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"""Common algorithms."""
import sys
__all__ = ["liangbarsky", "cohensutherland", "clipline", "point_on_line"]
def cohensutherland(left, top, right, bottom, x1, y1, x2, y2):
"""Clips a line to a rectangular area.
This implements the Cohen-Sutherland line clipping algorithm. ``left``,
``top``, ``right`` and ``bottom`` define the bounds of the clipping area,
by which the line from ``(x1, y1)`` to ``(x2, y2)`` will be clipped.
Args:
left (int): The left boundary of the clipping area.
top (int): The top boundary of the clipping area.
right (int): The right boundary of the clipping area.
bottom (int): The bottom boundary of the clipping area.
x1 (int): The x-coordinate of the starting point of the line.
y1 (int): The y-coordinate of the starting point of the line.
x2 (int): The x-coordinate of the end point of the line.
y2 (int): The y-coordinate of the end point of the line.
Returns:
tuple: The start and end coordinates of the clipped line in the form
``(cx1, cy1, cx2, cy2)``. If the line does not intersect with the
rectangular clipping area, all 4 values will be ``None``.
"""
LEFT, RIGHT, LOWER, UPPER = 1, 2, 4, 8
if bottom > top:
bottom, top = (top, bottom)
def _getclip(xa, ya):
p = 0
if xa < left:
p = LEFT
elif xa > right:
p = RIGHT
if ya < bottom:
p |= LOWER
elif ya > top:
p |= UPPER
return p
k1 = _getclip(x1, y1)
k2 = _getclip(x2, y2)
while (k1 | k2) != 0:
if (k1 & k2) != 0:
return None, None, None, None
opt = k2 if k2 > k1 else k1
if opt & UPPER:
x = x1 + (x2 - x1) * (1.0 * (top - y1)) / (y2 - y1)
y = top
elif opt & LOWER:
x = x1 + (x2 - x1) * (1.0 * (bottom - y1)) / (y2 - y1)
y = bottom
elif opt & RIGHT:
y = y1 + (y2 - y1) * (1.0 * (right - x1)) / (x2 - x1)
x = right
elif opt & LEFT:
y = y1 + (y2 - y1) * (1.0 * (left - x1)) / (x2 - x1)
x = left
else:
# this should not happen
raise RuntimeError("invalid clipping state")
if opt == k1:
x1, y1 = x, y
k1 = _getclip(x1, y1)
else:
x2, y2 = x, y
k2 = _getclip(x2, y2)
return x1, y1, x2, y2
def liangbarsky(left, top, right, bottom, x1, y1, x2, y2):
"""Clips a line to a rectangular area.
This implements the Liang-Barsky line clipping algorithm. ``left``,
``top``, ``right`` and ``bottom`` define the bounds of the clipping area,
by which the line from ``(x1, y1)`` to ``(x2, y2)`` will be clipped.
Args:
left (int): The left boundary of the clipping area.
top (int): The top boundary of the clipping area.
right (int): The right boundary of the clipping area.
bottom (int): The bottom boundary of the clipping area.
x1 (int): The x-coordinate of the starting point of the line.
y1 (int): The y-coordinate of the starting point of the line.
x2 (int): The x-coordinate of the end point of the line.
y2 (int): The y-coordinate of the end point of the line.
Returns:
tuple: The start and end coordinates of the clipped line in the form
``(cx1, cy1, cx2, cy2)``. If the line does not intersect with the
rectangular clipping area, all 4 values will be ``None``.
"""
dx = x2 - x1 * 1.0
dy = y2 - y1 * 1.0
dt0, dt1 = 0.0, 1.0
xx1 = x1
yy1 = y1
if bottom > top:
bottom, top = (top, bottom)
checks = ((-dx, x1 - left),
(dx, right - x1),
(-dy, y1 - bottom),
(dy, top - y1))
for p, q in checks:
if p == 0 and q < 0:
return None, None, None, None
if p != 0:
dt = q / (p * 1.0)
if p < 0:
if dt > dt1:
return None, None, None, None
dt0 = max(dt0, dt)
else:
if dt < dt0:
return None, None, None, None
dt1 = min(dt1, dt)
if dt0 > 0:
x1 += dt0 * dx
y1 += dt0 * dy
if dt1 < 1:
x2 = xx1 + dt1 * dx
y2 = yy1 + dt1 * dy
return x1, y1, x2, y2
def clipline(l, t, r, b, x1, y1, x2, y2, method='liangbarsky'):
"""Clips a line to a rectangular area using a given method.
Args:
l (int): The left boundary of the clipping area.
t (int): The top boundary of the clipping area.
r (int): The right boundary of the clipping area.
b (int): The bottom boundary of the clipping area.
x1 (int): The x-coordinate of the starting point of the line.
y1 (int): The y-coordinate of the starting point of the line.
x2 (int): The x-coordinate of the end point of the line.
y2 (int): The y-coordinate of the end point of the line.
method (str, optional): The method to use for clipping lines, can be
either 'cohensutherland' or 'liangbarsky'. Defaults to liangbarsky.
Returns:
tuple: The start and end coordinates of the clipped line in the form
``(cx1, cy1, cx2, cy2)``. If the line does not intersect with the
rectangular clipping area, all 4 values will be ``None``.
"""
if method == 'cohensutherland':
return cohensutherland(l, t, r, b, x1, y1, x2, y2)
elif method == 'liangbarsky':
return liangbarsky(l, t, r, b, x1, y1, x2, y2)
else:
raise ValueError("Unknown clipping method '{0}'".format(method))
def point_on_line(p1, p2, point):
"""Checks if a point falls along a given line segment.
Args:
p1 (tuple): The (x, y) coordinates of the starting point of the line.
p2 (tuple): The (x, y) coordinates of the end point of the line.
point (tuple): The (x, y) coordinates to test against the line.
Returns:
bool: ``True`` if the point falls along the line segment, otherwise
``False``.
"""
x1, y1 = p1
x2, y2 = p2
px, py = point
det = (py - y1) * (x2 - x1) - (px - x1) * (y2 - y1)
if abs(det) > sys.float_info.epsilon:
return False
return (min(x1, x2) <= px <= max(x1, x2) and
min(y1, y2) <= py <= max(y1, y2))
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