def distance(self, other):
"""The Euclidean distance between self and another GeometricEntity.
Returns
=======
distance : number or symbolic expression.
Raises
======
AttributeError : if other is a GeometricEntity for which
distance is not defined.
TypeError : if other is not recognized as a GeometricEntity.
See Also
========
sympy.geometry.line.Segment.length
sympy.geometry.point.Point.taxicab_distance
Examples
========
>>> from sympy.geometry import Point, Line
>>> p1, p2 = Point(1, 1), Point(4, 5)
>>> l = Line((3, 1), (2, 2))
>>> p1.distance(p2)
5
>>> p1.distance(l)
sqrt(2)
The computed distance may be symbolic, too:
>>> from sympy.abc import x, y
>>> p3 = Point(x, y)
>>> p3.distance((0, 0))
sqrt(x**2 + y**2)
"""
if not isinstance(other , GeometryEntity) :
try :
other = Point(other, dim=self.ambient_dimension)
except TypeError :
raise TypeError("not recognized as a GeometricEntity: %s" % type(other))
if isinstance(other , Point) :
s, p = Point._normalize_dimension(self, Point(other))
return sqrt(Add(*((a - b)**2 for a, b in zip(s, p))))
try :
return other.distance(self)
except AttributeError :
raise AttributeError("distance between Point and %s is not defined" % type(other))
def are_collinear(*points):
"""Is a sequence of points collinear?
Test whether or not a set of points are collinear. Returns True if
the set of points are collinear, or False otherwise.
Parameters
==========
points : sequence of Point
Returns
=======
are_collinear : boolean
See Also
========
sympy.geometry.line.Line3D
Examples
========
>>> from sympy import Point3D, Matrix
>>> from sympy.abc import x
>>> p1, p2 = Point3D(0, 0, 0), Point3D(1, 1, 1)
>>> p3, p4, p5 = Point3D(2, 2, 2), Point3D(x, x, x), Point3D(1, 2, 6)
>>> Point3D.are_collinear(p1, p2, p3, p4)
True
>>> Point3D.are_collinear(p1, p2, p3, p5)
False
"""
return Point.is_collinear(*points)
def intersection(self, other):
"""The intersection between this point and another GeometryEntity.
Parameters
==========
other : Point
Returns
=======
intersection : list of Points
Notes
=====
The return value will either be an empty list if there is no
intersection, otherwise it will contain this point.
Examples
========
>>> from sympy import Point
>>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(0, 0)
>>> p1.intersection(p2)
[]
>>> p1.intersection(p3)
[Point2D(0, 0)]
"""
if not isinstance(other, GeometryEntity):
other = Point(other)
if isinstance(other, Point):
if self == other:
return [self]
p1, p2 = Point._normalize_dimension(self, other)
if p1 == self and p1 == p2:
return [self]
return []
return other.intersection(self)
def project(a, b):
"""Project the point `a` onto the line between the origin
and point `b` along the normal direction.
Parameters
==========
a : Point
b : Point
Returns
=======
p : Point
See Also
========
sympy.geometry.line.LinearEntity.projection
Examples
========
>>> from sympy.geometry import Line, Point
>>> a = Point(1, 2)
>>> b = Point(2, 5)
>>> z = a.origin
>>> p = Point.project(a, b)
>>> Line(p, a).is_perpendicular(Line(p, b))
True
>>> Point.is_collinear(z, p, b)
True
"""
a, b = Point._normalize_dimension(Point(a), Point(b))
if b.is_zero:
raise ValueError("Cannot project to the zero vector.")
return b * (a.dot(b) / b.dot(b))
def intersection(self, other):
"""The intersection between this point and another GeometryEntity.
Parameters
==========
other : GeometryEntity or sequence of coordinates
Returns
=======
intersection : list of Points
Notes
=====
The return value will either be an empty list if there is no
intersection, otherwise it will contain this point.
