def byCenter2Points(cls, pc, p1, p2):
"""Create an ellipse by center and 2 points for axis.
/----p2----\
/ \
| pc p1
\ /
\----------/
"""
if not isinstance(pc, (QgsPoint, CADPoint)) \
or not isinstance(p1,
(QgsPoint, CADPoint)) \
or not isinstance(p2,
(QgsPoint, CADPoint)):
raise AttributeError
pc = CADPoint(pc)
p1 = CADPoint(p1)
p2 = CADPoint(p2)
angle_exist = pc.getAngleOfLineBetweenTwoPoints(p1)
axis_a = pc.distance(p1)
pp = CADLine.pointOnALine(CADLine(pc, p1), p2)
length = p2.distance(pp)
pp2 = pc.pointProjected(length, 90 + angle_exist)
axis_b = pc.distance(pp2)
return cls(pc, axis_a, axis_b, angle_exist)
def by2Corners(cls, p1, p2, nbEdges=5):
"""CADRegularPolygon by 2 corners (AB):
A----B
/ \
/ \
\ /
\------/
"""
if not isinstance(p1, (QgsPoint, CADPoint)) or \
not isinstance(p2, (QgsPoint, CADPoint)) or \
not isinstance(nbEdges, (long, int)):
raise AttributeError
else:
p1 = CADPoint(p1)
p2 = CADPoint(p2)
angle_exist = p1.getAngleOfLineBetweenTwoPoints(p2)
pm = p1.midpoint(p2)
length = p1.distance(pm)
angle = (180.0 - (360.0 / nbEdges)) / 2.0
hypo = length / math.cos(math.radians(angle))
pc = p1.pointProjected(hypo, angle_exist + angle)
return cls(pc, p1, nbEdges)
return None
def by3Points(cls, p1, p2, p3):
"""Create a CADRectangle with 2 points (AD) and a length (X - AD)
D-------C
| X
A-------B
"""
if not isinstance(p1, (CADPoint, QgsPoint)) or \
not isinstance(p2, (CADPoint, QgsPoint)) or \
not isinstance(p3, (CADPoint, QgsPoint)):
raise AttributeError
p1 = CADPoint(p1)
p2 = CADPoint(p2)
p3 = CADPoint(p3)
l = CADLine(p1, p2)
angle_exist = p1.getAngleOfLineBetweenTwoPoints(p2)
side = CADPoint.isCollinear(p1, p2, p3)
if side == 0:
return None
pp = CADLine.pointOnALine(CADLine(p1, p2), p3)
length = p3.distance(pp) * side
p3 = p2.pointProjected(length, 90 + angle_exist)
p4 = p1.pointProjected(length, 90 + angle_exist)
return cls(p1, p2, p3, p4)
def perpendicular_segment(self, p):
"""Create a perpendicular line segment from `p` to this line.
The enpoints of the segment are ``p`` and the closest point in
the line containing self. (If self is not a line, the point might
not be in self.)
"""
if not isinstance(p, (QgsPoint, CADPoint)):
raise AttributeError
p = CADPoint(p)
if p in self.points:
return p
a, b, c = self.coefficients
if a == 0: # horizontal
p2 = CADPoint(p.x, self.p1.y)
elif b == 0: # vertical
p2 = CADPoint(self.p1.x, p.y)
else:
# ax + by + c = 0
y = (-c - a * p.x) / b
m = self.slope
d2 = 1 + m**2
H = p.y - y
dx = m * H / d2
dy = m * dx
p2 = CADPoint(p.x + dx, y + dy)
return CADLine(p, p2)
def by2PointsAndWidth(cls, p1, p2, w):
"""Create a CADRectangle with 2 points (AD) and the width
D-------C
| |
A-------B
"""
if not isinstance(p1, (CADPoint, QgsPoint)) or \
not isinstance(p2, (CADPoint, QgsPoint)) or \
not isinstance(w, (float, long, int)):
raise AttributeError
p1 = CADPoint(p1)
p2 = CADPoint(p2)
angle_exist = p1.getAngleOfLineBetweenTwoPoints(p2)
pt1 = p1
pt2 = p1.pointProjected(w, 90 - angle_exist)
pt3 = p2.pointProjected(w, 90 - angle_exist)
pt4 = p2
l = CADLine(p1, p2)
if CADPoint.isCollinear(pt1, pt2, pt3) == 0:
pt2 = p1.pointProjected(w, 90 + angle_exist)
pt3 = p2.pointProjected(w, 90 + angle_exist)
return cls(pt1, pt2, pt3, pt4)
def fromFoci(cls, f1, f2, f3):
"""Create an ellipse from foci.
