Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 CubicSplineCurve

Source Notebook

Generate a cubic B-spline curve that passes through given points

Contributed by: Jan Mangaldan

ResourceFunction["CubicSplineCurve"][{{x1,y1,…},{x2,y2,…},…}]

constructs a cubic interpolating BSplineCurve that passes through the given set of points.

Details and Options

ResourceFunction["CubicSplineCurve"] returns a BSplineCurve object.
With the setting SplineClosed→True, ResourceFunction["CubicSplineCurve"] returns a curve that is closed.

Examples

Basic Examples (2) 

A list of points:

In[1]:=
pts = {{0., 0.}, {1., 2.}, {-1., 3.}, {0., 1.}, {3., 0.}};

Show the points along with an interpolating cubic B-spline:

In[2]:=
Graphics[{{Directive[AbsoluteThickness[3], ColorData[97, 1]], ResourceFunction["CubicSplineCurve"][pts]}, {Directive[ AbsolutePointSize[6], ColorData[97, 4]], Point[pts]}}]
Out[2]=

Scope (2) 

Choose six points in the plane to be interpolated:

In[3]:=
pts = {{1., 2.}, {0., 1.}, {2., 0.}, {2., 2.}, {3., 3.}, {5., 2.}};

Use CubicSplineCurve with Arrow:

In[4]:=
Graphics[{{Directive[ColorData[97, 5], Arrowheads[Medium]], Arrow[ResourceFunction["CubicSplineCurve"][pts]]}, {Directive[ ColorData[97, 3], AbsolutePointSize[4]], Point[pts]}}]
Out[4]=

Choose 3D points to be interpolated:

In[5]:=
pts = Table[N[{Cos[t], Sin[t], t/4}], {t, 0, 4 Pi, 2 Pi/10}];

Show the points along with an interpolating cubic B-spline:

In[6]:=
Graphics3D[{{Directive[AbsoluteThickness[3], ColorData[97, 1]], ResourceFunction["CubicSplineCurve"][pts]}, {Directive[ AbsolutePointSize[6], ColorData[97, 4]], Point[pts]}}]
Out[6]=

Show the interpolating cubic B-spline as a Tube:

In[7]:=
Graphics3D[{{Directive[AbsoluteThickness[3], ColorData[97, 1]], Tube[ResourceFunction["CubicSplineCurve"][pts], 0.03]}, {Directive[ AbsolutePointSize[6], ColorData[97, 4]], Sphere[pts, 0.05]}}]
Out[7]=

Options (1) 

SplineClosed (1) 

Use SplineClosed→True to interpolate a set of points with a closed B-spline:

In[8]:=
pts = With[{n = 12}, Table[N[AngleVector[{1 + (-1)^i/4, 2 \[Pi] i/n}]], {i, 0, n}]]; Graphics[{{Directive[AbsoluteThickness[3], ColorData[97, 1]], ResourceFunction["CubicSplineCurve"][pts, SplineClosed -> True]}, {Directive[AbsolutePointSize[6], ColorData[97, 4]], Point[pts]}}]
Out[8]=

Applications (2) 

Convert the result of KnotData into a BSplineCurve:

In[9]:=
pts = Transpose[ KnotData["FigureEight", "SpaceCurve"]["ValuesOnGrid"]] . DiagonalMatrix[{1, 1, 1/3}]; knot = ResourceFunction["CubicSplineCurve"][pts, SplineClosed -> True]; Graphics3D[{Directive[AbsoluteThickness[2], ColorData[97, 3]], knot}, Boxed -> False]
Out[9]=

Visualize the knot as a Tube:

In[10]:=
Graphics3D[{ColorData[97, 3], Tube[knot, 0.3]}, Boxed -> False, Lighting -> "Accent"]
Out[10]=

Version History

  • 1.0.0 – 03 August 2021

Source Metadata

  • Citation:
    • de Boor, C., A Practical Guide to Splines, Revised Edition. New York: Springer-Verlag, 2001.
    • Fritsch, F.N., "Representations for Parametric Cubic Splines." Computer Aided Geometric Design, vol. 6, no. 1, 79–82, 1989. DOI: 10.1016/0167-8396(89)90009-5

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