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Code rearrangement after the discussion on the issue #34
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Onur Rauf Bingol committed Jul 30, 2018
1 parent c4013a0 commit 5136fc3
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Showing 7 changed files with 110 additions and 358 deletions.
10 changes: 0 additions & 10 deletions geomdl/Abstract.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1176,11 +1176,6 @@ class CurveEvaluator(six.with_metaclass(abc.ABCMeta, object)):
def __init__(self, **kwargs):
pass

@abc.abstractmethod
def derivatives_ctrlpts(self, **kwargs):
""" Abstract method for implementation of the control points derivatives algorithm. """
pass

@abc.abstractmethod
def insert_knot(self, **kwargs):
""" Abstract method for implementation of knot insertion algorithm. """
Expand All @@ -1193,11 +1188,6 @@ class SurfaceEvaluator(six.with_metaclass(abc.ABCMeta, object)):
def __init__(self, **kwargs):
pass

@abc.abstractmethod
def derivatives_ctrlpts(self, **kwargs):
""" Abstract method for implementation of the control points derivatives algorithm. """
pass

@abc.abstractmethod
def insert_knot_u(self, **kwargs):
""" Abstract method for implementation of knot insertion algorithm on the u-direction. """
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66 changes: 0 additions & 66 deletions geomdl/BSpline.py
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Original file line number Diff line number Diff line change
Expand Up @@ -265,34 +265,6 @@ def derivatives(self, u=-1, order=0):
ctrlpts=self._control_points,
dimension=self._dimension)

# # Evaluates the curve derivative control points
# def derivatives_ctrlpts(self, order=0, **kwargs):
# """ Evaluates the n-th order curve derivative control points.
#
# Keyword arguments:
# * ``r1``: minimum span
# * ``r2``: maximum span
#
# :param order: derivative order
# :type order: integer
# :return: a list containing the control points of up to {order}-th derivative of the curve
# :rtype: list
# """
# # Check all parameters are set before the curve evaluation
# self._check_variables()
#
# # Get keyword arguments
# r1 = kwargs.get('r1', 0)
# r2 = kwargs.get('r2', len(self._control_points) - 1)
#
# # Evaluate and return the derivative control points
# return self._evaluator.derivatives_ctrlpts(r1=r1, r2=r2,
# deriv_order=order,
# degree=self.degree,
# knotvector=self.knotvector,
# ctrlpts=self._control_points,
# dimension=self._dimension)

# Evaluates the curve tangent at the given u parameter
def tangent(self, u=-1, normalize=False):
""" Evaluates the curve tangent vector at the given parameter value.
Expand Down Expand Up @@ -1086,44 +1058,6 @@ def derivatives(self, u=-1, v=-1, order=0):
ctrlpts=self._control_points2D,
dimension=self._dimension)

# # Evaluates the curve derivative control points
# def derivatives_ctrlpts(self, order=0, **kwargs):
# """ Evaluates the n-th order surface derivative control points.
#
# Returns a list PKL, where PKL[k][l][i][j] is the {i,j}-th control point of the derivative of the surface S(u,v)
# w.r.t u k times and v l times.
#
# Keyword arguments:
# * ``r1``: minimum span on the u-direction
# * ``r2``: maximum span on the u-direction
# * ``s1``: minimum span on the v-direction
# * ``s2``: maximum span on the v-direction
#
# :param order: derivative order
# :type order: integer
# :return: the list PKL (as defined in the description)
# :rtype: list
# """
# # Check all parameters are set before the surface evaluation
# self._check_variables()
#
# # Get keyword arguments
# r1 = kwargs.get('r1', 0)
# r2 = kwargs.get('r2', self.ctrlpts_size_u - 1)
# s1 = kwargs.get('s1', 0)
# s2 = kwargs.get('s2', self.ctrlpts_size_v - 1)
#
# # Evaluate and return the derivative control points
# return self._evaluator.derivatives_ctrlpts(r1=r1, r2=r2,
# s1=s1, s2=s2,
# degree_u=self.degree_u, degree_v=self.degree_v,
# knotvector_u=self.knotvector_u, knotvector_v=self.knotvector_v,
# ctrlpts_size_u=self.ctrlpts_size_u,
# ctrlpts_size_v=self.ctrlpts_size_v,
# ctrlpts=self._control_points2D,
# dimension=self._dimension,
# deriv_order=order)

