def _circular_coplanar_circular(self, other):
cc = other.point - self.point
d = cc.magnitude()
rS = self.radius
rO = other.radius
# too far apart?
if (rS + rO) < d - EPSILON:
return Nowhere()
# equal or circumscribed?
if zero(d):
if equal(rS, rO):
return self
return Nowhere()
# tangent?
if equal(d, rS + rO):
cc = cc.magnitude(rS)
return Unity(self.point + cc)
# find the midpoint where the "radical line" (chord) crosses cc
term = d * d - rS * rS + rO * rO
xS = term / 2 * d
xO = d - xS
# find the length of the radical line
leg = 4 * d * d * rS * rS - term * term
yy = 1 / d * sqrt(leg)
y = yy / 2
# find the intersection points
cross = cc * self.normal
chord = cc * cross
chord = chord.magnitude(y)
mark = cc
mark = mark.magnitude(xS)
mark += self.point
return Duality(mark + chord, mark - chord)
def __test__():
from testing import __ok__, __report__
import vectors ; from vectors import V,equal,zero
print 'Testing interpolations...'
__ok__( linear(0.5, 50, 60), 55 )
__ok__( linear(1, 2, 1.5, 50, 60), 55 )
__ok__( linear(1, 2, 1.5, V(50,500), V(60,600)), V(55,550) )
__ok__( bezier3(0.0, 0.0, 1.0, 0.0), 0.0 )
__ok__( bezier3(0.5, 0.0, 1.0, 0.0), 0.5 )
__ok__( equal( bezier3(0.2, 0.0, 1.0, 0.0),
bezier3(0.8, 0.0, 1.0, 0.0) ) )
__ok__( bezier3(1.0, 0.0, 1.0, 0.0), 0.0 )
__ok__( bezier4(0.0, 0.0, 1.0, 1.0, 0.0), 0.0 )
__ok__( bezier4(0.5, 0.0, 1.0, 1.0, 0.0), 0.75 )
__ok__( equal( bezier4(0.2, 0.0, 1.0, 1.0, 0.0),
bezier4(0.8, 0.0, 1.0, 1.0, 0.0) ) )
__ok__( bezier4(1.0, 0.0, 1.0, 1.0, 0.0), 0.0 )
__ok__( bezier(0.0, 0.0, 1.0, 1.0, 1.0, 0.0), 0.0 )
__ok__( bezier(0.5, 0.0, 1.0, 1.0, 1.0, 0.0), 0.875 )
__ok__( equal( bezier(0.2, 0.0, 1.0, 1.0, 1.0, 0.0),
bezier(0.8, 0.0, 1.0, 1.0, 1.0, 0.0) ) )
__ok__( bezier(1.0, 0.0, 1.0, 1.0, 1.0, 0.0), 0.0 )
__ok__( bezier(1.0, 0.0, 1.0, 1.0, 1.0, 0.0), 0.0 )
__report__()
def _circular_circular_test():
from testing import __ok__
# tangent at origin
c1 = Circular(V(-1, 0, 0), V.Y, 1)
c2 = Circular(V(1, 0, 0), V.Y, 1)
c1c2 = c1 * c2
__ok__(isinstance(c1c2, Unity))
__ok__(c1c2.point == V())
# cross off origin
c1 = Circular(V.O, V.Y, 1)
c2 = Circular(V.X, V.Y, 1)
c1c2 = c1 * c2
__ok__(isinstance(c1c2, Duality))
__ok__(c1c2.pointA[0] == c1c2.pointB[0])
__ok__(equal(c1c2.pointA[1], -c1c2.pointB[1]))
__ok__(equal(abs(c1c2.pointA[1]), 0.5 * sqrt(3)))
def _planar_linear_test():
from testing import __ok__
p = Planar(V(3, 0, -1), V(0, 3, 0))
__ok__(str(p) == "Planar(V(3.0, 0.0, -1.0), V(0.0, 1.0, 0.0))")
l = Linear(V(2, 1, 1), V(0, -1, 1))
u = p * l
__ok__(str(u) == "Unity(V(1.0, 0.0, 1.0))")
p = Planar(V(3, -7, -1), V(1, 1, 0))
__ok__(equal(sqrt(2) / 2, p.normal[1]))
def _spherical_spherical(self, other):
cc = other.point - self.point
d = cc.magnitude()
rS = self.radius
rO = other.radius
# too far apart?
if (rS + rO) < d - EPSILON:
return Nowhere()
# equal or circumscribed?
if zero(d):
if equal(rS, rO):
return self
return Nowhere()
# tangent?
if equal(d, rS + rO):
cc = cc.magnitude(rS)
return Unity(self.point + cc)
if max(rS, rO) - (d + min(rO, rS)) > 0:
#One sphere included in another
return Nowhere()
# find the midpoint where the "radical line" (chord) crosses cc
#print d,rS,rO
#print rS - (d+rO)
term = d * d - rS * rS + rO * rO
#print term
#term = rS*rS - rO*rO
xS = term / (2 * d)
#print xS
xO = d - xS
# find the length of the radical line
#leg = 4*d*d*rS*rS - term*term
#yy = 1/d * sqrt(leg)
#y = yy/2
y = sqrt(rS * rS - xO * xO)
# find the intersection points
cc.normalize()
#print cc,xS
mark = cc
mark = mark.magnitude(xO)
mark += self.point
return Circular(mark, cc, y)
def _planar_planar_test():
from testing import __ok__
p = Planar(V(3, 0, -1), V(0, 3, 0))
q = Planar(V(5, 0, -5), V(1, 1, 0))
pq = p * q
__ok__(isinstance(pq, Linear))
__ok__(equal(pq.pointB[1], pq.pointA[1]))
q = Planar(V(5, 0, -5), V(0, 1, 0))
pq = p * q
__ok__(pq is p)
q = Planar(V(5, 1, -5), V(0, 1, 0))
pq = p * q
__ok__(isinstance(pq, Nowhere))
def _circular_planar_test():
from testing import __ok__
# coplanar
c = Circular(V(-1, 0, 0), V.Y, 1)
p = Planar(V(1, 0, 0), V.Y)
cp = c * p
__ok__(cp is c)
# parallel planar
c = Circular(V(-1, 0, 0), V.Y, 1)
p = Planar(V(1, 1, 0), V.Y)
cp = c * p
__ok__(isinstance(cp, Nowhere))
# grab the tangent
c = Circular(V(0, 0, 0), V.Y, 1)
p = Planar(V(0, 1, 0), V(1, 1, 0))
cp = c * p
__ok__(isinstance(cp, Unity))
__ok__(equal(cp.point[0], 1))
# grab a duality
c = Circular(V(0, 0, 0), V.Y, 1)
p = Planar(V(0, .5, 0), V(1, 1, 0))
cp = c * p
__ok__(isinstance(cp, Duality))
__ok__(equal(abs(cp.pointA[2]), 0.5 * sqrt(3)))
def is_point_on_line(la, dir, p):
if not zero(dir[0]):
alpha = (p[0] - la[0]) / dir[0]
y = dir[1] * alpha + la[1]
z = dir[2] * alpha + la[2]
return equal(y, p[1]) and equal(z, p[2])
elif not zero(dir[1]):
alpha = (p[1] - la[1]) / dir[1]
z = dir[2] * alpha + la[2]
return equal(la[0], p[0]) and equal(z, p[2])
elif not zero(dir[2]): # else:
return equal(la[0], p[0]) and equal(la[1], p[1])
return False
def is_point_on_sphere(center, r, p):
return equal(r, center.distance(p))