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basics.rst

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Basics

In order to generate a spline shape with NURBS-Python, you need 3 components:

  • degree
  • knot vector
  • control points

The number of components depend on the parametric dimensionality of the shape regardless of the spatial dimensionality.

  • curve is parametrically 1-dimensional (or 1-manifold)
  • surface is parametrically 2-dimensional (or 2-manifold)
  • volume is parametrically 3-dimensional (or 3-manifold)

Parametric dimensions are defined by u, v, w and spatial dimensions are defined by x, y, z.

Working with the curves

In this section, we will cover the basics of spline curve generation using NURBS-Python. The following code snippet is an example to a 3-dimensional curve.

from geomdl import BSpline

# Create the curve instance
crv = BSpline.Curve()

# Set degree
crv.degree = 2

# Set control points
crv.ctrlpts = [[1, 0, 0], [1, 1, 0], [0, 1, 0]]

# Set knot vector
crv.knotvector = [0, 0, 0, 1, 1, 1]

As described in the introduction text, we set the 3 required components to generate a 3-dimensional spline curve.

Evaluating the curve points

The code snippet is updated to retrieve evaluated curve points.

from geomdl import BSpline

# Create the curve instance
crv = BSpline.Curve()

# Set degree
crv.degree = 2

# Set control points
crv.ctrlpts = [[1, 0, 0], [1, 1, 0], [0, 1, 0]]

# Set knot vector
crv.knotvector = [0, 0, 0, 1, 1, 1]

# Get curve points
points = crv.evalpts

# Do something with the evaluated points
for pt in points:
    print(pt)

evalpts property will automatically call evaluate() function.

Getting the curve point at a specific parameter

evaluate_single method will return the point evaluated as the specified parameter.

from geomdl import BSpline

# Create the curve instance
crv = BSpline.Curve()

# Set degree
crv.degree = 2

# Set control points
crv.ctrlpts = [[1, 0, 0], [1, 1, 0], [0, 1, 0]]

# Set knot vector
crv.knotvector = [0, 0, 0, 1, 1, 1]

# Get curve point at u = 0.5
point = crv.evaluate_single(0.5)

Setting the evaluation delta

Evaluation delta is used to change the number of evaluated points. Increasing the number of points will result in a bigger evaluated points array, as described with evalpts property and decreasing will reduce the size of the evalpts array. Therefore, evaluation delta can also be used to change smoothness of the plots generated using the visualization modules.

delta property will set the evaluation delta. It is also possible to use sample_size property to set the number of evaluated points.

from geomdl import BSpline

# Create the curve instance
crv = BSpline.Curve()

# Set degree
crv.degree = 2

# Set control points
crv.ctrlpts = [[1, 0, 0], [1, 1, 0], [0, 1, 0]]

# Set knot vector
crv.knotvector = [0, 0, 0, 1, 1, 1]

# Set evaluation delta
crv.delta = 0.005

# Get evaluated points
points_a = crv.evalpts

# Update delta
crv.delta = 0.1

# The curve will be automatically re-evaluated
points_b = crv.evalpts

Inserting a knot

insert_knot method is recommended for this purpose.

from geomdl import BSpline

# Create the curve instance
crv = BSpline.Curve()

# Set degree
crv.degree = 2

# Set control points
crv.ctrlpts = [[1, 0, 0], [1, 1, 0], [0, 1, 0]]

# Set knot vector
crv.knotvector = [0, 0, 0, 1, 1, 1]

# Insert knot
crv.insert_knot(0.5)

Plotting

To plot the curve, a visualization module should be imported and curve should be updated to use the visualization module.

from geomdl import BSpline

# Create the curve instance
crv = BSpline.Curve()

# Set degree
crv.degree = 2

# Set control points
crv.ctrlpts = [[1, 0, 0], [1, 1, 0], [0, 1, 0]]

# Set knot vector
crv.knotvector = [0, 0, 0, 1, 1, 1]

# Import Matplotlib visualization module
from geomdl.visualization import VisMPL

# Set the visualization component of the curve
crv.vis = VisMPL.VisCurve3D()

# Plot the curve
crv.render()

Convert non-rational to rational curve

The following code snippet generates a B-Spline (non-rational) curve and converts it into a NURBS (rational) curve.

from geomdl import BSpline

# Create the curve instance
crv = BSpline.Curve()

# Set degree
crv.degree = 2

# Set control points
crv.ctrlpts = [[1, 0, 0], [1, 1, 0], [0, 1, 0]]

# Set knot vector
crv.knotvector = [0, 0, 0, 1, 1, 1]

# Import convert module
from geomdl import convert

# BSpline to NURBS
crv_rat = convert.bspline_to_nurbs(crv)

Using knot vector generator

Knot vector generator is located in the :doc:`knotvector <module_knotvector>` module.

from geomdl import BSpline
from geomdl import knotvector

# Create the curve instance
crv = BSpline.Curve()

# Set degree
crv.degree = 2

# Set control points
crv.ctrlpts = [[1, 0, 0], [1, 1, 0], [0, 1, 0]]

# Generate a uniform knot vector
crv.knotvector = knotvector.generate(crv.degree, crv.ctrlpts_size)

Plotting multiple curves

:doc:`multi <module_container>` module can be used to plot multiple curves on the same figure.

from geomdl import BSpline
from geomdl import multi
from geomdl import knotvector

# Create the curve instance #1
crv1 = BSpline.Curve()

# Set degree
crv1.degree = 2

# Set control points
crv1.ctrlpts = [[1, 0, 0], [1, 1, 0], [0, 1, 0]]

# Generate a uniform knot vector
crv1.knotvector = knotvector.generate(crv1.degree, crv1.ctrlpts_size)

# Create the curve instance #2
crv2 = BSpline.Curve()

# Set degree
crv2.degree = 3

# Set control points
crv2.ctrlpts = [[1, 0, 0], [1, 1, 0], [2, 1, 0], [1, 1, 0]]

# Generate a uniform knot vector
crv2.knotvector = knotvector.generate(crv2.degree, crv2.ctrlpts_size)

# Create a curve container
mcrv = multi.CurveContainer(crv1, crv2)

# Import Matplotlib visualization module
from geomdl.visualization import VisMPL

# Set the visualization component of the curve container
mcrv.vis = VisMPL.VisCurve3D()

# Plot the curves in the curve container
mcrv.render()

Please refer to the :doc:`Examples Repository <examples_repo>` for more curve examples.

Working with the surfaces

The majority of the surface API is very similar to the curve API. Since a surface is defined on a 2-dimensional parametric space, the getters/setters have a suffix of _u and _v; such as knotvector_u and knotvector_v.

For setting up the control points, please refer to the :doc:`control points manager <module_cpmanager>` documentation.

Please refer to the :doc:`Examples Repository <examples_repo>` for surface examples.

Working with the volumes

Volumes are defined on a 3-dimensional parametric space. Working with the volumes are very similar to working with the surfaces. The only difference is the 3rd parametric dimension, w. For instance, to access the knot vectors, the properties you will use are knotvector_u, knotvector_v and knotvector_w.

For setting up the control points, please refer to the :doc:`control points manager <module_cpmanager>` documentation.

Please refer to the :doc:`Examples Repository <examples_repo>` for volume examples.