def get_vector_movement(self, func):
for v in self.moving_vectors:
v.target = Vector(func(v.get_end()), color=v.get_color())
norm = get_norm(v.target.get_end())
if norm < 0.1:
v.target.get_tip().scale_in_place(norm)
return self.get_piece_movement(self.moving_vectors)
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 /= get_norm(vect)
label.next_to(vector.get_end(), vect, buff=consts.SMALL_BUFF)
else:
angle = vector.get_angle()
if not rotate:
label.rotate(-angle, about_point=consts.ORIGIN)
if direction == "left":
label.shift(-label.get_bottom() + 0.1 * consts.UP)
else:
label.shift(-label.get_top() + 0.1 * consts.DOWN)
label.rotate(angle, about_point=consts.ORIGIN)
label.shift((vector.get_end() - vector.get_start()) / 2)
return label
def add_line(self, start, end, color=None):
start, end = list(map(np.array, [start, end]))
length = get_norm(end - start)
if length == 0:
points = [start]
else:
epsilon = self.epsilon / length
points = [
interpolate(start, end, t) for t in np.arange(0, 1, epsilon)
]
self.add_points(points, color=color)
def put_start_and_end_on(self, start, end):
curr_start, curr_end = self.get_start_and_end()
if np.all(curr_start == curr_end):
# TODO, any problems with resetting
# these attrs?
self.start = start
self.end = end
self.generate_points()
curr_vect = curr_end - curr_start
if np.all(curr_vect == 0):
raise Exception("Cannot position endpoints of closed loop")
target_vect = end - start
self.scale(
get_norm(target_vect) / get_norm(curr_vect),
about_point=curr_start,
)
self.rotate(angle_of_vector(target_vect) - angle_of_vector(curr_vect),
about_point=curr_start)
self.shift(start - curr_start)
return self
def path_along_arc(arc_angle, axis=consts.OUT):
"""
If vect is vector from start to end, [vect[:,1], -vect[:,0]] is
perpendicular to vect in the left direction.
"""
if abs(arc_angle) < STRAIGHT_PATH_THRESHOLD:
return straight_path
if get_norm(axis) == 0:
axis = consts.OUT
unit_axis = axis / get_norm(axis)
def path(start_points, end_points, alpha):
vects = end_points - start_points
centers = start_points + 0.5 * vects
if arc_angle != np.pi:
centers += np.cross(unit_axis, vects / 2.0) / np.tan(arc_angle / 2)
rot_matrix = rotation_matrix(alpha * arc_angle, unit_axis)
return centers + np.dot(start_points - centers, rot_matrix.T)
return path
def __init__(self, func, **kwargs):
VGroup.__init__(self, **kwargs)
self.func = func
dt = self.dt
start_points = self.get_start_points(
**self.start_points_generator_config
)
for point in start_points:
points = [point]
for t in np.arange(0, self.virtual_time, dt):
last_point = points[-1]
points.append(last_point + dt * func(last_point))
if get_norm(last_point) > self.cutoff_norm:
break
line = VMobject()
step = max(1, int(len(points) / self.n_anchors_per_line))
line.set_points_smoothly(points[::step])
self.add(line)
self.set_stroke(self.stroke_color, self.stroke_width)
if self.color_by_arc_length:
len_to_rgb = get_rgb_gradient_function(
self.min_arc_length,
self.max_arc_length,
colors=self.colors,
)
for line in self:
arc_length = line.get_arc_length()
rgb = len_to_rgb([arc_length])[0]
color = rgb_to_color(rgb)
line.set_color(color)
elif self.color_by_magnitude:
image_file = get_color_field_image_file(
lambda p: get_norm(func(p)),
min_value=self.min_magnitude,
max_value=self.max_magnitude,
colors=self.colors,
)
self.color_using_background_image(image_file)
def begin(self):
super().begin()
car = self.mobject
distance = get_norm(
op.sub(
self.target_mobject.get_right(),
self.starting_mobject.get_right(),
))
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_path(self):
new_point = self.traced_point_func()
if self.has_no_points():
self.start_new_path(new_point)
self.add_line_to(new_point)
else:
# Set the end to be the new point
self.points[-1] = new_point
# Second to last point
nppcc = self.n_points_per_cubic_curve
dist = get_norm(new_point - self.points[-nppcc])
if dist >= self.min_distance_to_new_point:
self.add_line_to(new_point)
def get_3d_vmob_unit_normal(vmob, point_index):
n_points = vmob.get_num_points()
if len(vmob.get_anchors()) <= 2:
return np.array(consts.consts.UP)
i = point_index
im3 = i - 3 if i > 2 else (n_points - 4)
ip3 = i + 3 if i < (n_points - 3) else 3
unit_normal = get_unit_normal(
vmob.points[ip3] - vmob.points[i],
vmob.points[im3] - vmob.points[i],
)
if get_norm(unit_normal) == 0:
return np.array(consts.consts.UP)
return unit_normal
def get_vector(self, point, **kwargs):
output = np.array(self.func(point))
norm = get_norm(output)
if norm == 0:
output *= 0
else:
output *= self.length_func(norm) / norm
vector_config = dict(self.vector_config)
vector_config.update(kwargs)
vect = Vector(output, **vector_config)
vect.shift(point)
fill_color = rgb_to_color(
self.rgb_gradient_function(np.array([norm]))[0]
)
vect.set_color(fill_color)
return vect
def set_submobject_colors_by_radial_gradient(
self,
center=None,
radius=1,
inner_color=Color('WHITE'),
outer_color=Color('BLACK')):
if center is None:
center = self.get_center()
for mob in self.family_members_with_points():
t = get_norm(mob.get_center() - center) / radius
t = min(t, 1)
mob_color = interpolate_color(inner_color, outer_color, t)
mob.set_color(mob_color, family=False)
return self
def get_length(self):
return get_norm(self.get_vector())
def get_length(self):
start, end = self.get_start_and_end()
return get_norm(start - end)
def get_direction(self):
vect = self.get_tip() - self.get_center()
return vect / get_norm(vect)