Examples
========
>>> from sympy import Point3D
>>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(0, 0, 0)
>>> p1.intersection(p2)
[]
>>> p1.intersection(p3)
[Point3D(0, 0, 0)]
"""
if not isinstance(other, GeometryEntity):
other = Point(other, dim=3)
if isinstance(other, Point3D):
if self == other:
return [self]
return []
return other.intersection(self)
def drawExWall(xSmallExWall, xBigExWall, ySmallExWall, yBigExWall, msp):
'''
Draw external wall lines.
uppose that buildings are ractangle.
Args:
xSmallExWall,
xBigExWall,
ySmallExWall,
yBigExWall,
msp, en ezdxf.modelspace() object used to create a new dxf file.
'''
recognizeObject = recognize.Recognize()
xMax, xMin, yMax, yMin = recognizeObject.getExtremePointInLines(
xSmallExWall)
msp.add_line((xMin, yMin, 0), (xMin, yMax, 0)) # add a LINE entity
'''xMax,xMin,yMax,yMin = recognizeObject.getExtremePointInLines(xBigExWall)
msp.add_line((xMax,yMin,0),(xMax,yMax,0)) # add a LINE entity
xMax,xMin,yMax,yMin = recognizeObject.getExtremePointInLines(ySmallExWall)
msp.add_line((xMin,yMin,0),(xMax,yMin,0)) # add a LINE entity
xMax,xMin,yMax,yMin = recognizeObject.getExtremePointInLines(yBigExWall)
msp.add_line((xMin,yMax,0),(xMax,yMax,0)) # add a LINE entity
'''
del recognizeObject
return Point(xMin, yMin), Point(xMin, yMax)
def paralline(nl=2, x0=0, y0=100, x1=33, y1=66):
p1, p2 = Point(x0, y0), Point(x1, y1)
s1 = Segment(p1, p2)
# Create a new Line perpendicular to this linear entity which passes through the point p1.
l1 = s1.perpendicular_line(p1)
l2 = s1.perpendicular_line(p2)
p1 in l1
p2 in l2
s1.is_perpendicular(l2)
s1.is_perpendicular(l1)
#p11 = subs_point(l1, s1.length)
# find coords of parallel nl segments from each side of the transect
x11, y11 = zeros(2*nl+1), zeros(2*nl+1)
x22, y22 = zeros(2*nl+1), zeros(2*nl+1)
j=0
for i in range(-nl,nl+1):
p11 = subs_point(l1, 1*i/s1.length) # divide unit segment on its length
x111, y111 = p11.args
x11[j], y11[j] = float64(x111), float64(y111)
p22 = subs_point(l2, 1*i/s1.length) # divide unit segment on its length
x222, y222 = p22.args
x22[j], y22[j] = float64(x222), float64(y222)
j+=1
# # Checking that segments are parallel and same length
# s2 = Segment(p11,p22)
# s2.is_parallel(s1)
# s1.length - s2.length
# plt.plot([x0, x1], [y0, y1])
# plt.plot([x11, x22],[y11, y22], 'k')
return x11, y11, x22, y22
def orthogonal_direction(self):
"""Returns a non-zero point that is orthogonal to the
line containing `self` and the origin.
Examples
========
>>> from sympy.geometry import Line, Point
>>> a = Point(1, 2, 3)
>>> a.orthogonal_direction
Point3D(-2, 1, 0)
>>> b = _
>>> Line(b, b.origin).is_perpendicular(Line(a, a.origin))
True
"""
dim = self.ambient_dimension
# if a coordinate is zero, we can put a 1 there and zeros elsewhere
if self[0] == S.Zero:
return Point([1] + (dim - 1)*[0])
if self[1] == S.Zero:
return Point([0,1] + (dim - 2)*[0])
# if the first two coordinates aren't zero, we can create a non-zero
# orthogonal vector by swapping them, negating one, and padding with zeros
return Point([-self[1], self[0]] + (dim - 2)*[0])
def sphere_impact_points(self):
impact_points = getattr(self, '_impact_points', None)
print round(self.semi_major_axis, 2)
if impact_points:
# TODO should include semi minor too
"""Invalid ellipse on change of semi major axis"""
if round(self.semi_major_axis, 2) != round(self._impact_sma, 2):
impact_points = None
print 'invalid!'
