def __init__(self, pointA, pointB):
Constraint.__init__(self)
if pointA == pointB:
raise ValueError, 'A Linear must refer to two different points.'
self.pointA = V(pointA)
self.pointB = V(pointB)
self.dir = self.pointB - self.pointA
def closest_point_on_circle(center, normal, radius, p):
planar = closest_point_on_plane(center, normal, p)
spoke = planar - center
if not spoke: spoke = V(1, 0, 0) * normal
if not spoke: spoke = V(0, 1, 0) * normal
spoke = spoke.magnitude(radius)
return center + spoke
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 _circular_linear_test():
from testing import __ok__
c = Circular(V(), V.Y, 1)
l = Linear(V.Y, V(2, -1, 0))
__ok__(str(c * l) == "Unity(V(1.0, 0.0, 0.0))")
l = Linear(V.Y, -V.Y)
__ok__(str(c * l) == "Nowhere()")
l = Linear(V(0.5, 0, 0.5), V(0.5, 0, -0.5))
cl = c * l
__ok__(isinstance(cl, Duality))
__ok__(cl.pointA[0] == cl.pointB[0])
def get_random(self):
if self.normal[0] != 0 or self.normal[1] != 0:
x0 = V(-self.normal[1], self.normal[0], 0)
else:
x0 = V(-self.normal[2], 0, self.normal[0])
x0 = x0.normalize()
self.normal = self.normal.normalize()
x1 = self.normal.cross(x0)
alpha = 2 * math.pi * random.random()
return self.point + self.radius * (x0 * math.cos(alpha) +
x1 * math.sin(alpha))
def generate_N(self, N):
if self.normal[0] != 0 or self.normal[1] != 0:
x0 = V(-self.normal[1], self.normal[0], 0)
else:
x0 = V(-self.normal[2], 0, self.normal[0])
x0 = x0.normalize()
self.normal = self.normal.normalize()
x1 = self.normal.cross(x0)
alphas = [(2 * 3.1415 * i) / N for i in range(N)]
return [
self.point + self.radius *
(x0 * math.cos(alpha) + x1 * math.sin(alpha)) for alpha in alphas
]
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 _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 get_random(self):
phi = 2 * math.pi * random.random()
theta = math.pi * random.random()
return self.point + self.radius * (V([
math.sin(theta) * math.cos(phi),
math.sin(theta) * math.sin(phi),
math.cos(theta)
]))
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 _spherical_linear(self, other):
mark = other.closest(self.point)
aa = mark.dsquared(self.point)
cc = self.radius * self.radius
if aa > cc + EPSILON:
return Nowhere()
if aa < cc - EPSILON:
chord = V(other.dir)
b = sqrt(cc - aa)
chord = chord.magnitude(b)
return Duality(mark + chord, mark - chord)
return Unity(mark)
def _circular_coplanar_linear(self, other):
# might find unity, might find duality, might find nowhere
mark = other.closest(self.point)
aa = mark.dsquared(self.point)
cc = self.radius * self.radius
if aa > cc + EPSILON:
return Nowhere()
if aa < cc - EPSILON:
chord = V(other.dir)
b = sqrt(cc - aa)
chord = chord.magnitude(b)
return Duality(mark + chord, mark - chord)
return Unity(mark)
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 _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 __init__(self, point):
Constraint.__init__(self)
self.point = V(point)
def _linear_linear_test():
from testing import __ok__
# simple intersect at origin, commutative checks
u = V(-1, 0, 0)
v = -u
c1 = Linear(u, v)
r = V(0, -1, 0)
s = -r
c2 = Linear(r, s)
__ok__(str(c1 * c2) == "Unity(V(0.0, 0.0, 0.0))")
__ok__(str(c2 * c1) == "Unity(V(0.0, 0.0, 0.0))")
c1 = Linear(v, u)
__ok__(str(c1 * c2) == "Unity(V(0.0, 0.0, 0.0))")
__ok__(str(c2 * c1) == "Unity(V(0.0, 0.0, 0.0))")
# intersect away from origin
o = V(0.125, 0.25, 0.5)
u = V(-2, 3, -4)
v = -u
u += o
v += o
c1 = Linear(u, v)
r = V(-3, 8, 21)
s = -r
r += o
s += o
c2 = Linear(r, s)
__ok__(str(c2 * c1) == str(Unity(o)))
__ok__(str(c1 * c2) == str(Unity(o)))
# non-intersecting
u = V(-1, 0, 0)
v = -u
u += V(0.0, 0.0, 0.5)
v += V(0.0, 0.0, 0.5)
c1 = Linear(u, v)
r = V(0, -1, 0)
s = -r
c2 = Linear(r, s)
__ok__(str(c1 * c2) == "Nowhere()")
# intersecting
r += 0.5
s += 0.5
c2 = Linear(r, s)
__ok__(str(c1 * c2) == "Unity(V(0.5, 0.0, 0.5))")
# colinear
u = s + V(0, 0.5, 0)
v = r + V(0, 0.5, 0)
c1 = Linear(u, v)
__ok__(str(c1 * c2) == str(c1))
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 closest_point_on_sphere(center, r, p):
dir = p - center
if dir.zero():
return center + V(r, 0, 0)
dir = dir.magnitude(r)
return center + dir
def __init__(self, point, normal):
Constraint.__init__(self)
self.point = V(point)
self.normal = V(normal).normalize()
self.d = self.normal.dot(self.point)
def __init__(self, pointA, pointB):
Constraint.__init__(self)
if pointA == pointB:
raise ValueError, 'Duality must refer to two different points.'
self.pointA = V(pointA)
self.pointB = V(pointB)