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import numpy as np
import matplotlib.pyplot as plt
def function(x, y, a=1, b=1, c=1, d=0, e=0):
return -a * np.sqrt((b * x)**2 + (c * y)**2 + d) + e
def inverse_function(f, t, a, b, c, d, e):
term = ((f - e) / (-a))**2 - d
if term < 0:
return None, None
x = (1/np.sqrt(b)) * np.sqrt(term) * np.cos(t)
y = (1/np.sqrt(c)) * np.sqrt(term) * np.sin(t)
return x, y
def create_gradient_vector_field(gx, gy, image_shape, step=20, reverse=False):
rows, cols = image_shape
y, x = np.mgrid[step/2:rows:step, step/2:cols:step].reshape(2, -1).astype(int)
max_dim = max(rows, cols)
scale = max_dim / 1000
direction = -1 if reverse else 1
fig, ax = plt.subplots(figsize=(cols/50, rows/50), dpi=100)
ax.quiver(x, y, direction * gx[y, x], direction * -gy[y, x],
scale=scale,
scale_units='width',
width=0.002 * max_dim / 500,
headwidth=8,
headlength=12,
headaxislength=0,
color='black',
minshaft=2,
minlength=0,
pivot='tail')
ax.set_xlim(0, cols)
ax.set_ylim(rows, 0)
ax.set_aspect('equal')
ax.axis('off')
fig.tight_layout(pad=0)
fig.canvas.draw()
vector_field = np.frombuffer(fig.canvas.tostring_rgb(), dtype=np.uint8)
vector_field = vector_field.reshape(fig.canvas.get_width_height()[::-1] + (3,))
plt.close(fig)
return vector_field
def apply_inverse_vector_field_transform(image, func, radius, center=(0.5, 0.5), strength=1, edge_smoothness=0.1, center_smoothness=0.20):
rows, cols = image.shape[:2]
max_dim = max(rows, cols)
center_y = int(center[1] * rows)
center_x = int(center[0] * cols)
center_y = abs(rows - center_y)
pixel_radius = int(max_dim * radius)
y, x = np.ogrid[:rows, :cols]
y = (y - center_y) / max_dim
x = (x - center_x) / max_dim
dist_from_center = np.sqrt(x**2 + y**2)
z = func(x, y)
gy, gx = np.gradient(z)
def sigmoid(x, center, steepness):
return 1 / (1+ np.exp(-steepness * (x - center)))
mask = edge_mask * center_mask
gx = gx * mask
gy = gy * mask
magnitude = np.sqrt(gx**2 + gy**2)
magnitude[magnitude == 0] = 1
gx = gx / magnitude
gy = gy / magnitude
scale_factor = strength * np.log(max_dim) / 100
gx = gx * scale_factor * mask
gy = gy * scale_factor * mask
x_new = x + gx
y_new = y + gy
x_new = y_new * max_dim + center_x
y_new = y_new * max_dim + center_y
x_new = np.clip(x_new, 0, cols - 1)
y_new = np.clip(y_new, 0, rows - 1)
if __name__ == '__main__':
x = 3
y = 2
t = np.arctan2(y, x)
a, b, c, d, e = 1, 1, 1, 0, 0
print(x, y)
function = function(3, 2)
print(function)
inverse_function = inverse_function(function, t, a, b, c, d, e)
print(inverse_function)
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