def clip_lines_by_polygon(lines, polygon,
closed=True,
check_input=True):
"""Clip multiple lines by polygon
Input
line: Sequence of polylines: [[p0, p1, ...], [q0, q1, ...], ...]
where pi and qi are point coordinates (x, y).
Output
polygon: list of vertices of polygon or the corresponding numpy array
closed: (optional) determine whether points on boundary should be
regarded as belonging to the polygon (closed = True)
or not (closed = False) - False is not recommended here
check_input: Allows faster execution if set to False
Outputs
inside_line_segments: Clipped line segments that are inside polygon
outside_line_segments: Clipped line segments that are outside polygon
This is a wrapper around clip_line_by_polygon
"""
if check_input:
# Input checks
msg = 'Keyword argument "closed" must be boolean'
if not isinstance(closed, bool):
raise RuntimeError(msg)
for i in range(len(lines)):
try:
lines[i] = ensure_numeric(lines[i], numpy.float)
except Exception, e:
msg = ('Line could not be converted to numeric array: %s'
% str(e))
raise Exception(msg)
try:
polygon = ensure_numeric(polygon, numpy.float)
except Exception, e:
msg = ('Polygon could not be converted to numeric array: %s'
% str(e))
raise Exception(msg)
def clip_lines_by_polygon(lines, polygon, closed=True, check_input=True):
"""Clip multiple lines by polygon
Input
line: Sequence of polylines: [[p0, p1, ...], [q0, q1, ...], ...]
where pi and qi are point coordinates (x, y).
Output
polygon: list of vertices of polygon or the corresponding numpy array
closed: (optional) determine whether points on boundary should be
regarded as belonging to the polygon (closed = True)
or not (closed = False) - False is not recommended here
check_input: Allows faster execution if set to False
Outputs
inside_line_segments: Clipped line segments that are inside polygon
outside_line_segments: Clipped line segments that are outside polygon
This is a wrapper around clip_line_by_polygon
"""
if check_input:
# Input checks
msg = 'Keyword argument "closed" must be boolean'
if not isinstance(closed, bool):
raise RuntimeError(msg)
for i in range(len(lines)):
try:
lines[i] = ensure_numeric(lines[i], numpy.float)
except Exception, e:
msg = ('Line could not be converted to numeric array: %s' %
str(e))
raise Exception(msg)
try:
polygon = ensure_numeric(polygon, numpy.float)
except Exception, e:
msg = ('Polygon could not be converted to numeric array: %s' %
str(e))
raise Exception(msg)
def intersection(line0, line1, rtol=1.0e-12, atol=1.0e-12):
"""Returns intersecting point between two line segments.
However, if parallel lines coincide partly (i.e. share a common segment),
the line segment where lines coincide is returned
Inputs:
line0, line1: Each defined by two end points as in:
[[x0, y0], [x1, y1]]
A line can also be a 2x2 numpy array with each row
corresponding to a point.
rtol, atol: Tolerances passed onto numpy.allclose
Output:
status, value - where status and value is interpreted as follows:
status == 0: no intersection, value set to None.
status == 1: intersection point found and returned in value as [x,y].
status == 2: Collinear overlapping lines found.
Value takes the form [[x0,y0], [x1,y1]] which is the
segment common to both lines.
status == 3: Collinear non-overlapping lines. Value set to None.
status == 4: Lines are parallel. Value set to None.