if impact_points is None:
print 'create!'
self._impact_sma = self.semi_major_axis
r = self.equatorial_radius
a = self.semi_major_axis
b = self.semi_minor_axis
c = math.sqrt(a ** 2 - b ** 2) # linear eccentricity
elp = Ellipse(Point(c, 0), a, b)
crc = Circle(Point(0, 0), r)
self._impact_points = sorted(list(set([(float(point.x), float(point.y)) for point in elp.intersection(crc)])))
return self._impact_points
def separaArestas(p1, p2, p3, p4=None):
"""."""
arestas_separadas = []
if p1 != p2:
arestas_separadas.append(Segment(Point(p1.x, p1.y), Point(p2.x, p2.y)))
if p2 != p3:
arestas_separadas.append(Segment(Point(p2.x, p2.y), Point(p3.x, p3.y)))
if p3 != p4 and not (p4 is None):
arestas_separadas.append(Segment(Point(p3.x, p3.y), Point(p4.x, p4.y)))
return arestas_separadas
def transform(self, matrix):
"""Return the point after applying the transformation described
by the 3x3 Matrix, ``matrix``.
See Also
========
sympy.geometry.point.Point2D.rotate
sympy.geometry.point.Point2D.scale
sympy.geometry.point.Point2D.translate
"""
if not (matrix.is_Matrix and matrix.shape == (3, 3)):
raise ValueError("matrix must be a 3x3 matrix")
col, row = matrix.shape
x, y = self.args
return Point(*(Matrix(1, 3, [x, y, 1]) * matrix).tolist()[0][:2])
def handle_position_request(self, req):
x, y = req.current_pose.pose.position.x, req.current_pose.pose.position.y
rospy.loginfo(
"Received request for topological pose: x={0:.3f}, y={1:.3f} (frame: {2})"
.format(x, y, req.current_pose.header.frame_id))
robot_pose = Point(x, y) # Inspection test pose
for room in self.rooms:
if not self.rooms[room].encloses_point(robot_pose):
continue
rospy.loginfo('robot is in room: ' + room)
return TopologicalPositionResponse(room)
position = 'hallway'
rospy.logwarn("Failed to find room, using default location: %s" %
position)
return TopologicalPositionResponse(position)
def print_display(screen):
lowest_x = sorted(screen, key=lambda point: point.x)
lowest_y = sorted(screen, key=lambda point: point.y)
highest_x = sorted(screen, key=lambda point: point.x, reverse=True)
highest_y = sorted(screen, key=lambda point: point.y, reverse=True)
print("Part2")
for y in range(lowest_y[0].y, highest_y[0].y + 1):
row = ""
for x in range(lowest_x[0].x, highest_x[0].x):
current = Point(x, y)
if current not in screen:
row += "0"
else:
row += str(screen[current])
print(row)
def _normalize_dimension(cls, *points, **kwargs):
"""Ensure that points have the same dimension.
By default `on_morph='warn'` is passed to the
`Point` constructor."""
# if we have a built-in ambient dimension, use it
dim = getattr(cls, '_ambient_dimension', None)
# override if we specified it
dim = kwargs.get('dim', dim)
# if no dim was given, use the highest dimensional point
if dim is None:
dim = max(i.ambient_dimension for i in points)
if all(i.ambient_dimension == dim for i in points):
return list(points)
kwargs['dim'] = dim
kwargs['on_morph'] = kwargs.get('on_morph', 'warn')
return [Point(i, **kwargs) for i in points]
def create_segments(line):
segs = []
pos = Point(0, 0)
steps = 0
for movement in line:
match = re.match(dir_re, movement)
direction = match.group(1)
amount = int(match.group(2))
new_pos = pos + maps[direction] * amount
segs.append((Segment(pos, new_pos), steps))
steps = steps + amount
pos = new_pos
return segs
def transform(self, matrix):
"""Return the point after applying the transformation described
by the 3x3 Matrix, ``matrix``.
