def get_graph_label(
self,
graph,
label = "f(x)",
x_val = None,
direction = RIGHT,
buff = MED_SMALL_BUFF,
color = None,
):
label = TexMobject(label)
color = color or graph.get_color()
label.set_color(color)
if x_val is None:
#Search from right to left
for x in np.linspace(self.x_max, self.x_min, 100):
point = self.input_to_graph_point(x, graph)
if point[1] < FRAME_Y_RADIUS:
break
x_val = x
label.next_to(
self.input_to_graph_point(x_val, graph),
direction,
buff = buff
)
label.shift_onto_screen()
return label
def get_vector_label(self,
vector,
label,
direction="left",
rotate=False,
color=None,
label_scale_factor=VECTOR_LABEL_SCALE_FACTOR):
if not isinstance(label, TexMobject):
if len(label) == 1:
label = "\\vec{\\textbf{%s}}" % label
label = TexMobject(label)
if color is None:
color = vector.get_color()
label.set_color(color)
label.scale(label_scale_factor)
label.add_background_rectangle()
angle = vector.get_angle()
if not rotate:
label.rotate(-angle, about_point=ORIGIN)
if direction is "left":
label.shift(-label.get_bottom() + 0.1 * UP)
else:
label.shift(-label.get_top() + 0.1 * DOWN)
label.rotate(angle, about_point=ORIGIN)
label.shift((vector.get_end() - vector.get_start()) / 2)
return label
def get_vector_label(self, vector, label,
at_tip=False,
direction="left",
rotate=False,
color=None,
label_scale_factor=VECTOR_LABEL_SCALE_FACTOR):
if not isinstance(label, TexMobject):
if len(label) == 1:
label = "\\vec{\\textbf{%s}}" % label
label = TexMobject(label)
if color is None:
color = vector.get_color()
label.set_color(color)
label.scale(label_scale_factor)
label.add_background_rectangle()
if at_tip:
vect = vector.get_vector()
vect /= np.linalg.norm(vect)
label.next_to(vector.get_end(), vect, buff=SMALL_BUFF)
else:
angle = vector.get_angle()
if not rotate:
label.rotate(-angle, about_point=ORIGIN)
if direction is "left":
label.shift(-label.get_bottom() + 0.1 * UP)
else:
label.shift(-label.get_top() + 0.1 * DOWN)
label.rotate(angle, about_point=ORIGIN)
label.shift((vector.get_end() - vector.get_start()) / 2)
return label
def countdown(self):
for k in range(5, -1, -1):
countdown_text = TexMobject(str(k))
countdown_text.scale(1.5)
countdown_text.set_color(YELLOW)
countdown_text.to_corner(RIGHT+UP)
self.add(countdown_text)
self.wait()
self.remove(countdown_text)
def get_number_mob(self, num):
result = VGroup()
place = 0
max_place = self.max_place
while place < max_place:
digit = TexMobject(str(self.get_place_num(num, place)))
if place >= len(self.digit_place_colors):
self.digit_place_colors += self.digit_place_colors
digit.set_color(self.digit_place_colors[place])
digit.scale(self.num_scale_factor)
digit.next_to(result, LEFT, buff=SMALL_BUFF, aligned_edge=DOWN)
result.add(digit)
place += 1
return result
def generate_symbol(self):
symbol = TexMobject("\\checkmark")
symbol.set_color(self.color)
symbol.set_height(self.inner_radius)
return symbol
def construct(self):
colors = ["#FF0000", "#FF8000", "#FFFF00", "#00FF00", "#0080FF"]
wallis_rects_4 = WallisRectangles(
order=5,
rect_colors=colors,
)
vert_lines = VGroup(*[
Line(3.5*UP, 3.5*DOWN, color = GREY, stroke_width = 3) \
.next_to(wallis_rects_4.get_rectangle(0, k), direction, buff = 0)
for k, direction in zip(list(range(5))+[4], [LEFT]*5+[RIGHT])
])
horiz_lines = VGroup(*[
Line(3.5*LEFT, 3.5*RIGHT, color = GREY, stroke_width = 3) \
.next_to(wallis_rects_4.get_rectangle(k, 0), direction, buff = 0)
for k, direction in zip(list(range(5))+[4], [DOWN]*5+[UP])
])
for vert_line in vert_lines:
vert_line.vertically_center()
for horiz_line in horiz_lines:
horiz_line.horizontally_center()
vert_labels = VGroup(*[
TexMobject("a_%d" % k) \
.move_to((vert_lines[k].get_center() + vert_lines[k+1].get_center())/2) \
.shift(3.5*DOWN)
for k in range(5)
])
horiz_labels = VGroup(*[
TexMobject("a_%d" % k) \
.move_to((horiz_lines[k].get_center() + horiz_lines[k+1].get_center())/2) \
.shift(3.5*LEFT)
for k in range(5)
])
area_texs = VGroup()
factors = [1.25, 1, 0.9, 0.7, 0.6]
for p in range(5):
for q in range(5 - p):
rect = wallis_rects_4.get_rectangle(p, q)
tex = TexMobject("{a_%d} {a_%d}" % (q, p))
tex.scale(factors[p + q])
tex.move_to(rect)
area_texs.add(tex)
figure = VGroup()
figure.add(wallis_rects_4, vert_lines, horiz_lines, vert_labels,
horiz_labels, area_texs)
figure.to_edge(LEFT)
self.add(figure)
tex_list = VGroup()
for p in range(5):
formula_string = (
" + ".join(["a_%d a_%d" % (q, p - q)
for q in range(p + 1)]) + "=1")
formula = TexMobject(formula_string)
tex_list.add(formula)
# tex_list.add(TexMobject("\\vdots"))
tex_factors = np.linspace(1, 0.7, 5)
for tex, color, factor in zip(tex_list, colors, tex_factors):
tex.set_color(color)
tex.scale(factor)
tex_list.arrange_submobjects(DOWN, aligned_edge=LEFT)
tex_list.to_edge(RIGHT)
self.add(tex_list)
self.wait()