"""
line0 = ensure_numeric(line0, numpy.float)
line1 = ensure_numeric(line1, numpy.float)
x0, y0 = line0[0, :]
x1, y1 = line0[1, :]
x2, y2 = line1[0, :]
x3, y3 = line1[1, :]
denom = (y3 - y2) * (x1 - x0) - (x3 - x2) * (y1 - y0)
u0 = (x3 - x2) * (y0 - y2) - (y3 - y2) * (x0 - x2)
u1 = (x2 - x0) * (y1 - y0) - (y2 - y0) * (x1 - x0)
if numpy.allclose(denom, 0.0, rtol=rtol, atol=atol):
# Lines are parallel - check if they are collinear
if numpy.allclose([u0, u1], 0.0, rtol=rtol, atol=atol):
# We now know that the lines are collinear
state = (point_on_line([x0, y0], line1, rtol=rtol, atol=atol),
point_on_line([x1, y1], line1, rtol=rtol, atol=atol),
point_on_line([x2, y2], line0, rtol=rtol, atol=atol),
point_on_line([x3, y3], line0, rtol=rtol, atol=atol))
return collinearmap[state]([x0, y0], [x1, y1], [x2, y2], [x3, y3])
else:
# Lines are parallel but aren't collinear
return 4, None # FIXME (Ole): Add distance here instead of None
else:
# Lines are not parallel, check if they intersect
u0 = u0 / denom
u1 = u1 / denom
x = x0 + u0 * (x1 - x0)
y = y0 + u0 * (y1 - y0)
# Sanity check - can be removed to speed up if needed
if not numpy.allclose(x, x2 + u1 * (x3 - x2), rtol=rtol, atol=atol):
raise Exception
if not numpy.allclose(y, y2 + u1 * (y3 - y2), rtol=rtol, atol=atol):
raise Exception
# Check if point found lies within given line segments
if 0.0 <= u0 <= 1.0 and 0.0 <= u1 <= 1.0:
# We have intersection
return 1, numpy.array([x, y])
else:
# No intersection
return 0, None
def clip_line_by_polygon(line, polygon, closed=True, check_input=True):
"""Clip line segments by polygon
Input
line: Sequence of line nodes: [[x0, y0], [x1, y1], ...] or
the equivalent Nx2 numpy array
polygon: list of vertices of polygon or the corresponding numpy array
closed: (optional) determine whether points on boundary should be
regarded as belonging to the polygon (closed = True)
or not (closed = False) - False is not recommended here
check_input: Allows faster execution if set to False
Outputs
inside_lines: Clipped lines that are inside polygon
outside_lines: Clipped lines that are outside polygon
Both outputs take the form of lists of Nx2 line arrays
Example:
U = [[0,0], [1,0], [1,1], [0,1]] # Unit square
# Simple horizontal fully intersecting line
line = [[-1, 0.5], [2, 0.5]]
inside_line_segments, outside_line_segments = \
clip_line_by_polygon(line, polygon)
print numpy.allclose(inside_line_segments,
[[[0, 0.5], [1, 0.5]]])
print numpy.allclose(outside_line_segments,
[[[-1, 0.5], [0, 0.5]],
[[1, 0.5], [2, 0.5]]])
Remarks:
The assumptions listed in separate_points_by_polygon apply
Output line segments are listed as separate lines i.e. not joined
"""
if check_input:
# Input checks
msg = 'Keyword argument "closed" must be boolean'
if not isinstance(closed, bool):
raise RuntimeError(msg)
try:
line = ensure_numeric(line, numpy.float)
except Exception, e:
msg = ('Line could not be converted to numeric array: %s' % str(e))
raise Exception(msg)
msg = 'Line segment array must be a 2d array of vertices'
if not len(line.shape) == 2:
raise RuntimeError(msg)
msg = 'Line array must have two columns'
if not line.shape[1] == 2:
raise RuntimeError(msg)
try:
polygon = ensure_numeric(polygon, numpy.float)
except Exception, e:
msg = ('Polygon could not be converted to numeric array: %s' %
str(e))
raise Exception(msg)
def point_on_line(points, line, rtol=1.0e-5, atol=1.0e-8):
"""Determine if a point is on a line segment
Input
points: Coordinates of either
* one point given by sequence [x, y]
* multiple points given by list of points or Nx2 array
line: Endpoint coordinates [[x0, y0], [x1, y1]] or
the equivalent 2x2 numeric array with each row corresponding
to a point.
rtol: Relative error for how close a point must be to be accepted
atol: Absolute error for how close a point must be to be accepted
Output
True or False
Notes
Line can be degenerate and function still works to discern coinciding
points from non-coinciding.