See Also
========
geometry.entity.rotate
geometry.entity.scale
geometry.entity.translate
"""
if not (matrix.is_Matrix and matrix.shape == (3, 3)):
raise ValueError("matrix must be a 3x3 matrix")
col, row = matrix.shape
valid_matrix = matrix.is_square and col == 3
x, y = self.args
return Point(*(Matrix(1, 3, [x, y, 1]) * matrix).tolist()[0][:2])
def rotate(self, angle, pt=None):
"""Rotate the object about pt by the given angle (in radians).
The default pt is the origin, Point(0, 0)
XXX geometry needs a modify_points method which operates
on only the points of the object
See Also
========
scale, translate
Examples
========
>>> from sympy import Point, RegularPolygon, Polygon, pi
>>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices)
>>> t # vertex on x axis
Triangle(Point(1, 0), Point(-1/2, sqrt(3)/2), Point(-1/2, -sqrt(3)/2))
>>> t.rotate(pi/2) # vertex on y axis now
Triangle(Point(0, 1), Point(-sqrt(3)/2, -1/2), Point(sqrt(3)/2, -1/2))
"""
from sympy import cos, sin, Point
c = cos(angle)
s = sin(angle)
if isinstance(self, Point):
rv = self
if pt is not None:
rv -= pt
x, y = rv
rv = Point(c * x - s * y, s * x + c * y)
if pt is not None:
rv += pt
return rv
newargs = []
for a in self.args:
if isinstance(a, GeometryEntity):
newargs.append(a.rotate(angle, pt))
else:
newargs.append(a)
return type(self)(*newargs)
def canberra_distance(self, p):
"""The Canberra Distance from self to point p.
Returns the weighted sum of horizontal and vertical distances to
point p.
Parameters
==========
p : Point
Returns
=======
canberra_distance : The weighted sum of horizontal and vertical
distances to point p. The weight used is the sum of absolute values
of the coordinates.
Examples
========
>>> from sympy.geometry import Point
>>> p1, p2 = Point(1, 1), Point(3, 3)
>>> p1.canberra_distance(p2)
1
>>> p1, p2 = Point(0, 0), Point(3, 3)
>>> p1.canberra_distance(p2)
2
Raises
======
ValueError when both vectors are zero.
See Also
========
sympy.geometry.point.Point.distance
"""
s, p = Point._normalize_dimension(self, Point(p))
if self.is_zero and p.is_zero:
raise ValueError("Cannot project to the zero vector.")
return Add(*((abs(a - b) / (abs(a) + abs(b))) for a, b in zip(s, p)))
def testFindIntersection1(self):
buyerPoints = [Point(2, 3), Point(3, 3), Point(3, 2), Point(5, 2)]
sellerPoints = [Point(1, 1), Point(4, 1), Point(4, 4)]
buyerIntersectPoint, sellerIntersectPoint = findIntersection(
buyerPoints, sellerPoints)
self.assertEqual(buyerIntersectPoint[0].x.evalf(), 3)
self.assertEqual(buyerIntersectPoint[0].y.evalf(), 2)
self.assertEqual(buyerIntersectPoint[1].x.evalf(), 5)
self.assertEqual(buyerIntersectPoint[1].y.evalf(), 2)
self.assertEqual(sellerIntersectPoint[0].x.evalf(), 4)
self.assertEqual(sellerIntersectPoint[0].y.evalf(), 1)
self.assertEqual(sellerIntersectPoint[1].x.evalf(), 4)
self.assertEqual(sellerIntersectPoint[1].y.evalf(), 4)
def affine_rank(*args):
"""The affine rank of a set of points is the dimension
of the smallest affine space containing all the points.
