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 intersection(self, other):
if not isinstance(other, CADLine):
raise AttributeError
# public domain function by Darel Rex Finley, 2006
# http://alienryderflex.com/intersect/
pt_inter = CADPoint()
Ax, Ay, Bx, By = self.pointsXY
Cx, Cy, Dx, Dy = other.pointsXY
if ((Ax == Bx and Ay == By) or (Cx == Dx and Cy == Dy)):
return None
# (1) Translate the system so that point A is on the origin.
Bx -= Ax
By -= Ay
Cx -= Ax
Cy -= Ay
Dx -= Ax
Dy -= Ay
# Discover the length of segment A-B.
distAB = math.sqrt(Bx * Bx + By * By)
# (2) Rotate the system so that point B is on the positive X axis.
theCos = Bx / distAB
theSin = By / distAB
newX = Cx * theCos + Cy * theSin
Cy = Cy * theCos - Cx * theSin
Cx = newX
newX = Dx * theCos + Dy * theSin
Dy = Dy * theCos - Dx * theSin
Dx = newX
# Fail if the lines are parallel.
if (Cy == Dy):
return None
# (3) Discover the position of the intersection point along line A-B.
ABpos = Dx + (Cx - Dx) * Dy / (Dy - Cy)
# (4) Apply the discovered position to line A-B
# in the original coordinate system.
pt_inter.x = Ax + ABpos * theCos
pt_inter.y = Ay + ABpos * theSin
# Success.
return pt_inter