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import math
import numpy as np
def downsample(img, factor):
"""
Downsample an image along both dimensions by some factor
"""
assert img.shape[0] % factor == 0
assert img.shape[1] % factor == 0
img = img.reshape([img.shape[0]//factor, factor, img.shape[1]//factor, factor, 3])
img = img.mean(axis=3)
img = img.mean(axis=1)
return img
def fill_coords(img, fn, color):
"""
Fill pixels of an image with coordinates matching a filter function
"""
for y in range(img.shape[0]):
for x in range(img.shape[1]):
yf = (y + 0.5) / img.shape[0]
xf = (x + 0.5) / img.shape[1]
if fn(xf, yf):
img[y, x] = color
return img
def rotate_fn(fin, cx, cy, theta):
def fout(x, y):
x = x - cx
y = y - cy
x2 = cx + x * math.cos(-theta) - y * math.sin(-theta)
y2 = cy + y * math.cos(-theta) + x * math.sin(-theta)
return fin(x2, y2)
return fout
def point_in_line(x0, y0, x1, y1, r):
p0 = np.array([x0, y0])
p1 = np.array([x1, y1])
dir = p1 - p0
dist = np.linalg.norm(dir)
dir = dir / dist
xmin = min(x0, x1) - r
xmax = max(x0, x1) + r
ymin = min(y0, y1) - r
ymax = max(y0, y1) + r
def fn(x, y):
# Fast, early escape test
if x < xmin or x > xmax or y < ymin or y > ymax:
return False
q = np.array([x, y])
pq = q - p0
# Closest point on line
a = np.dot(pq, dir)
a = np.clip(a, 0, dist)
p = p0 + a * dir
dist_to_line = np.linalg.norm(q - p)
return dist_to_line <= r
return fn
def point_in_circle(cx, cy, r):
def fn(x, y):
return (x-cx)*(x-cx) + (y-cy)*(y-cy) <= r * r
return fn
def point_in_circle_clip(cx, cy, r, theta_start=0, theta_end=-np.pi):
def fn(x, y):
if (x-cx)*(x-cx) + (y-cy)*(y-cy) <= r * r:
if theta_start < 0:
return theta_start > np.arctan2(y-cy, x-cx) > theta_end
else:
return theta_start < np.arctan2(y - cy, x - cx) < theta_end
return fn
def point_in_rect(xmin, xmax, ymin, ymax):
def fn(x, y):
return x >= xmin and x <= xmax and y >= ymin and y <= ymax
return fn
def point_in_triangle(a, b, c):
a = np.array(a)
b = np.array(b)
c = np.array(c)
def fn(x, y):
v0 = c - a
v1 = b - a
v2 = np.array((x, y)) - a
# Compute dot products
dot00 = np.dot(v0, v0)
dot01 = np.dot(v0, v1)
dot02 = np.dot(v0, v2)
dot11 = np.dot(v1, v1)
dot12 = np.dot(v1, v2)
# Compute barycentric coordinates
inv_denom = 1 / (dot00 * dot11 - dot01 * dot01)
u = (dot11 * dot02 - dot01 * dot12) * inv_denom
v = (dot00 * dot12 - dot01 * dot02) * inv_denom
# Check if point is in triangle
return (u >= 0) and (v >= 0) and (u + v) < 1
return fn
def point_in_quadrangle(a, b, c, d):
fn1 = point_in_triangle(a, b, c)
fn2 = point_in_triangle(b, c, d)
fn = lambda x, y: fn1(x, y) or fn2(x, y)
return fn
def highlight_img(img, color=(255, 255, 255), alpha=0.30):
"""
Add highlighting to an image
"""
blend_img = img + alpha * (np.array(color, dtype=np.uint8) - img)
blend_img = blend_img.clip(0, 255).astype(np.uint8)
img[:, :, :] = blend_img
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