For example, if the points lie on a line (and are not all
the same) their affine rank is 1. If the points lie on a plane
but not a line, their affine rank is 2. By convention, the empty
set has affine rank -1."""
if len(args) == 0:
return -1
# make sure we're genuinely points
# and translate every point to the origin
points = Point._normalize_dimension(*[Point(i) for i in args])
origin = points[0]
points = [i - origin for i in points[1:]]
m = Matrix([i.args for i in points])
return m.rank()
def is_scalar_multiple(self, p):
"""Returns whether each coordinate of `self` is a scalar
multiple of the corresponding coordinate in point p.
"""
s, o = Point._normalize_dimension(self, Point(p))
# 2d points happen a lot, so optimize this function call
if s.ambient_dimension == 2:
(x1, y1), (x2, y2) = s.args, o.args
rv = (x1*y2 - x2*y1).equals(0)
if rv is None:
raise Undecidable(filldedent(
'''can't determine if %s is a scalar multiple of
%s''' % (s, o)))
# if the vectors p1 and p2 are linearly dependent, then they must
# be scalar multiples of each other
m = Matrix([s.args, o.args])
return m.rank() < 2
def are_coplanar(cls, *points):
"""Return True if there exists a plane in which all the points
lie. A trivial True value is returned if `len(points) < 3` or
all Points are 2-dimensional.
Parameters
==========
A set of points
Raises
======
ValueError : if less than 3 unique points are given
Returns
=======
boolean
Examples
========
>>> from sympy import Point3D
>>> p1 = Point3D(1, 2, 2)
>>> p2 = Point3D(2, 7, 2)
>>> p3 = Point3D(0, 0, 2)
>>> p4 = Point3D(1, 1, 2)
>>> Point3D.are_coplanar(p1, p2, p3, p4)
True
>>> p5 = Point3D(0, 1, 3)
>>> Point3D.are_coplanar(p1, p2, p3, p5)
False
"""
if len(points) <= 1:
return True
points = cls._normalize_dimension(*[Point(i) for i in points])
# quick exit if we are in 2D
if points[0].ambient_dimension == 2:
return True
points = list(uniq(points))
return Point.affine_rank(*points) <= 2
def singlearearoute(cell, inputwidth, Entrance, Exit):
mintime = float('inf')
optimalangle = 0
optimalpath = []
isoptrf = False
Entrance = Point(Entrance)
Exit = Point(Exit)
for angle in range(0, 180, 90):
angle = float(angle)
rcell = cell.rotate(angle / 180 * math.pi)
rentrance = Entrance.rotate(angle / 180 * math.pi)
rexit = Exit.rotate(angle / 180 * math.pi)
rcell = roundpolygon(rcell)
waypoint = createallwaypoint(rcell, inputwidth)
time = timeconsume(waypoint, rentrance, rexit)
if (time < mintime):
mintime = time
optimalangle = angle
optimalpath = waypoint
isoptrf = False
rvwaypoint = waypoint[:]
rvwaypoint.reverse()
time = timeconsume(rvwaypoint, rentrance, rexit)
if (time < mintime):
mintime = time
optimalangle = angle
optimalpath = rvwaypoint
isoptrf = False
rfcell = reflectpolygon(rcell)
rfentrance = rentrance.reflect(xaxis)
rfexit = rexit.reflect(xaxis)
waypoint = createallwaypoint(rfcell, inputwidth)
time = timeconsume(waypoint, rfentrance, rfexit)
if (time < mintime):
mintime = time
optimalangle = angle
optimalpath = waypoint
isoptrf = True
rvwaypoint = waypoint[:]
rvwaypoint.reverse()
time = timeconsume(rvwaypoint, rfentrance, rfexit)
if (time < mintime):
mintime = time
optimalangle = angle
optimalpath = rvwaypoint
isoptrf = True
for i in range(len(optimalpath)):
if (isoptrf):
optimalpath[i] = optimalpath[i].reflect(xaxis)
optimalpath[i] = optimalpath[i].rotate(-optimalangle / 180 * math.pi)
return optimalpath
def __add__(self, other):
"""Add other to self by incrementing self's coordinates by those of other.