# Evaluates the surface tangent vectors at the given (u,v) parameter
def tangent(self, u=-1, v=-1, normalize=False):
""" Evaluates the surface tangent vector at the given (u,v) parameter pair.
Expand Down
202 changes: 110 additions & 92 deletions geomdl/evaluators.py
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Original file line number Diff line number Diff line change
Expand Up @@ -20,7 +20,6 @@ class CurveEvaluator(Abstract.Evaluator, Abstract.CurveEvaluator):
* Algorithm A3.1: CurvePoint
* Algorithm A3.2: CurveDerivsAlg1
* Algorithm A3.3: CurveDerivCpts
* Algorithm A5.1: CurveKnotIns
"""
Expand Down Expand Up @@ -118,20 +117,6 @@ def derivatives(self, **kwargs):
# Not implemented, yet...
raise NotImplementedError("This functionality is not implemented at the moment")

# Computes the control points of all derivative curves up to and including the {degree}-th derivative
def derivatives_ctrlpts(self, **kwargs):
""" Computes the control points of all derivative curves up to and including the {degree}-th derivative. """
# r1 - minimum span, r2 - maximum span
r1 = kwargs.get('r1')
r2 = kwargs.get('r2')
deriv_order = kwargs.get('deriv_order')
degree = kwargs.get('degree')
knot_vector = kwargs.get('knotvector')
control_points = kwargs.get('ctrlpts')
dimension = kwargs.get('dimension')

return helpers.derivatives_ctrlpts(r1, r2, degree, knot_vector, control_points, dimension, order=deriv_order)

def insert_knot(self, **kwargs):
""" Insert knot multiple times at a single parameter. """
# Call parent method
Expand Down Expand Up @@ -207,6 +192,40 @@ class CurveEvaluator2(CurveEvaluator):
def __init__(self, **kwargs):
super(CurveEvaluator2, self).__init__(**kwargs)

# Computes the control points of all derivative curves up to and including the {degree}-th derivative
@staticmethod
def derivatives_ctrlpts(**kwargs):
""" Computes the control points of all derivative curves up to and including the {degree}-th derivative.
Implementation of Algorithm A3.3 from The NURBS Book by Piegl & Tiller.
Output is PK[k][i], i-th control point of the k-th derivative curve where 0 <= k <= degree and r1 <= i <= r2-k.
"""
# r1 - minimum span, r2 - maximum span
r1 = kwargs.get('r1')
r2 = kwargs.get('r2')
deriv_order = kwargs.get('deriv_order')
degree = kwargs.get('degree')
knot_vector = kwargs.get('knotvector')
control_points = kwargs.get('ctrlpts')
dimension = kwargs.get('dimension')

# Algorithm A3.3
r = r2 - r1
PK = [[[None for _ in range(dimension)] for _ in range(r + 1)] for _ in range(deriv_order + 1)]
for i in range(0, r + 1):
PK[0][i][:] = [elem for elem in control_points[r1 + i]]

for k in range(1, deriv_order + 1):
tmp = degree - k + 1
for i in range(0, r - k + 1):
PK[k][i][:] = [tmp * (elem1 - elem2) /
(knot_vector[r1 + i + degree + 1] - knot_vector[r1 + i + k]) for elem1, elem2
in zip(PK[k - 1][i + 1], PK[k - 1][i])]

# Return a 2-dimensional list of control points
return PK

# Evaluates the curve derivative using "CurveDerivsAlg2" algorithm
def derivatives_single(self, **kwargs):
""" Evaluates n-th order curve derivatives at a single parameter. """
Expand All @@ -227,12 +246,14 @@ def derivatives_single(self, **kwargs):

span = helpers.find_span(knot_vector, len(control_points), knot)
bfuns = helpers.basis_function_all(degree, tuple(knot_vector), span, knot)
PK = helpers.derivatives_ctrlpts(r1=(span - degree), r2=span,
degree=degree,
knot_vector=knot_vector,
control_points=control_points,
dimension=dimension,
order=du)

