Evaluators

Evaluators allow users to change the evaluation algorithms that are used to evaluate curves, surfaces and volumes, take derivatives and more. All geometry classes set an evaluator by default. Users may switch between the evaluation algorithms at runtime. It is also possible to implement different algorithms (e.g. T-splines) or extend existing ones.

How to Use

All geometry classes come with a default specialized evaluator class, the algorithms are generally different for rational and non-rational geometries. The evaluator class instance can be accessed and/or updated using evaluator property. For instance, the following code snippet changes the evaluator of a B-Spline curve.

from geomdl import BSpline
from geomdl import evaluators

crv = BSpline.Curve()
cevaltr = evaluators.CurveEvaluator2()
crv.evaluator = cevaltr

# Curve "evaluate" method will use CurveEvaluator2.evaluate() method
crv.evaluate()

# Get evaluated points
curve_points = crv.evalpts

Implementing Evaluators

All evaluators should be extended from evaluators.AbstractEvaluator abstract base class. This class provides a point evaluation and a derivative computation methods. Both methods take a data input which contains the geometry data as a dict object (refer to BSpline.Surface.data property as an example). The derivative computation method also takes additional arguments, such as the parametric position and the derivative order.

Inheritance Diagram

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Abstract Base

class geomdl.evaluators.AbstractEvaluator(**kwargs)

Bases: object

Abstract base class for implementations of fundamental spline algorithms, such as evaluate and derivative.

Abstract Methods:

  • evaluate is used for computation of the complete spline shape

  • derivative_single is used for computation of derivatives at a single parametric coordinate

Please note that this class requires the keyword argument find_span_func to be set to a valid find_span function implementation. Please see helpers module for details.

abstractmethod derivatives(datadict, parpos, deriv_order=0, **kwargs)

Abstract method for evaluation of the n-th order derivatives at the input parametric position.

Note

This is an abstract method and it must be implemented in the subclass.

Parameters:

  • datadict (dict) – data dictionary containing the necessary variables

  • parpos (list, tuple) – parametric position where the derivatives will be computed

  • deriv_order (int) – derivative order; to get the i-th derivative

abstractmethod evaluate(datadict, **kwargs)

Abstract method for evaluation of points on the spline geometry.

Note

This is an abstract method and it must be implemented in the subclass.

Parameters:

datadict (dict) – data dictionary containing the necessary variables

property name

Evaluator name.

Getter:

Gets the name of the evaluator

Type:

str

Curve Evaluators

class geomdl.evaluators.CurveEvaluator(**kwargs)

Bases: AbstractEvaluator

Sequential curve evaluation algorithms.

This evaluator implements the following algorithms from The NURBS Book:

  • Algorithm A3.1: CurvePoint

  • Algorithm A3.2: CurveDerivsAlg1

Please note that knot vector span finding function may be changed by setting find_span_func keyword argument during the initialization. By default, this function is set to helpers.find_span_linear(). Please see Helpers Module Documentation for more details.

derivatives(datadict, parpos, deriv_order=0, **kwargs)

Evaluates the n-th order derivatives at the input parametric position.

Parameters:

  • datadict (dict) – data dictionary containing the necessary variables

  • parpos (list, tuple) – parametric position where the derivatives will be computed

  • deriv_order (int) – derivative order; to get the i-th derivative

Returns:

evaluated derivatives

Return type:

list

evaluate(datadict, **kwargs)

Evaluates the curve.

Keyword Arguments:

  • start: starting parametric position for evaluation

  • stop: ending parametric position for evaluation

Parameters:

datadict (dict) – data dictionary containing the necessary variables

Returns:

evaluated points

Return type:

list

property name

Evaluator name.

Getter:

Gets the name of the evaluator

Type:

str

class geomdl.evaluators.CurveEvaluatorRational(**kwargs)

Bases: CurveEvaluator

Sequential rational curve evaluation algorithms.

This evaluator implements the following algorithms from The NURBS Book:

  • Algorithm A3.1: CurvePoint

  • Algorithm A4.2: RatCurveDerivs

Please note that knot vector span finding function may be changed by setting find_span_func keyword argument during the initialization. By default, this function is set to helpers.find_span_linear(). Please see Helpers Module Documentation for more details.

derivatives(datadict, parpos, deriv_order=0, **kwargs)

Evaluates the n-th order derivatives at the input parametric position.