See Also
========
sympy.geometry.entity.translate
"""
if isinstance(other, Point):
if len(other.args) == len(self.args):
return Point(
*[simplify(a + b) for a, b in zip(self.args, other.args)])
else:
raise TypeError(
"Points must have the same number of dimensions")
else:
raise ValueError('Cannot add non-Point, %s, to a Point' % other)
def affine_rank(*args):
"""The affine rank of a set of points is the dimension
of the smallest affine space containing all the points.
For example, if the points lie on a line (and are not all
the same) their affine rank is 1. If the points lie on a plane
but not a line, their affine rank is 2. By convention, the empty
set has affine rank -1."""
if len(args) == 0:
return -1
# make sure we're genuinely points
# and translate every point to the origin
points = Point._normalize_dimension(*[Point(i) for i in args])
origin = points[0]
points = [i - origin for i in points[1:]]
m = Matrix([i.args for i in points])
# XXX fragile -- what is a better way?
return m.rank(iszerofunc=lambda x: abs(x.n(2)) < 1e-12
if x.is_number else x.is_zero)
def findPathOld(roada, lanea, roadb, laneb, width, maxRadius=10., midPoint=5):
dxa, dya = getRoadUnitVector(roada)
dxb, dyb = getRoadUnitVector(roadb)
pxa, pya = getOutPoint(roada, width, lanea)
pxb, pyb = getInPoint(roadb, width, laneb)
pa = Point(pxa, pya)
pb = Point(pxb, pyb)
da = Point(dxa, dya)
db = Point(dxb, dyb)
la = Line(pa, pa + da)
lb = Line(pb, pb + db)
inter = la.intersection(lb)
# print(roada, roadb)
disa = inter.disntance(pa)
disb = inter.disntance(pb)
distance = np.min([disa, disb, maxRadius])
ca = pa + da * (disa - distance)
cb = pb - db * (disb - distance)
o = (ca, ca + da.rotate(pi / 2)).intersection(cb, cb + db.rotate(pi / 2))
oa = ca - o
ob = cb - o
angle = oa.dot(ob)
dangle = angle / midPoint
path = [pa]
for i in range(midPoint + 1):
path.append(o + oa.rotate(dangle * i))
path.append(pb)
# ix, iy = computeIntersection(pxa, pya, dxa, dya, pxb, pyb, dxb, dyb)
# _width = (dxa * (pxb - pxa) + dya * (pyb - pya)) / 3
# print(dxa, dya, (pxb - pxa), (pyb - pya), _width)
# return getOutTurnPoints(roada, _width, lanea, width) + getInTurnPoints(roadb, _width, laneb, width)
return list(map(pointToDict2, path))
def transform(self, matrix):
"""Return the point after applying the transformation described
by the 3x3 Matrix, ``matrix``.
See Also
========
geometry.entity.rotate
geometry.entity.scale
geometry.entity.translate
"""
try:
col, row = matrix.shape
valid_matrix = matrix.is_square and col == 3
except AttributeError:
# We hit this block if matrix argument is not actually a Matrix.
valid_matrix = False
if not valid_matrix:
raise ValueError("The argument to the transform function must be " \
+ "a 3x3 matrix")
x, y = self.args
return Point(*(Matrix(1, 3, [x, y, 1])*matrix).tolist()[0][:2])
def Angle(self):
yAxis = Line(Point(0, 1), Point(0, 0))
point1 = Point(self.Box[1][0], self.Box[1][1])
point2 = Point(self.Box[0][0], self.Box[0][1])
point3 = Point(self.Box[2][0], self.Box[2][1])
if point1.distance(point2) > point1.distance(point3):
longerLine = Line(point1, point2)
else:
longerLine = Line(point1, point3)
angle = int(math.degrees(yAxis.angle_between(longerLine)))
if (int(angle) > 90):
if angle - 180 + 80 >= 0:
return angle - 180 + 80
else:
return 0
else:
if angle + 80 >= 0:
return angle + 80
else:
return 0
def Tangent_lines(circle_C, point_P):
R = float(circle_C.radius.evalf())
circle = [float(circle_C.center.x.evalf()), float(circle_C.center.y.evalf())]
point = [float(point_P.x.evalf()), float(point_P.y.evalf())]
circle_point_angle = np.arctan2(point[1] - circle[1], point[0] - circle[0])
cos = R / np.sqrt(np.sum((np.array(circle) - np.array(point)) ** 2))
radian_half = np.arccos(cos)
tangent_angle1 = circle_point_angle + radian_half
tangent_point1 = Point(circle[0] + R * np.cos(tangent_angle1), circle[1] + R * np.sin(tangent_angle1))
tangent_angle2 = circle_point_angle - radian_half
tangent_point2 = Point(circle[0] + R * np.cos(tangent_angle2), circle[1] + R * np.sin(tangent_angle2))
return [Line(Point(point), Point(tangent_point1)), Line(Point(point), Point(tangent_point2))]
def translate(self, x=0, y=0):
"""Shift the Point by adding x and y to the coordinates of the Point.
See Also
========
rotate, scale
Examples
========
>>> from sympy import Point
>>> t = Point(0, 1)
>>> t.translate(2)
Point(2, 1)
>>> t.translate(2, 2)
Point(2, 3)
>>> t + Point(2, 2)
Point(2, 3)
"""
return Point(self.x + x, self.y + y)
def scale(self, x=1, y=1):
"""Scale the object by multiplying the x,y-coordinates by x and y.
>>> from sympy import RegularPolygon, Point, Polygon
>>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices)
>>> t
Triangle(Point(1, 0), Point(-1/2, sqrt(3)/2), Point(-1/2, -sqrt(3)/2))
>>> t.scale(2)
Triangle(Point(2, 0), Point(-1, sqrt(3)/2), Point(-1, -sqrt(3)/2))
>>> t.scale(2,2)
Triangle(Point(2, 0), Point(-1, sqrt(3)), Point(-1, -sqrt(3)))
"""
from sympy import Point
if isinstance(self, Point):
return Point(self[0] * x, self[1] * y)
newargs = []
for a in self.args:
if isinstance(a, GeometryEntity):
newargs.append(a.scale(x, y))
else:
newargs.append(a)
return type(self)(*newargs)
def _collect_shapes(self, d, materials):
"""
Collect and instantiate the dictionary stored in the shapes attribute
given a dictionary describing the shapes in the layer
"""
shapes = OrderedDict()
sorted_d = OrderedDict(
sorted(d.items(), key=lambda tup: tup[1]['order']))
for name, data in sorted_d.items():
shape = data['type'].lower()
if shape == 'circle':
center = Point(data['center']['x'], data['center']['y'])
radius = data['radius']
material = data['material']
if material not in self.materials:
self.materials[material] = materials[material]
shape_obj = Circle(center, radius)
else:
raise NotImplementedError('Can only handle circles right now')
shapes[name] = (shape_obj, material)
self.shapes = shapes
return shapes
def is_collinear(self, *args):
"""Returns `True` if there exists a line
that contains `self` and `points`. Returns `False` otherwise.
A trivially True value is returned if no points are given.