# "derivatives_ctrlpts" is a static method that could be called like below
PK = CurveEvaluator2.derivatives_ctrlpts(r1=(span - degree), r2=span,
degree=degree,
knotvector=knot_vector,
ctrlpts=control_points,
dimension=dimension,
deriv_order=du)

for k in range(0, du + 1):
CK[k] = [0.0 for _ in range(dimension)]
Expand Down Expand Up @@ -313,7 +334,6 @@ class SurfaceEvaluator(Abstract.Evaluator, Abstract.SurfaceEvaluator):
* Algorithm A3.5: SurfacePoint
* Algorithm A3.6: SurfaceDerivsAlg1
* Algorithm A3.7: SurfaceDerivCpts
* Algorithm A5.3: SurfaceKnotIns
"""
Expand Down Expand Up @@ -456,76 +476,6 @@ def derivatives(self, **kwargs):
# Not implemented, yet
raise NotImplementedError("This functionality is not implemented at the moment")

def derivatives_ctrlpts(self, **kwargs):
""" Computes the control points of all derivative surfaces up to and including the {degree}-th derivative.
Output is PKL[k][l][i][j], i,j-th control point of the surface differentiated k times w.r.t to u and
l times w.r.t v.
"""
# Call parent method
super(SurfaceEvaluator, self).derivatives_ctrlpts(**kwargs)

r1 = kwargs.get('r1') # minimum span on the u-direction
r2 = kwargs.get('r2') # maximum span on the u-direction
s1 = kwargs.get('s1') # minimum span on the v-direction
s2 = kwargs.get('s2') # maximum span on the v-direction

ctrlpts_size_u = kwargs.get('ctrlpts_size_u')
degree_u = kwargs.get('degree_u')
knot_vector_u = kwargs.get('knotvector_u')

ctrlpts_size_v = kwargs.get('ctrlpts_size_v')
degree_v = kwargs.get('degree_v')
knot_vector_v = kwargs.get('knotvector_v')

ctrlpts2d = kwargs.get('ctrlpts')
deriv_order = kwargs.get('deriv_order')

dimension = kwargs.get('dimension')

PKL = [[[[[None for _ in range(dimension)]
for _ in range(ctrlpts_size_v)] for _ in range(ctrlpts_size_u)]
for _ in range(deriv_order + 1)] for _ in range(deriv_order + 1)]

du = min(degree_u, deriv_order)
dv = min(degree_v, deriv_order)

r = r2 - r1
s = s2 - s1

# Control points of the U derivatives of every U-curve
for j in range(s1, s2 + 1):
PKu = helpers.derivatives_ctrlpts(r1=r1, r2=r2,
degree=degree_u,
knot_vector=knot_vector_u,
control_points=[ctrlpts2d[_][j] for _ in range(len(ctrlpts2d))],
dimension=dimension,
order=du)

# Copy into output as the U partial derivatives
for k in range(0, du + 1):
for i in range(0, r - k + 1):
PKL[k][0][i][j - s1] = PKu[k][i]

# Control points of the V derivatives of every U-differentiated V-curve
for k in range(0, du):
for i in range(0, r - k + 1):
dd = min(deriv_order - k, dv)

PKuv = helpers.derivatives_ctrlpts(r1=0, r2=s,
degree=degree_v,
knot_vector=knot_vector_v[s1:],
control_points=PKL[k][0][i],
dimension=dimension,
order=dd)

# Copy into output
for l in range(1, dd + 1):
for j in range(0, s - l + 1):
PKL[k][l][i][j] = PKuv[l][j]

return PKL

def insert_knot_u(self, **kwargs):
""" Inserts knot(s) in u-direction. """
# Call parent method
Expand Down Expand Up @@ -668,6 +618,74 @@ class SurfaceEvaluator2(SurfaceEvaluator):
def __init__(self, **kwargs):
super(SurfaceEvaluator2, self).__init__(**kwargs)