Tolerances rtol and atol are used with numpy.allclose()
"""
# Prepare input data
points = ensure_numeric(points)
line = ensure_numeric(line)
if len(points.shape) == 1:
# One point only - make into 1 x 2 array
points = points[numpy.newaxis, :]
one_point = True
else:
one_point = False
msg = 'Argument points must be either [x, y] or an Nx2 array of points'
if len(points.shape) != 2:
raise Exception(msg)
if not points.shape[0] > 0:
raise Exception(msg)
if points.shape[1] != 2:
raise Exception(msg)
N = points.shape[0] # Number of points
x = points[:, 0]
y = points[:, 1]
x0, y0 = line[0]
x1, y1 = line[1]
# Vector from beginning of line to point
a0 = x - x0
a1 = y - y0
# It's normal vector
a_normal0 = a1
a_normal1 = -a0
# Vector parallel to line
b0 = x1 - x0
b1 = y1 - y0
# Dot product
nominator = abs(a_normal0 * b0 + a_normal1 * b1)
denominator = b0 * b0 + b1 * b1
# Determine if point vector is parallel to line up to a tolerance
is_parallel = numpy.zeros(N, dtype=numpy.bool) # All False
is_parallel[nominator <= atol + rtol * denominator] = True
# Determine for points parallel to line if they are within end points
a0p = a0[is_parallel]
a1p = a1[is_parallel]
len_a = numpy.sqrt(a0p * a0p + a1p * a1p)
len_b = numpy.sqrt(b0 * b0 + b1 * b1)
cross = a0p * b0 + a1p * b1
# Initialise result to all False
result = numpy.zeros(N, dtype=numpy.bool)
# Result is True only if a0 * b0 + a1 * b1 >= 0 and len_a <= len_b
result[is_parallel] = (cross >= 0) * (len_a <= len_b)
# Return either boolean scalar or boolean vector
if one_point:
return result[0]
else:
return result
def separate_points_by_polygon(points,
polygon,
closed=True,
check_input=True,
numpy_version=True):
"""Determine whether points are inside or outside a polygon
Input:
points - Tuple of (x, y) coordinates, or list of tuples
polygon - list of vertices of polygon
closed - (optional) determine whether points on boundary should be
regarded as belonging to the polygon (closed = True)
or not (closed = False)
check_input: Allows faster execution if set to False
Outputs:
indices: array of same length as points with indices of points falling
inside the polygon listed from the beginning and indices of points
falling outside listed from the end.
count: count of points falling inside the polygon
The indices of points inside are obtained as indices[:count]
The indices of points outside are obtained as indices[count:]
Examples:
U = [[0,0], [1,0], [1,1], [0,1]] # Unit square
separate_points_by_polygon( [[0.5, 0.5], [1, -0.5], [0.3, 0.2]], U)
will return the indices [0, 2, 1] and count == 2 as only the first
and the last point are inside the unit square
Remarks:
The vertices may be listed clockwise or counterclockwise and
the first point may optionally be repeated.
Polygons do not need to be convex.
Polygons can have holes in them and points inside a hole is
regarded as being outside the polygon.
Algorithm is based on work by Darel Finley,
http://www.alienryderflex.com/polygon/
"""
if check_input:
# Input checks
msg = 'Keyword argument "closed" must be boolean'
if not isinstance(closed, bool):
raise Exception(msg)
try:
points = ensure_numeric(points, numpy.float)
except Exception, e:
msg = ('Points could not be converted to numeric array: %s' %
str(e))
raise Exception(msg)
try:
polygon = ensure_numeric(polygon, numpy.float)
except Exception, e:
msg = ('Polygon could not be converted to numeric array: %s' %
str(e))
raise Exception(msg)
def intersection(line0, line1, rtol=1.0e-12, atol=1.0e-12):
"""Returns intersecting point between two line segments.
However, if parallel lines coincide partly (i.e. share a common segment),
the line segment where lines coincide is returned
Inputs:
line0, line1: Each defined by two end points as in:
[[x0, y0], [x1, y1]]
A line can also be a 2x2 numpy array with each row
corresponding to a point.
rtol, atol: Tolerances passed onto numpy.allclose
Output:
status, value - where status and value is interpreted as follows:
status == 0: no intersection, value set to None.
status == 1: intersection point found and returned in value as [x,y].
status == 2: Collinear overlapping lines found.
Value takes the form [[x0,y0], [x1,y1]] which is the
segment common to both lines.
status == 3: Collinear non-overlapping lines. Value set to None.
status == 4: Lines are parallel. Value set to None.