Parameters
==========
args : sequence of Points
Returns
=======
is_collinear : boolean
See Also
========
sympy.geometry.line.Line
Examples
========
>>> from sympy import Point
>>> from sympy.abc import x
>>> p1, p2 = Point(0, 0), Point(1, 1)
>>> p3, p4, p5 = Point(2, 2), Point(x, x), Point(1, 2)
>>> Point.is_collinear(p1, p2, p3, p4)
True
>>> Point.is_collinear(p1, p2, p3, p5)
False
"""
points = (self,) + args
points = Point._normalize_dimension(*[Point(i) for i in points])
points = list(uniq(points))
return Point.affine_rank(*points) <= 1
def sendFaceImages(self):
self.statusLabel.set_text("Obrada uzoraka")
detector = dlib.get_frontal_face_detector()
predictor = dlib.shape_predictor("ldm.dat")
for i in range(0, 7):
gray = cv2.imread("Camera/Resources/" + str(i) + '.png', cv2.CV_8UC1)
#gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
rects = detector(gray, 1)
# loop over the face detections
for (j, rect) in enumerate(rects):
shape = predictor(gray, rect)
shape = face_utils.shape_to_np(shape)
angle = self.calculateFaceTilt(Point(shape[39]), Point(shape[42]))
gray = self.rotateImage(gray, angle, tuple(shape[33]))
#gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
rects = detector(gray, 1)
# loop over the face detections
for (k, rect) in enumerate(rects):
shape = predictor(gray, rect)
shape = face_utils.shape_to_np(shape)
eye = Point(shape[37])
eyebrow = Point(shape[19])
left = Point(min(shape, key=itemgetter(0)))
top = Point(min(shape, key=itemgetter(1)))
right = Point(max(shape, key=itemgetter(0)))
bottom = Point(max(shape, key=itemgetter(1)))
gray = gray[int(top.y - eye.distance(eyebrow) / 2):int(top.y + top.distance(bottom)),
int(left.x):int(left.x + left.distance(right))]
#ujednacavanje histograma
clahe = cv2.createCLAHE(clipLimit=2.0, tileGridSize=(8, 8))
gray = clahe.apply(gray)
#gray = cv2.bilateralFilter(gray, 9, 75, 75)
ratio = 300.0 / gray.shape[1]
dimensions = (300, int(gray.shape[0] * ratio))
gray = cv2.resize(gray, dimensions, interpolation=cv2.INTER_AREA)
cv2.imwrite("Camera/Resources/" + str(i) + '.png', gray)
for i in range(0, 7):
self.statusLabel.set_text("Slanje uzoraka")
client.send("ftp:" + str(i))
self.waitForResponse()
imageFile = open("Camera/Resources/" + str(i) + '.png', "rb")
offset = 0
while True:
sent = sendfile(client.fileno(), imageFile.fileno(), offset, 4096)
if sent == 0:
client.send("EOF")
break # EOF
offset += sent
self.statusLabel.set_text("Potvrdite PIN")
self.btnConfirm.set_sensitive(True)
self.waitForResponse()
for (j, rect) in enumerate(rects):
shape = predictor(gray, rect)
shape = face_utils.shape_to_np(shape)
angle = calculateFaceTilt(Point(shape[39]), Point(shape[42]))
gray = rotateImage(gray, angle, tuple(shape[33]))
# gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
rects = detector(gray, 1)
# loop over the face detections
for (k, rect) in enumerate(rects):
shape = predictor(gray, rect)
shape = face_utils.shape_to_np(shape)
eye = Point(shape[37])
eyebrow = Point(shape[19])
left = Point(min(shape, key=itemgetter(0)))
top = Point(min(shape, key=itemgetter(1)))
right = Point(max(shape, key=itemgetter(0)))
bottom = Point(max(shape, key=itemgetter(1)))
gray = gray[int(top.y - eye.distance(eyebrow) / 2):int(top.y + top.distance(bottom)),
int(left.x):int(left.x + left.distance(right))]
# ujednacavanje histograma
clahe = cv2.createCLAHE(clipLimit=2.0, tileGridSize=(8, 8))
gray = clahe.apply(gray)
# gray = cv2.bilateralFilter(gray, 9, 75, 75)
ratio = 300.0 / gray.shape[1]
def __abs__(self):
"""Returns the distance between this point and the origin."""
origin = Point([0]*len(self.args))
return Point.distance(origin, self)