Parameters:

  • datadict (dict) – data dictionary containing the necessary variables

  • parpos (list, tuple) – parametric position where the derivatives will be computed

  • deriv_order (int) – derivative order; to get the i-th derivative

Returns:

evaluated derivatives

Return type:

list

evaluate(datadict, **kwargs)

Evaluates the rational curve.

Keyword Arguments:

  • start: starting parametric position for evaluation

  • stop: ending parametric position for evaluation

Parameters:

datadict (dict) – data dictionary containing the necessary variables

Returns:

evaluated points

Return type:

list

property name

Evaluator name.

Getter:

Gets the name of the evaluator

Type:

str

class geomdl.evaluators.CurveEvaluator2(**kwargs)

Bases: CurveEvaluator

Sequential curve evaluation algorithms (alternative).

This evaluator implements the following algorithms from The NURBS Book:

  • Algorithm A3.1: CurvePoint

  • Algorithm A3.3: CurveDerivCpts

  • Algorithm A3.4: CurveDerivsAlg2

Please note that knot vector span finding function may be changed by setting find_span_func keyword argument during the initialization. By default, this function is set to helpers.find_span_linear(). Please see Helpers Module Documentation for more details.

derivatives(datadict, parpos, deriv_order=0, **kwargs)

Evaluates the n-th order derivatives at the input parametric position.

Parameters:

  • datadict (dict) – data dictionary containing the necessary variables

  • parpos (list, tuple) – parametric position where the derivatives will be computed

  • deriv_order (int) – derivative order; to get the i-th derivative

Returns:

evaluated derivatives

Return type:

list

evaluate(datadict, **kwargs)

Evaluates the curve.

Keyword Arguments:

  • start: starting parametric position for evaluation

  • stop: ending parametric position for evaluation

Parameters:

datadict (dict) – data dictionary containing the necessary variables

Returns:

evaluated points

Return type:

list

property name

Evaluator name.

Getter:

Gets the name of the evaluator

Type:

str

Surface Evaluators

class geomdl.evaluators.SurfaceEvaluator(**kwargs)

Bases: AbstractEvaluator

Sequential surface evaluation algorithms.

This evaluator implements the following algorithms from The NURBS Book:

  • Algorithm A3.5: SurfacePoint

  • Algorithm A3.6: SurfaceDerivsAlg1

Please note that knot vector span finding function may be changed by setting find_span_func keyword argument during the initialization. By default, this function is set to helpers.find_span_linear(). Please see Helpers Module Documentation for more details.

derivatives(datadict, parpos, deriv_order=0, **kwargs)

Evaluates the n-th order derivatives at the input parametric position.

Parameters:

  • datadict (dict) – data dictionary containing the necessary variables

  • parpos (list, tuple) – parametric position where the derivatives will be computed

  • deriv_order (int) – derivative order; to get the i-th derivative

Returns:

evaluated derivatives

Return type:

list

evaluate(datadict, **kwargs)

Evaluates the surface.

Keyword Arguments:

  • start: starting parametric position for evaluation

  • stop: ending parametric position for evaluation

Parameters:

datadict (dict) – data dictionary containing the necessary variables

Returns:

evaluated points

Return type:

list

property name

Evaluator name.

Getter:

Gets the name of the evaluator

Type:

str

class geomdl.evaluators.SurfaceEvaluatorRational(**kwargs)

Bases: SurfaceEvaluator

Sequential rational surface evaluation algorithms.

This evaluator implements the following algorithms from The NURBS Book:

  • Algorithm A4.3: SurfacePoint

  • Algorithm A4.4: RatSurfaceDerivs

Please note that knot vector span finding function may be changed by setting find_span_func keyword argument during the initialization. By default, this function is set to helpers.find_span_linear(). Please see Helpers Module Documentation for more details.

derivatives(datadict, parpos, deriv_order=0, **kwargs)

Evaluates the n-th order derivatives at the input parametric position.