"""
line0 = ensure_numeric(line0, numpy.float)
line1 = ensure_numeric(line1, numpy.float)
x0, y0 = line0[0, :]
x1, y1 = line0[1, :]
x2, y2 = line1[0, :]
x3, y3 = line1[1, :]
denom = (y3 - y2) * (x1 - x0) - (x3 - x2) * (y1 - y0)
u0 = (x3 - x2) * (y0 - y2) - (y3 - y2) * (x0 - x2)
u1 = (x2 - x0) * (y1 - y0) - (y2 - y0) * (x1 - x0)
if numpy.allclose(denom, 0.0, rtol=rtol, atol=atol):
# Lines are parallel - check if they are collinear
if numpy.allclose([u0, u1], 0.0, rtol=rtol, atol=atol):
# We now know that the lines are collinear
state = (point_on_line([x0, y0], line1, rtol=rtol, atol=atol),
point_on_line([x1, y1], line1, rtol=rtol, atol=atol),
point_on_line([x2, y2], line0, rtol=rtol, atol=atol),
point_on_line([x3, y3], line0, rtol=rtol, atol=atol))
return collinearmap[state]([x0, y0], [x1, y1],
[x2, y2], [x3, y3])
else:
# Lines are parallel but aren't collinear
return 4, None # FIXME (Ole): Add distance here instead of None
else:
# Lines are not parallel, check if they intersect
u0 = u0 / denom
u1 = u1 / denom
x = x0 + u0 * (x1 - x0)
y = y0 + u0 * (y1 - y0)
# Sanity check - can be removed to speed up if needed
if not numpy.allclose(x, x2 + u1 * (x3 - x2), rtol=rtol, atol=atol):
raise Exception
if not numpy.allclose(y, y2 + u1 * (y3 - y2), rtol=rtol, atol=atol):
raise Exception
# Check if point found lies within given line segments
if 0.0 <= u0 <= 1.0 and 0.0 <= u1 <= 1.0:
# We have intersection
return 1, numpy.array([x, y])
else:
# No intersection
return 0, None
def clip_line_by_polygon(line, polygon,
closed=True,
check_input=True):
"""Clip line segments by polygon
Input
line: Sequence of line nodes: [[x0, y0], [x1, y1], ...] or
the equivalent Nx2 numpy array
polygon: list of vertices of polygon or the corresponding numpy array
closed: (optional) determine whether points on boundary should be
regarded as belonging to the polygon (closed = True)
or not (closed = False) - False is not recommended here
check_input: Allows faster execution if set to False
Outputs
inside_lines: Clipped lines that are inside polygon
outside_lines: Clipped lines that are outside polygon
Both outputs take the form of lists of Nx2 line arrays
Example:
U = [[0,0], [1,0], [1,1], [0,1]] # Unit square
# Simple horizontal fully intersecting line
line = [[-1, 0.5], [2, 0.5]]
inside_line_segments, outside_line_segments = \
clip_line_by_polygon(line, polygon)
print numpy.allclose(inside_line_segments,
[[[0, 0.5], [1, 0.5]]])
print numpy.allclose(outside_line_segments,
[[[-1, 0.5], [0, 0.5]],
[[1, 0.5], [2, 0.5]]])
Remarks:
The assumptions listed in separate_points_by_polygon apply
Output line segments are listed as separate lines i.e. not joined
"""
if check_input:
# Input checks
msg = 'Keyword argument "closed" must be boolean'
if not isinstance(closed, bool):
raise RuntimeError(msg)
try:
line = ensure_numeric(line, numpy.float)
except Exception, e:
msg = ('Line could not be converted to numeric array: %s'
% str(e))
raise Exception(msg)
msg = 'Line segment array must be a 2d array of vertices'
if not len(line.shape) == 2:
raise RuntimeError(msg)
msg = 'Line array must have two columns'
if not line.shape[1] == 2:
raise RuntimeError(msg)
try:
polygon = ensure_numeric(polygon, numpy.float)
except Exception, e:
msg = ('Polygon could not be converted to numeric array: %s'
% str(e))
raise Exception(msg)
def point_on_line(points, line, rtol=1.0e-5, atol=1.0e-8):
"""Determine if a point is on a line segment
Input
points: Coordinates of either
* one point given by sequence [x, y]
* multiple points given by list of points or Nx2 array
line: Endpoint coordinates [[x0, y0], [x1, y1]] or
the equivalent 2x2 numeric array with each row corresponding
to a point.
rtol: Relative error for how close a point must be to be accepted
atol: Absolute error for how close a point must be to be accepted
Output
True or False
Notes
Line can be degenerate and function still works to discern coinciding
points from non-coinciding.
