def projection(self, obj):
assert isinstance(obj, baseGeometryObject), 'incorrect object for projection'
if isinstance(obj, Line):
# TODO: remove 0.0 for future Python 3.X versions
tmp = dot(self-obj.basePoint, obj.direction)
if isinstance(tmp, oofun): tmp.size = 1
tmp1 = obj.direction*tmp / (0.0+sum(obj.direction**2))
tmp2 = obj.basePoint
if type(tmp1) == ooarray: # hence tmp2 is array
tmp2 = tmp2.view(ooarray)
return Point(tmp1+tmp2)
elif isinstance(obj, Plane):
d1, d2 = obj.directions
bp = obj.basePoint
a = sum(d1**2)
b = d = dot(d1, d2)
e = sum(d2**2)
c = dot(self-bp, d1)
f = dot(self-bp, d2)
delta = a*e-b*d + 0.0 # TODO: remove 0.0 when Python 2.x will be deprecated
alpha = (c*e-b*f) / delta
beta = (a*f-c*d)/delta
return Point(bp + alpha * d1 + beta * d2)
else:
raise SpaceFuncsException('not implemented for this geometry object yet')
def projection(self, obj):
assert isinstance(
obj, baseGeometryObject), 'incorrect object for projection'
if isinstance(obj, Line):
# TODO: remove 0.0 for future Python 3.X versions
tmp = dot(self - obj.basePoint, obj.direction)
if isinstance(tmp, oofun): tmp.size = 1
tmp1 = obj.direction * tmp / (0.0 + sum(obj.direction**2))
tmp2 = obj.basePoint
if type(tmp1) == ooarray: # hence tmp2 is array
tmp2 = tmp2.view(ooarray)
return Point(tmp1 + tmp2)
elif isinstance(obj, Plane):
d1, d2 = obj.directions
bp = obj.basePoint
a = sum(d1**2)
b = d = dot(d1, d2)
e = sum(d2**2)
c = dot(self - bp, d1)
f = dot(self - bp, d2)
delta = a * e - b * d + 0.0 # TODO: remove 0.0 when Python 2.x will be deprecated
alpha = (c * e - b * f) / delta
beta = (a * f - c * d) / delta
return Point(bp + alpha * d1 + beta * d2)
else:
raise SpaceFuncsException(
'not implemented for this geometry object yet')
def skewLinesNearestPoints(line1, line2):
assert isinstance(line1, Line) and isinstance(line2, Line)
p1, p2 = line1.basePoint, line2.basePoint
d1, d2 = line1.direction, line2.direction
Delta = sum(d1**2)*sum(d2**2) - dot(d1, d2)**2
Delta1 = dot(d2, p1-p2) * dot(d1, d2) - dot(d1, p1-p2) * sum(d2**2)
Delta2 = dot(d2, p1-p2) * sum(d1**2) - dot(d1, d2) * dot(d1, p1-p2)
t1 = Delta1 / Delta
t2 = Delta2 / Delta
for t in [t1, t2]:
if isinstance(t, oofun): t.size = 1
return Point(p1+t1*d1), Point(p2+t2*d2)
def skewLinesNearestPoints(line1, line2):
assert isinstance(line1, Line) and isinstance(line2, Line)
p1, p2 = line1.basePoint, line2.basePoint
d1, d2 = line1.direction, line2.direction
Delta = sum(d1**2) * sum(d2**2) - dot(d1, d2)**2
Delta1 = dot(d2, p1 - p2) * dot(d1, d2) - dot(d1, p1 - p2) * sum(d2**2)
Delta2 = dot(d2, p1 - p2) * sum(d1**2) - dot(d1, d2) * dot(d1, p1 - p2)
t1 = Delta1 / Delta
t2 = Delta2 / Delta
for t in [t1, t2]:
if isinstance(t, oofun): t.size = 1
return Point(p1 + t1 * d1), Point(p2 + t2 * d2)
def _circumSphereCenter(self):
a, b, c = self.reducedVertices
bc, ca, ab = self.reducedVerticesCrossProduct
return (sum(a**2) * bc + sum(b**2) * ca + sum(c**2) * ab) / (2.0*dot(a, bc)) + self.vertices[-1]