Parameters:

  • datadict (dict) – data dictionary containing the necessary variables

  • parpos (list, tuple) – parametric position where the derivatives will be computed

  • deriv_order (int) – derivative order; to get the i-th derivative

Returns:

evaluated derivatives

Return type:

list

evaluate(datadict, **kwargs)

Evaluates the rational surface.

Keyword Arguments:

  • start: starting parametric position for evaluation

  • stop: ending parametric position for evaluation

Parameters:

datadict (dict) – data dictionary containing the necessary variables

Returns:

evaluated points

Return type:

list

property name

Evaluator name.

Getter:

Gets the name of the evaluator

Type:

str

class geomdl.evaluators.SurfaceEvaluator2(**kwargs)

Bases: SurfaceEvaluator

Sequential surface evaluation algorithms (alternative).

This evaluator implements the following algorithms from The NURBS Book:

  • Algorithm A3.5: SurfacePoint

  • Algorithm A3.7: SurfaceDerivCpts

  • Algorithm A3.8: SurfaceDerivsAlg2

Please note that knot vector span finding function may be changed by setting find_span_func keyword argument during the initialization. By default, this function is set to helpers.find_span_linear(). Please see Helpers Module Documentation for more details.

derivatives(datadict, parpos, deriv_order=0, **kwargs)

Evaluates the n-th order derivatives at the input parametric position.

Parameters:

  • datadict (dict) – data dictionary containing the necessary variables

  • parpos (list, tuple) – parametric position where the derivatives will be computed

  • deriv_order (int) – derivative order; to get the i-th derivative

Returns:

evaluated derivatives

Return type:

list

evaluate(datadict, **kwargs)

Evaluates the surface.

Keyword Arguments:

  • start: starting parametric position for evaluation

  • stop: ending parametric position for evaluation

Parameters:

datadict (dict) – data dictionary containing the necessary variables

Returns:

evaluated points

Return type:

list

property name

Evaluator name.

Getter:

Gets the name of the evaluator

Type:

str

Volume Evaluators

class geomdl.evaluators.VolumeEvaluator(**kwargs)

Bases: AbstractEvaluator

Sequential volume evaluation algorithms.

Please note that knot vector span finding function may be changed by setting find_span_func keyword argument during the initialization. By default, this function is set to helpers.find_span_linear(). Please see Helpers Module Documentation for more details.

derivatives(datadict, parpos, deriv_order=0, **kwargs)

Evaluates the n-th order derivatives at the input parametric position.

Parameters:

  • datadict (dict) – data dictionary containing the necessary variables

  • parpos (list, tuple) – parametric position where the derivatives will be computed

  • deriv_order (int) – derivative order; to get the i-th derivative

Returns:

evaluated derivatives

Return type:

list

evaluate(datadict, **kwargs)

Evaluates the volume.

Keyword Arguments:

  • start: starting parametric position for evaluation

  • stop: ending parametric position for evaluation

Parameters:

datadict (dict) – data dictionary containing the necessary variables

Returns:

evaluated points

Return type:

list

property name

Evaluator name.

Getter:

Gets the name of the evaluator

Type:

str

class geomdl.evaluators.VolumeEvaluatorRational(**kwargs)

Bases: VolumeEvaluator

Sequential rational volume evaluation algorithms.

Please note that knot vector span finding function may be changed by setting find_span_func keyword argument during the initialization. By default, this function is set to helpers.find_span_linear(). Please see Helpers Module Documentation for more details.

derivatives(datadict, parpos, deriv_order=0, **kwargs)

Evaluates the n-th order derivatives at the input parametric position.

Parameters:

  • datadict (dict) – data dictionary containing the necessary variables

  • parpos (list, tuple) – parametric position where the derivatives will be computed

  • deriv_order (int) – derivative order; to get the i-th derivative

Returns:

evaluated derivatives

Return type:

list

evaluate(datadict, **kwargs)

Evaluates the rational volume.

Keyword Arguments:

  • start: starting parametric position for evaluation

  • stop: ending parametric position for evaluation

Parameters:

datadict (dict) – data dictionary containing the necessary variables

Returns:

evaluated points

Return type:

list

property name

Evaluator name.

Getter:

Gets the name of the evaluator

Type:

str