@staticmethod
def derivatives_ctrlpts(**kwargs):
""" Computes the control points of all derivative surfaces up to and including the {degree}-th derivative.
Output is PKL[k][l][i][j], i,j-th control point of the surface differentiated k times w.r.t to u and
l times w.r.t v.
"""
r1 = kwargs.get('r1') # minimum span on the u-direction
r2 = kwargs.get('r2') # maximum span on the u-direction
s1 = kwargs.get('s1') # minimum span on the v-direction
s2 = kwargs.get('s2') # maximum span on the v-direction

ctrlpts_size_u = kwargs.get('ctrlpts_size_u')
degree_u = kwargs.get('degree_u')
knot_vector_u = kwargs.get('knotvector_u')

ctrlpts_size_v = kwargs.get('ctrlpts_size_v')
degree_v = kwargs.get('degree_v')
knot_vector_v = kwargs.get('knotvector_v')

ctrlpts2d = kwargs.get('ctrlpts')
deriv_order = kwargs.get('deriv_order')

dimension = kwargs.get('dimension')

PKL = [[[[[None for _ in range(dimension)]
for _ in range(ctrlpts_size_v)] for _ in range(ctrlpts_size_u)]
for _ in range(deriv_order + 1)] for _ in range(deriv_order + 1)]

du = min(degree_u, deriv_order)
dv = min(degree_v, deriv_order)

r = r2 - r1
s = s2 - s1

# Control points of the U derivatives of every U-curve
for j in range(s1, s2 + 1):
PKu = CurveEvaluator2.derivatives_ctrlpts(r1=r1, r2=r2,
degree=degree_u,
knotvector=knot_vector_u,
ctrlpts=[ctrlpts2d[_][j] for _ in range(len(ctrlpts2d))],
dimension=dimension,
deriv_order=du)

# Copy into output as the U partial derivatives
for k in range(0, du + 1):
for i in range(0, r - k + 1):
PKL[k][0][i][j - s1] = PKu[k][i]

# Control points of the V derivatives of every U-differentiated V-curve
for k in range(0, du):
for i in range(0, r - k + 1):
dd = min(deriv_order - k, dv)

PKuv = CurveEvaluator2.derivatives_ctrlpts(r1=0, r2=s,
degree=degree_v,
knotvector=knot_vector_v[s1:],
ctrlpts=PKL[k][0][i],
dimension=dimension,
deriv_order=dd)

# Copy into output
for l in range(1, dd + 1):
for j in range(0, s - l + 1):
PKL[k][l][i][j] = PKuv[l][j]

return PKL

# Evaluates the surface derivatives using "SurfaceDerivsAlg2"
def derivatives_single(self, **kwargs):
""" Evaluates the n-th order surface derivatives at (u,v) parameters.
Expand Down
33 changes: 0 additions & 33 deletions geomdl/helpers.py
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Original file line number Diff line number Diff line change
Expand Up @@ -429,36 +429,3 @@ def basis_function_ders_one(degree, knot_vector, span, knot, order):
ders[k] = ND[0]

return ders


def derivatives_ctrlpts(r1, r2, degree, knot_vector, control_points, dimension, order=0):
""" Computes the control points of all derivative curves up to and including the {degree}-th derivative.
Implementation of Algorithm A3.3 from The NURBS Book by Piegl & Tiller.
Output is PK[k][i], i-th control point of the k-th derivative curve where 0 <= k <= degree and r1 <= i <= r2-k.
:param r1: minimum span
:param r2: maximum span
:param degree: degree
:param knot_vector: knot vector
:param control_points: control points
:param dimension: dimensionality
:param order: derivative order
:return: the list PK
"""
# Algorithm A3.3
r = r2 - r1
PK = [[[None for _ in range(dimension)] for _ in range(r + 1)] for _ in range(order + 1)]
for i in range(0, r + 1):
PK[0][i][:] = [elem for elem in control_points[r1 + i]]

for k in range(1, order + 1):
tmp = degree - k + 1
for i in range(0, r - k + 1):
PK[k][i][:] = [tmp * (elem1 - elem2) /
(knot_vector[r1 + i + degree + 1] - knot_vector[r1 + i + k]) for elem1, elem2
in zip(PK[k - 1][i + 1], PK[k - 1][i])]

# Return a 2-dimensional list of control points
return PK

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