f1 and f2 are foci
f3 is the axis_b
/----f3----\
/ \
| f1 f2 |
\ /
\----------/
"""
if not isinstance(f1, (QgsPoint, CADPoint)) \
or not isinstance(f2,
(QgsPoint, CADPoint)) \
or not isinstance(f3,
(QgsPoint, CADPoint)):
raise AttributeError
f1 = CADPoint(f1)
f2 = CADPoint(f2)
f3 = CADPoint(f3)
dist_f1f2 = f1.distance(f2)
dist_f1f3 = f1.distance(f3)
dist_f2f3 = f2.distance(f3)
dist_tot = dist_f1f3 + dist_f2f3
angle_exist = f1.getAngleOfLineBetweenTwoPoints(f2)
center_f1f2 = f1.midpoint(f2)
axis_a = dist_tot / 2.0
axis_b = math.sqrt((dist_tot / 2.0)**2.0 - (dist_f1f2 / 2.0)**2.0)
return cls(center_f1f2, axis_a, axis_b, angle_exist)
def quadrant(self):
"""Return 4 coordinates [East, North, West, South]
of circle's quadrant"""
N = CADPoint(self._center.x, self._center.y + self._radius)
S = CADPoint(self._center.x, self._center.y - self._radius)
E = CADPoint(self._center.x + self._radius, self._center.y)
W = CADPoint(self._center.x - self._radius, self._center.y)
return [E, N, W, S]
def fromQgsRectangle(cls, r):
"""Create a CADRectangle from a QgsRectangle
"""
if not isinstance(r, QgsRectangle):
raise AttributeError("Error:" + cls.__name__ + " - " + __file__)
return cls()
return cls.byExtent(CADPoint(r.xMinimum(), r.yMinimum()),
CADPoint(r.xMaximum(), r.yMaximum()))
def by3Points(cls, p1, p2, p3, epsilon=1e-8):
"""Create a CADCircle with 3 points ABC
/------\
| |
A C
| |
\--B---/
"""
if not all(isinstance(p, (QgsPoint, CADPoint)) for p in [p1, p2, p3]):
raise AttributeError
p1 = CADPoint(p1)
p2 = CADPoint(p2)
p3 = CADPoint(p3)
# Paul Bourke's algorithm
m_Center = CADPoint()
m_dRadius = -1
yDelta_a = p2.y - p1.y
xDelta_a = p2.x - p1.x
yDelta_b = p3.y - p2.y
xDelta_b = p3.x - p2.x
try:
aSlope = yDelta_a / xDelta_a
except ZeroDivisionError:
return None
try:
bSlope = yDelta_b / xDelta_b
except ZeroDivisionError:
return None
if (math.fabs(xDelta_a) <= epsilon and math.fabs(yDelta_b) <= epsilon):
m_Center.x = (0.5 * (p2.x + p3.x))
m_Center.y = (0.5 * (p1.y + p2.y))
m_dRadius = m_Center.distance(p1)
return cls(m_Center, m_dRadius)
if math.fabs(aSlope-bSlope) <= epsilon:
return None
m_Center.x = (
(aSlope * bSlope * (p1.y - p3.y) +
bSlope * (p1.x + p2.x) -
aSlope * (p2.x + p3.x)) /
(2.0 * (bSlope - aSlope))
)
m_Center.y = (
-1.0 * (m_Center.x - (p1.x + p2.x) / 2.0) /
aSlope + (p1.y + p2.y) / 2.0
)
m_dRadius = m_Center.distance(p1)
return cls(m_Center, m_dRadius)
def __init__(self, p1, p2):
if not all([isinstance(p, (QgsPoint, CADPoint)) for p in [p1, p2]]):
raise AttributeError
if p1 == p2:
# Adapted from SymPy
# if it makes sense to return a Point, handle in subclass
raise ValueError("CADLine requires two unique Points.")
self._p1 = CADPoint(p1)
self._p2 = CADPoint(p2)
def __init__(self, pCenter, pCorner, nbEdges=5):
if not isinstance(pCenter, (QgsPoint, CADPoint)) \
or not isinstance(pCorner, (QgsPoint, CADPoint)) \
or not isinstance(nbEdges,
(long, int)):
raise AttributeError
else:
self._center = CADPoint(pCenter)
self._corner = CADPoint(pCorner)
self._nbEdges = nbEdges
self.__points = self.__updatePoints()
def __init__(self, ptStart, ptEnd, ptArc):
if not all([
isinstance(p, (CADPoint, QgsPoint))
for p in [ptStart, ptEnd, ptArc]
]):
raise AttributeError
else:
self._ptStart = CADPoint(ptStart)
self._ptEnd = CADPoint(ptEnd)
self._ptArc = CADPoint(ptArc)
self._ptCenter = self.__getArcCenter()
def byCenterPoint(cls, pc, p1):
"""Create a CADCircle by Extent CA
/------\A
| |
| C |
| |
\------/
"""
if not all(isinstance(p, (QgsPoint, CADPoint)) for p in [p1, pc]):
raise AttributeError
p1 = CADPoint(p1)
pc = CADPoint(pc)
return cls(pc, pc.distance(p1))
def trim(self, other, p):
"""Return the new CADLine result of intersection with other.
