def _LF_ij(self, i, j, epsilon):
bottom, top = 0, 1
bp = Point([bottom * x + (1 - bottom) * y for x, y in zip(self.Q[j + 1], self.Q[j])])
tp = Point([top * x + (1 - top) * y for x, y in zip(self.Q[j + 1], self.Q[j])])
d, loop = bp.dist_sq(self.P[i]), 1
prime = self.epsDot(self.Q[j + 1], self.Q[j], self.P[i], bottom)
while d != epsilon and loop < 52:
if d < epsilon and bottom == 0:
loop = 52
else:
bottom = self._editLB(bottom, loop, d, epsilon, prime)
loop += 1
bp = Point([bottom * x + (1 - bottom) * y for x, y in zip(self.Q[j + 1], self.Q[j])])
prime = self.epsDot(self.Q[j + 1], self.Q[j], self.P[i], bottom)
d = bp.dist_sq(self.P[i])
if abs(d - epsilon) > 0.00000000002 and bottom != 0:
bottom = 2
d, loop = tp.dist_sq(self.P[i]), 1
prime = self.epsDot(self.Q[j + 1], self.Q[j], self.P[i], top)
while d != epsilon and loop < 52:
if d < epsilon and top == 1:
loop = 52
else:
top = self._editRT(top, loop, d, epsilon, prime)
loop += 1
tp = Point([top * x + (1 - top) * y for x, y in zip(self.Q[j + 1], self.Q[j])])
prime = self.epsDot(self.Q[j + 1], self.Q[j], self.P[i], top)
d = tp.dist_sq(self.P[i])
if abs(d - epsilon) > 0.00000000002 and top != 1:
top = 2
return (bottom, top)
def _BF_ij(self, i, j, epsilon):
left, right = 0, 1
lp = Point([left * x + (1-left) * y for x, y in zip(self.P[i+1], self.P[i])])
rp = Point([right * x + (1-right) * y for x, y in zip(self.P[i+1], self.P[i])])
d, loop = lp.dist_sq(self.Q[j]), 1
prime = self.epsDot(self.P[i+1], self.P[i], self.Q[j], left)
while d != epsilon and loop < 52:
if d < epsilon and left == 0:
loop = 52
else:
left = self._editLB(left, loop, d, epsilon, prime)
loop += 1
lp = Point([left * x + (1 - left) * y for x, y in zip(self.P[i + 1], self.P[i])])
prime = self.epsDot(self.P[i + 1], self.P[i], self.Q[j], left)
d = lp.dist_sq(self.Q[j])
if abs(d - epsilon) > 0.00000000002 and left != 0:
left = 2
d, loop = rp.dist_sq(self.Q[j]), 1
prime = self.epsDot(self.P[i + 1], self.P[i], self.Q[j], right)
while d != epsilon and loop < 52:
if d < epsilon and right == 1:
loop = 52
else:
right = self._editRT(right, loop, d, epsilon, prime)
loop += 1
rp = Point([right * x + (1-right) * y for x,y in zip(self.P[i+1], self.P[i])])
prime = self.epsDot(self.P[i + 1], self.P[i], self.Q[j], right)
d = rp.dist_sq(self.Q[j])
if abs(d - epsilon) > 0.00000000002 and right != 1:
right = 2
return (left, right)
def test_3D_point_sq_dist(self):
coords1 = [-1, 2, 3]
coords2 = [4, 0, -3]
coords3 = [7, 4, 3]
coords4 = [17, 6, 2]
p1 = Point(coords1, 0)
p2 = Point(coords2, 0)
p3 = Point(coords3, 0)
p4 = Point(coords4, 0)
self.assertEqual(p1.dist_sq(p2), 65)
self.assertEqual(p1.dist_sq(p1), 0.0)
self.assertEqual(p3.dist_sq(p4), 105)
def test_2D_point_sq_dist(self):
coords1 = [-7, -4]
coords2 = [17, 6]
coords3 = [3, 4]
coords4 = [0, 0]
p1 = Point(coords1)
p2 = Point(coords2)
p3 = Point(coords3)
p4 = Point(coords4)
self.assertEqual(p1.dist_sq(p2), 676.0)
self.assertEqual(p1.dist_sq(p1), 0.0)
self.assertEqual(p3.dist_sq(p4), 25.0)
def _critB(self, i, j):
dirv = Point([x - y for x, y in zip(self.Q[j + 1], self.Q[j])])
mag = math.sqrt(dot(dirv, dirv))
n = Point([x / mag for x in dirv])
qp = Point([w - z for w, z in zip(self.Q[j], self.P[i])])
c = dot(n, qp)
v = Point([c * x for x in n])
return qp.dist_sq(v)
def _critCQ(self, k, l):
p = Point([0.5 * x + 0.5 * y for x, y in zip(self.Q[k], self.Q[l])])
n = Point([y - x for x, y in zip(self.Q[k], self.Q[l])])
d = dict()
B = getBasis(p, n)
for x in range(len(self.P) - 1):
M, M2 = getMatrix(B, self.P[x]), getMatrix(B, self.P[x+1])
d1, d2 = getMatrixDeterminant(M), getMatrixDeterminant(M2)
if d1 * d2 <= 0:
d1, d2 = abs(d1), abs(d2)
if d1 - d2 == 0:
q = Point([0.5 * x + 0.5 * y for x, y in zip(self.P[x], self.P[x+1])])
else:
q = Point([(d2 * x + d1 * y)/(d1 + d2) for x, y in zip(self.P[x], self.P[x+1])])
d[x] = q.dist_sq(self.Q[k])
return d