opacity=1,
start_color=None,
end_color=None,
show_signed_area=True,
width_scale_factor=1.001
):
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
if start_color is None:
start_color = self.default_riemann_start_color
if end_color is None:
end_color = self.default_riemann_end_color
rectangles = VGroup()
x_range = np.arange(x_min, x_max, dx)
colors = color_gradient([start_color, end_color], len(x_range))
for x, color in zip(x_range, colors):
if input_sample_type == "left":
sample_input = x
elif input_sample_type == "right":
sample_input = x + dx
elif input_sample_type == "center":
sample_input = x + 0.5 * dx
else:
raise Exception("Invalid input sample type")
graph_point = self.input_to_graph_point(sample_input, graph)
points = VGroup(*list(map(VectorizedPoint, [
self.coords_to_point(x, 0),
self.coords_to_point(x + width_scale_factor * dx, 0),
graph_point
])))
rect = Rectangle()
rect.replace(points, stretch=True)
if graph_point[1] < self.graph_origin[1] and show_signed_area:
fill_color = invert_color(color)
else:
fill_color = color
rect.set_fill(fill_color, opacity=fill_opacity)
rect.set_stroke(stroke_color, width=stroke_width)
rectangles.add(rect)
return rectangles
def add_shadow_mobjects(self,
shadow=2,
mobject=None,
color=WHITE,
opacity=0.9,
shift=([0.03, -0.01, 0]),
**kwargs):
from manimlib.mobject.types.vectorized_mobject import VGroup
group = VGroup()
if mobject == None:
mobject = self
if shadow == 2:
if isinstance(mobject, (Mobject)):
mobject_2 = mobject.copy()
mobject = mobject.copy()
if isinstance(color, (list, tuple)) and len(color) == 2:
color_2 = color[1]
color = color[0]
else:
color_2 = invert_color(color)
if isinstance(opacity, (list, tuple)) and len(opacity) == 2:
opacity_2 = opacity[1]
opacity = opacity[0]
else:
opacity_2 = opacity
if isinstance(shift, (tuple)) and len(shift) == 2:
shift_2 = shift[1]
shift = shift[0]
else:
shift_2 = [each * -1 for each in shift]
group.add(
mobject_2.set_color(color_2).set_opacity(opacity_2).shift(
shift_2)) #
elif shadow == 1:
mobject = mobject.copy()
else:
return self
group.add(mobject.set_color(color).set_opacity(opacity).shift(shift))
self.remove(self.submobjects)
return self.add_to_back(group, **kwargs).push_self_into_submobjects()
def get_riemann_rectangles(self,
graph,
x_min=None,
x_max=None,
dx=0.1,
input_sample_type="left",
stroke_width=1,
stroke_color=BLACK,
fill_opacity=1,
start_color=None,
end_color=None,
show_signed_area=True,
width_scale_factor=1.001):
"""
This method returns the VGroup() of the Riemann Rectangles for
a particular curve.
Parameters
----------
graph (ParametricFunction)
The graph whose area needs to be approximated
by the Riemann Rectangles.
x_min Union[int,float]
The lower bound from which to start adding rectangles
x_max Union[int,float]
The upper bound where the rectangles stop.
dx Union[int,float]
The smallest change in x-values that is
considered significant.
input_sample_type str
Can be any of "left", "right" or "center
stroke_width : Union[int, float]
The stroke_width of the border of the rectangles.
stroke_color : str
The string of hex colour of the rectangle's border.
fill_opacity Union[int, float]
The opacity of the rectangles.
start_color : str,
The hex starting colour for the rectangles,
this will, if end_color is a different colour,
make a nice gradient.
end_color : str,
The hex ending colour for the rectangles,
this will, if start_color is a different colour,
make a nice gradient.
show_signed_area : bool (True)
Whether or not to indicate -ve area if curve dips below
x-axis.
width_scale_factor : Union[int, float]
How much the width of the rectangles are scaled by when transforming.
Returns
-------
VGroup
A VGroup containing the Riemann Rectangles.
"""
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
if start_color is None:
start_color = self.default_riemann_start_color
if end_color is None:
end_color = self.default_riemann_end_color
rectangles = VGroup()
x_range = np.arange(x_min, x_max, dx)
colors = color_gradient([start_color, end_color], len(x_range))
for x, color in zip(x_range, colors):
if input_sample_type == "left":
sample_input = x
elif input_sample_type == "right":
sample_input = x + dx
elif input_sample_type == "center":
sample_input = x + 0.5 * dx
else:
raise Exception("Invalid input sample type")
graph_point = self.input_to_graph_point(sample_input, graph)
points = VGroup(*list(
map(VectorizedPoint, [
self.coords_to_point(x, 0),
self.coords_to_point(x + width_scale_factor *
dx, 0), graph_point
])))
rect = Rectangle()
rect.replace(points, stretch=True)
if graph_point[1] < self.graph_origin[1] and show_signed_area:
fill_color = invert_color(color)
else:
fill_color = color
rect.set_fill(fill_color, opacity=fill_opacity)
rect.set_stroke(stroke_color, width=stroke_width)
rectangles.add(rect)
return rectangles
