def _planar_planar(self, other):
crossSO = self.normal * other.normal
# are we coplanar (Planar) or parallel (Nowhere)?
if crossSO.zero():
if self.accepts(other.point): return self
return Nowhere()
# find the intersection (Linear)
dir = crossSO
point = V()
if not zero(crossSO[2]):
point[0] = (other.normal[1] * self.d -
self.normal[1] * other.d) / crossSO[2]
point[1] = (self.normal[0] * other.d -
other.normal[0] * self.d) / crossSO[2]
point[2] = 0.0
elif not zero(crossSO[1]):
point[0] = (self.normal[2] * other.d -
other.normal[2] * self.d) / crossSO[1]
point[1] = 0.0
point[2] = (other.normal[0] * self.d -
self.normal[0] * other.d) / crossSO[1]
elif not zero(crossSO[0]): # else:
point[0] = 0.0
point[1] = (other.normal[1] * self.d -
self.normal[1] * other.d) / crossSO[0]
point[2] = (self.normal[0] * other.d -
other.normal[0] * self.d) / crossSO[0]
return Linear(point, point + dir)
def _linear_linear(self, other):
# linear vs linear
# are we colinear (self) or parallel (Nowhere)?
dirS = self.pointB - self.pointA
dirO = other.pointB - other.pointA
crossSO = dirO * dirS
if crossSO.zero():
if self.accepts(other.pointA): return self
return Nowhere()
# make an arbitrary line joining our two lines; get their crosses
# if the crosses are parallel, the three form a coplanar triangle
# if the crosses are not parallel, our lines don't meet (Nowhere)
span = self.pointA - other.pointA
crossO = span * dirO
if crossO.zero(): return Unity(self.pointA)
crossS = span * dirS
if crossS.zero(): return Unity(other.pointA)
crossXSO = crossO * crossS
if not crossXSO.zero(): return Nowhere()
# find the intersection (Unity)
dist = 0.0
if not zero(crossSO[2]):
dist = crossO[2] / crossSO[2]
elif not zero(crossAB[1]):
dist = crossO[1] / crossSO[1]
elif not zero(crossAB[0]): # else:
dist = crossO[0] / crossSO[0]
return Unity(self.pointA + (dirS * dist))
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 _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 __init__(self, point, normal, radius):
Constraint.__init__(self)
if zero(radius):
raise ValueError, 'A circle must have a non-zero radius.'
self.point = V(point)
self.normal = V(normal).normalize()
self.radius = abs(float(radius))
self.d = self.normal.dot(self.point)
def _planar_linear(self, other):
dir = other.dir
dot = self.normal.dot(dir)
# are we coplanar (Linear) or parallel (Nowhere)?
if zero(dot):
if self.accepts(other.pointA): return other
return Nowhere()
# find the intersection (Unity)
intersect = intersect_plane_and_line(self.point, self.normal,
other.pointA, other.dir)
return Unity(intersect)
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 __init__(self, point, radius):
Constraint.__init__(self)
if zero(radius):
raise ValueError, 'A sphere must have a non-zero radius.'
self.point = V(point)
self.radius = abs(float(radius))
def is_point_on_plane(ppoint, normal, p):
return zero(distance_from_plane(ppoint, normal, p))
def begin_training_1 (self) : self.prototype_numerators = list () self.prototype_denominators = list () for index in xrange (self.prototype_count) : self.prototype_numerators.append (vectors.zero (self.vector_length)) self.prototype_denominators.append (0)