def derivatives(self, u=-1, order=0):
""" Evaluates n-th order curve derivatives at the given u from the rational curve.
:param u: knot value
:type u: float
:param order: derivative order
:type order: integer
:return: A list containing up to {order}-th derivative of the curve
:rtype: list
"""
# Call the parent function to evaluate A(u) and w(u) derivatives
CKw = super(Curve, self).derivatives(u, order)
# Algorithm A4.2
CK = [[None for x in range(self._dimension - 1)]
for y in range(order + 1)]
for k in range(0, order + 1):
v = []
for idx in range(self._dimension - 1):
v.append(CKw[idx])
for i in range(1, order + 1):
v[:] = [
tmp - (utils.binomial_coefficient(k, i) * CKw[i][-1] * drv)
for tmp, drv in zip(v, CK[k - i])
]
CK[k][:] = [tmp / CKw[0][-1] for tmp in v]
# Return C(u) derivatives
return CK
def test_binomial_coefficient3():
result = 680.0
to_check = utilities.binomial_coefficient(17, 3)
assert to_check == result
def test_binomial_coefficient2():
result = 1.0
to_check = utilities.binomial_coefficient(13, 13)
assert to_check == result
def test_binomial_coefficient1():
result = 0.0
to_check = utilities.binomial_coefficient(13, 14)
assert to_check == result
def derivatives(self, u=-1, v=-1, order=0):
""" Evaluates n-th order surface derivatives at the given (u,v) parameter from the rational surface.
* SKL[0][0] will be the surface point itself
* SKL[0][1] will be the 1st derivative w.r.t. v
* SKL[2][1] will be the 2nd derivative w.r.t. u and 1st derivative w.r.t. v
:param u: parameter in the U direction
:type u: float
:param v: parameter in the V direction
:type v: float
:param order: derivative order
:type order: integer
:return: A list SKL, where SKL[k][l] is the derivative of the surface S(u,v) w.r.t. u k times and v l times
:rtype: list
"""
# Call the parent function to evaluate A(u) and w(u) derivatives
SKLw = super(Surface, self).derivatives(u, v, order)
# Algorithm A4.4
du = min(self._degree_u, order)
dv = min(self._degree_v, order)
# Generate an empty list of derivatives
SKL = [[[None for x in range(self._dimension)] for y in range(dv + 1)]
for z in range(du + 1)]
for k in range(0, order + 1):
for l in range(0, order - k + 1):
v = []
for idx in range(self._dimension - 1):
v.append(SKLw[idx])
for j in range(1, l + 1):
v[:] = [
tmp - (utils.binomial_coefficient(l, j) *
SKLw[0][j][-1] * drv)
for tmp, drv in zip(v, SKL[k][l - j])
]
for i in range(1, k + 1):
v[:] = [
tmp - (utils.binomial_coefficient(k, i) *
SKLw[i][0][-1] * drv)
for tmp, drv in zip(v, SKL[k - i][l])
]
v2 = [0.0 for x in range(self._dimension - 1)]
for j in range(1, l + 1):
v2[:] = [
tmp + (utils.binomial_coefficient(l, j) *
SKLw[i][j][-1] * drv)
for tmp, drv in zip(v2, SKL[k - i][l - j])
]
v[:] = [
tmp - (utils.binomial_coefficient(k, i) * tmp2)
for tmp, tmp2 in zip(v, v2)
]
SKL[k][l][:] = [tmp / SKLw[0][0][-1] for tmp in v]
# Return S(u,v) derivatives
return SKL