For segment AB intersected at i and clicked on p, the CADLine returned
will iB
A-----i------p---B
return:
i----------B
"""
if isinstance(p, (QgsPoint, CADPoint)) and \
isinstance(other, CADLine) and \
self.intersects(other):
p = CADPoint(p)
try:
pt_inter = self.intersection(other)
p1pi = CADLine(pt_inter, self.p1)
p2pi = CADLine(self.p2, pt_inter)
if p1pi.isOnSegment(p) == 2:
return p1pi
elif p2pi.isOnSegment(p) == 2:
return p2pi
else:
return None
except:
return None
return None
else:
raise AttributeError
def __init__(self, pc, radius):
if not isinstance(pc, (CADPoint, QgsPoint)) or \
not isinstance(radius, (float, long, int)):
raise AttributeError
else:
self._center = CADPoint(pc)
self._radius = radius
def isOnSegment(self, p):
"""Test if this point is on the segment defined by points a, b.
Returns
0 if this point is not on the open ray through a and b,
1 if point is on open ray a,
2 if point is within line segment,
3 if point is on open ray b.
"""
if not isinstance(p, (QgsPoint, CADPoint)):
raise AttributeError
p = CADPoint(p)
a, b = self.points
# algorithm from 'graphics GEMS',
# A. Paeth: 'A Fast 2D Point-on-line test'
if (abs((b.y - a.y) * (p.x - a.x) - (p.y - a.y) *
(b.x - a.x)) >= max(abs(b.x - a.x), abs(b.y - a.y))):
return 0
if ((b.x < a.x and a.x < p.x) or (b.y < a.y and a.y < p.y)):
return 1
if ((p.x < a.x and a.x < b.x) or (p.y < a.y and a.y < b.y)):
return 1
if ((a.x < b.x and b.x < p.x) or (a.y < b.y and b.y < p.y)):
return 3
if ((p.x < b.x and b.x < a.x) or (p.y < b.y and b.y < a.y)):
return 3
return 2
def corner(self, pc):
"""Set the first corner (edge) of the RegularPolygon
"""
if not isinstance(pc, (QgsPoint, CADPoint)):
raise AttributeError
self._corner = CADPoint(pc)
self.__update()
def isValid(self, tolerance=0.1):
"""Return True if is really a rectangle"""
if not isinstance(tolerance, (float, int, long)):
tolerance = 0.1
p1, p2, p3, p4 = self.__points[:]
p12 = p1.getAngleOfLineBetweenTwoPoints(p2)
p23 = p2.getAngleOfLineBetweenTwoPoints(p3)
a1 = p23 - p12
p34 = p3.getAngleOfLineBetweenTwoPoints(p4)
p41 = p4.getAngleOfLineBetweenTwoPoints(p1)
a2 = p41 - p34
if self.__points == [CADPoint(0.0, 0.0)] * 4:
return False
if len(set(self.__points)) != 4:
return False
if not near(a1 % 90, 0.0, tolerance) or not near(
a2 % 90, 0.0, tolerance):
return False
return True
def __contains__(self, other):
if isinstance(other, (QgsPoint, CADPoint)):
other = CADPoint(other)
return bool(self.isOnSegment(other) == 2)
elif isinstance(other, CADLine):
return self.intersects(other)
else:
return False
def byCenter2Points(cls, ptCenter, ptStart, ptEnd, direction=1):
"""Create a CADCirclurArc with by Center C and 2 points AB
A C B
| |
\------/
"""
if all([isinstance(p, (CADPoint, QgsPoint))
for p in [ptCenter, ptStart, ptEnd]]) and \
isinstance(direction, (int, long)):
ptCenter = CADPoint(ptCenter)
ptStart = CADPoint(ptStart)
ptEnd = CADPoint(ptEnd)
a1 = ptCenter.getAngleOfLineBetweenTwoPoints(ptStart)
a2 = ptCenter.getAngleOfLineBetweenTwoPoints(ptEnd)
return cls.byCenterPointAngle(ptCenter, ptStart, a2 - a1,
direction)
def __iter__(self, segments=36):
angle = math.radians(self._angle)
for t in [(2 * math.pi) / segments * i for i in range(segments)]:
p = CADPoint(
self._center.x + self._axis_a * math.cos(t) * math.cos(angle) -