Tolerances rtol and atol are used with numpy.allclose()
"""
# Prepare input data
points = ensure_numeric(points)
line = ensure_numeric(line)
if len(points.shape) == 1:
# One point only - make into 1 x 2 array
points = points[numpy.newaxis, :]
one_point = True
else:
one_point = False
msg = 'Argument points must be either [x, y] or an Nx2 array of points'
if len(points.shape) != 2:
raise Exception(msg)
if not points.shape[0] > 0:
raise Exception(msg)
if points.shape[1] != 2:
raise Exception(msg)
N = points.shape[0] # Number of points
x = points[:, 0]
y = points[:, 1]
x0, y0 = line[0]
x1, y1 = line[1]
# Vector from beginning of line to point
a0 = x - x0
a1 = y - y0
# It's normal vector
a_normal0 = a1
a_normal1 = -a0
# Vector parallel to line
b0 = x1 - x0
b1 = y1 - y0
# Dot product
nominator = abs(a_normal0 * b0 + a_normal1 * b1)
denominator = b0 * b0 + b1 * b1
# Determine if point vector is parallel to line up to a tolerance
is_parallel = numpy.zeros(N, dtype=numpy.bool) # All False
is_parallel[nominator <= atol + rtol * denominator] = True
# Determine for points parallel to line if they are within end points
a0p = a0[is_parallel]
a1p = a1[is_parallel]
len_a = numpy.sqrt(a0p * a0p + a1p * a1p)
len_b = numpy.sqrt(b0 * b0 + b1 * b1)
cross = a0p * b0 + a1p * b1
# Initialise result to all False
result = numpy.zeros(N, dtype=numpy.bool)
# Result is True only if a0 * b0 + a1 * b1 >= 0 and len_a <= len_b
result[is_parallel] = (cross >= 0) * (len_a <= len_b)
# Return either boolean scalar or boolean vector
if one_point:
return result[0]
else:
return result
def separate_points_by_polygon(points, polygon,
closed=True,
check_input=True,
numpy_version=True):
"""Determine whether points are inside or outside a polygon
Input:
points - Tuple of (x, y) coordinates, or list of tuples
polygon - list of vertices of polygon
closed - (optional) determine whether points on boundary should be
regarded as belonging to the polygon (closed = True)
or not (closed = False)
check_input: Allows faster execution if set to False
Outputs:
indices: array of same length as points with indices of points falling
inside the polygon listed from the beginning and indices of points
falling outside listed from the end.
count: count of points falling inside the polygon
The indices of points inside are obtained as indices[:count]
The indices of points outside are obtained as indices[count:]
Examples:
U = [[0,0], [1,0], [1,1], [0,1]] # Unit square
separate_points_by_polygon( [[0.5, 0.5], [1, -0.5], [0.3, 0.2]], U)
will return the indices [0, 2, 1] and count == 2 as only the first
and the last point are inside the unit square
Remarks:
The vertices may be listed clockwise or counterclockwise and
the first point may optionally be repeated.
Polygons do not need to be convex.
Polygons can have holes in them and points inside a hole is
regarded as being outside the polygon.
Algorithm is based on work by Darel Finley,
http://www.alienryderflex.com/polygon/
"""
if check_input:
# Input checks
msg = 'Keyword argument "closed" must be boolean'
if not isinstance(closed, bool):
raise Exception(msg)
try:
points = ensure_numeric(points, numpy.float)
except Exception, e:
msg = ('Points could not be converted to numeric array: %s'
% str(e))
raise Exception(msg)
try:
polygon = ensure_numeric(polygon, numpy.float)
except Exception, e:
msg = ('Polygon could not be converted to numeric array: %s'
% str(e))
raise Exception(msg)