`NURBSCurve`#

class ansys.geometry.core.shapes.curves.nurbs.NURBSCurve#

Bases: ansys.geometry.core.shapes.curves.curve.Curve

Represents a NURBS curve.

Notes

This class is a wrapper around the NURBS curve class from the geomdl library. By leveraging the geomdl library, this class provides a high-level interface to create and manipulate NURBS curves. The geomdl library is a powerful library for working with NURBS curves and surfaces. For more information, see https://pypi.org/project/geomdl/.

Overview#

Abstract methods

`contains_param`	Check a parameter is within the parametric range of the curve.
`contains_point`	Check a point is contained by the curve.

Constructors

from_control_points

Create a NURBS curve from control points.

Methods

`parameterization`	Get the parametrization of the NURBS curve.
`transformed_copy`	Create a transformed copy of the curve.
`evaluate`	Evaluate the curve at the given parameter.
`project_point`	Project a point to the NURBS curve.

Properties

`geomdl_nurbs_curve`	Get the underlying NURBS curve.
`control_points`	Get the control points of the curve.
`degree`	Get the degree of the curve.
`knots`	Get the knot vector of the curve.
`weights`	Get the weights of the control points.

Special methods

__eq__

Determine if two curves are equal.

Import detail#

from ansys.geometry.core.shapes.curves.nurbs import NURBSCurve

Property detail#

property NURBSCurve.geomdl_nurbs_curve: geomdl.NURBS.Curve#

Get the underlying NURBS curve.

Notes

This property gives access to the full functionality of the NURBS curve coming from the geomdl library. Use with caution.

property NURBSCurve.control_points: list[ansys.geometry.core.math.Point3D]#: Get the control points of the curve.

property NURBSCurve.degree: int#: Get the degree of the curve.

property NURBSCurve.knots: list[ansys.geometry.core.typing.Real]#: Get the knot vector of the curve.

property NURBSCurve.weights: list[ansys.geometry.core.typing.Real]#: Get the weights of the control points.

Method detail#

classmethod NURBSCurve.from_control_points(control_points: list[ansys.geometry.core.math.Point3D], degree: int, knots: list[ansys.geometry.core.typing.Real], weights: list[ansys.geometry.core.typing.Real] = None) → NURBSCurve#

Create a NURBS curve from control points.

Parameters:

control_pointslist[Point3D]: Control points of the curve.
degreeint: Degree of the curve.
knotslist[Real]: Knot vector of the curve.
weightslist[Real], optional: Weights of the control points.

Returns:

NURBSCurve: NURBS curve.

NURBSCurve.__eq__(other: NURBSCurve) → bool#: Determine if two curves are equal.

NURBSCurve.parameterization() → ansys.geometry.core.shapes.parameterization.Parameterization#

Get the parametrization of the NURBS curve.

The parameter is defined in the interval [0, 1] by default. Information is provided about the parameter type and form.

Returns:

Parameterization: Information about how the NURBS curve is parameterized.

NURBSCurve.transformed_copy(matrix: ansys.geometry.core.math.Matrix44) → NURBSCurve#

Create a transformed copy of the curve.

Parameters:

matrixMatrix44: Transformation matrix.

Returns:

NURBSCurve: Transformed copy of the curve.

NURBSCurve.evaluate(parameter: ansys.geometry.core.typing.Real) → ansys.geometry.core.shapes.curves.curve_evaluation.CurveEvaluation#

Evaluate the curve at the given parameter.

Parameters:

parameterReal: Parameter to evaluate the curve at.

Returns:

CurveEvaluation: Evaluation of the curve at the given parameter.

abstract NURBSCurve.contains_param(param: ansys.geometry.core.typing.Real) → bool#: Check a parameter is within the parametric range of the curve.

abstract NURBSCurve.contains_point(point: ansys.geometry.core.math.Point3D) → bool#

Check a point is contained by the curve.

The point can either lie within the curve or on its boundary.

NURBSCurve.project_point(point: ansys.geometry.core.math.Point3D, initial_guess: ansys.geometry.core.typing.Real | None = None) → ansys.geometry.core.shapes.curves.curve_evaluation.CurveEvaluation#

Project a point to the NURBS curve.

This method returns the evaluation at the closest point.

Parameters:

pointPoint3D: Point to project to the curve.
initial_guessReal, optional: Initial guess for the optimization algorithm. If not provided, the midpoint of the domain is used.

Returns:

CurveEvaluation: Evaluation at the closest point on the curve.

Notes

Based on the NURBS book, the projection of a point to a NURBS curve is the solution to the following optimization problem: minimize the distance between the point and the curve. The distance is defined as the Euclidean distance squared. For more information, please refer to the implementation of the distance_squared function.