def smooth(t, inflection=10.0):
error = sigmoid(-inflection / 2)
return np.clip(
(sigmoid(inflection * (t - 0.5)) - error) / (1 - 2 * error),
0,
1,
)
class VectorField(VGroup):
CONFIG = {
"delta_x": 0.5,
"delta_y": 0.5,
"x_min": int(np.floor(-FRAME_WIDTH / 2)),
"x_max": int(np.ceil(FRAME_WIDTH / 2)),
"y_min": int(np.floor(-FRAME_HEIGHT / 2)),
"y_max": int(np.ceil(FRAME_HEIGHT / 2)),
"min_magnitude": 0,
"max_magnitude": 2,
"colors": DEFAULT_SCALAR_FIELD_COLORS,
# Takes in actual norm, spits out displayed norm
"length_func": lambda norm: 0.45 * sigmoid(norm),
"opacity": 1.0,
"vector_config": {},
}
def __init__(self, func, **kwargs):
VGroup.__init__(self, **kwargs)
self.func = func
self.rgb_gradient_function = get_rgb_gradient_function(
self.min_magnitude,
self.max_magnitude,
self.colors,
flip_alphas=False
)
x_range = np.arange(
self.x_min,
self.x_max + self.delta_x,
self.delta_x
)
y_range = np.arange(
self.y_min,
self.y_max + self.delta_y,
self.delta_y
)
for x, y in it.product(x_range, y_range):
point = x * RIGHT + y * UP
self.add(self.get_vector(point))
self.set_opacity(self.opacity)
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
class VectorField(VGroup):
CONFIG = {
"step_multiple": 0.5,
"magnitude_range": (0, 2),
"color_map": "3b1b_colormap",
# Takes in actual norm, spits out displayed norm
"length_func": lambda norm: 0.45 * sigmoid(norm),
"opacity": 1.0,
"vector_config": {},
}
def __init__(
self,
func: Callable[[float, float], Sequence[float]],
coordinate_system: CoordinateSystem,
**kwargs
):
super().__init__(**kwargs)
self.func = func
self.coordinate_system = coordinate_system
self.value_to_rgb = get_rgb_gradient_function(
*self.magnitude_range, self.color_map,
)
samples = get_sample_points_from_coordinate_system(
coordinate_system, self.step_multiple
)
self.add(*(
self.get_vector(coords)
for coords in samples
))
def get_vector(self, coords: Iterable[float], **kwargs) -> Arrow:
vector_config = merge_dicts_recursively(
self.vector_config,
kwargs
)
output = np.array(self.func(*coords))
norm = get_norm(output)
if norm > 0:
output *= self.length_func(norm) / norm
origin = self.coordinate_system.get_origin()
_input = self.coordinate_system.c2p(*coords)
_output = self.coordinate_system.c2p(*output)
vect = Arrow(
origin, _output, buff=0,
**vector_config
)
vect.shift(_input - origin)
vect.set_rgba_array([[*self.value_to_rgb(norm), self.opacity]])
return vect
def smooth(t, inflection=10.0):
error = sigmoid(-inflection / 2)
return np.clip(
(sigmoid(inflection * (t - 0.5)) - error) / (1 - 2 * error),
0, 1,
)