self._axis_b * math.sin(t) * math.sin(angle),
self._center.y + self._axis_a * math.cos(t) * math.sin(angle) +
self._axis_b * math.sin(t) * math.cos(angle))
yield p
def by2Points(cls, p1, p2):
"""Create a CADCircle with 2 points (from diameter : AB)
/------\
| |
A B
| |
\------/
"""
if not all(isinstance(p, (QgsPoint, CADPoint)) for p in [p1, p2]):
raise AttributeError
p1 = CADPoint(p1)
p2 = CADPoint(p2)
center = p1.midpoint(p2)
radius = p1.distance(center)
return cls(center, radius)
def nearestPoints(self, other):
if isinstance(other, (QgsPoint, CADPoint)):
other = CADPoint(other)
dist = [other.distance(p) for p in self.points]
neareastDist = min(dist)
idx = dist.index(neareastDist)
return (self.points[idx], idx)
else:
raise AttributeError
def center(self, pointC):
if isinstance(pointC, CADPoint):
offsetX = pointC.x - self._center.x
offsetY = pointC.y - self._center.y
self._center = pointC
for i, p in enumerate(self.__points):
self.__points[i] = CADPoint(p.x + offsetX, p.y + offsetY)
self.__updateMin()
self.__updateMax
def perpendicular_line(self, p):
"""Create a new Line perpendicular to this linear entity which passes
through the point `p`.
"""
if not isinstance(p, (QgsPoint, CADPoint)):
raise AttributeError
p = CADPoint(p)
d1, d2 = (self.p1.x - self.p2.x, self.p1.y - self.p2.y)
if d2 == 0: # If a horizontal line
if p.y == self.p1.y: # if p is on this linear entity
return CADLine(p, p + CADPoint(0, 1))
else:
p2 = CADPoint(p.x, self.p1.y)
return CADLine(p, p2)
else:
p2 = CADPoint(p.x - d2, p.y + d1)
return CADLine(p, p2)
def parallel_line(self, p):
"""Create a new Line parallel to this linear entity which passes
through the point `p`.
"""
if not isinstance(p, (QgsPoint, CADPoint)):
raise AttributeError
p = CADPoint(p)
d = self.p1 - self.p2
return CADLine(p, p + d)
def pointOnALine(line, pp):
"""Return orthogonal point projected (pp) on line
"""
if not isinstance(pp, (QgsPoint, CADPoint)) or \
not isinstance(line, CADLine):
raise AttributeError
p1, p2 = line.points
pp = CADPoint(pp)
# http://stackoverflow.com/a/15187473
t_num = ((pp.x - p1.x) * (p2.x - p1.x) + (pp.y - p1.y) * (p2.y - p1.y))
t_denum = ((p2.x - p1.x)**2 + (p2.y - p1.y)**2)
t = t_num / t_denum
Dx = p1.x + t * (p2.x - p1.x)
Dy = p1.y + t * (p2.y - p1.y)
return CADPoint(Dx, Dy)
def by2Points(cls, p1, p2):
"""Create a CADRectangle with 2 points (from extent : AC)
D-------C
| |
A-------B
"""
if not isinstance(p1, (CADPoint, QgsPoint)) or \
not isinstance(p2, (CADPoint, QgsPoint)):
raise AttributeError
p1 = CADPoint(p1)
p2 = CADPoint(p2)
pt0 = p1
pt1 = CADPoint(p2.x, p1.y)
pt2 = p2
pt3 = CADPoint(p1.x, p2.y)
return cls(pt0, pt1, pt2, pt3)
def center(self, pc):
"""Set the center of the RegularPolygon
"""
if not isinstance(pc, (QgsPoint, CADPoint)):
raise AttributeError
angle_exist = self._rotation
dist_exist = self._radius
self._center = CADPoint(pc)
self._corner = self._center.pointProjected(dist_exist, angle_exist)
self._update()
def byCenterPoint(cls, pc, p1):
"""Create an ellipse by this center and an extent point
/----------\ p1
/ \
| pc |
\ /
\----------/
"""
if not isinstance(pc, (QgsPoint, CADPoint)) \
or not isinstance(p1,
(QgsPoint, CADPoint)):
raise AttributeError
pc = CADPoint(pc)
p1 = CADPoint(p1)
xOffset = abs(pc.x - p1.x)
yOffset = abs(pc.y - p1.y)
return cls(pc, xOffset, yOffset)