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SplineClosed

is an option for B-spline functions and graphics primitives that specifies whether spline curves or surfaces should be closed.

Details
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Examples  
Basic Examples  
Scope  
Properties & Relations  
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SplineClosed

SplineClosed

is an option for B-spline functions and graphics primitives that specifies whether spline curves or surfaces should be closed.

Details

  • For curves, the setting SplineClosed->True makes the first and last points be connected smoothly.
  • For higher-dimension surfaces and manifolds, SplineClosed->True makes all boundaries be connected smoothly.
  • With the setting SplineClosed->True, all boundaries are connected smoothly.
  • With the setting SplineClosed->{c1,c2,…}, the boundaries are connected in directions i for which ci is True.

Examples

open all close all

Basic Examples  (2)

Generally, a B-spline curve is open and passes through the first and last control points:

Wolfram Language code: pts = {{0, 0}, {0, 1}, {1, 1}, {1, 0}};
Wolfram Language code: Graphics[{Point[pts], BSplineCurve[pts]}]

Smoothly closed B-spline curve with the same control points:

Wolfram Language code: Graphics[{Point[pts], BSplineCurve[pts, SplineClosed -> True]}]

B-spline closed in the -direction:

Wolfram Language code: Graphics3D[BSplineSurface[{{{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}}, {{0, 0, 1}, {0, 1, 1}, {1, 1, 1}, {1, 0, 1}}}, SplineClosed -> {False, True}]]

Scope  (1)

B-spline surface closed in both directions:

Wolfram Language code: Graphics3D[{BSplineSurface[{{{1, 0, -.5}, {2, 0, -.5}, {2, 0, .5}, {1, 0, .5}}, {{0, 1, -.5}, {0, 2, -.5}, {0, 2, .5}, {0, 1, .5}}, {{-1, 0, -.5}, {-2, 0, -.5}, {-2, 0, .5}, {-1, 0, .5}}, {{0, -1, -.5}, {0, -2, -.5}, {0, -2, .5}, {0, -1, .5}}}, SplineClosed -> True]}, PlotRange -> 1.5, Axes -> True]

Properties & Relations  (2)

Construct an open B-spline curve from B-spline basis functions:

Wolfram Language code: pts = {{0, 0}, {0, 1}, {1, 1}, {1, 0}}; basis = Table[BSplineBasis[{3, {0, 0, 0, 0, 1, 1, 1, 1}}, i, x], {i, 0, 3}]; f[x_] := Dot[basis, pts];
Wolfram Language code: {ParametricPlot[f[x], {x, 0, 1}, PlotRange -> {0, 1}], Graphics[BSplineCurve[pts], Axes -> True]}

The basis functions differ by their indices:

Wolfram Language code: Plot[Evaluate[basis], {x, 0, 1}]

Construct a closed B-spline curve from uniform B-spline basis functions:

Wolfram Language code: pts = {{0, 0}, {0, 1}, {1, 1}, {1, 0}}; cbasis = Table[BSplineBasis[3, i, x], {i, 0, 6}]; g[x_] := Dot[cbasis, Join[pts, pts[[1 ;; 3]]]];
Wolfram Language code: {ParametricPlot[g[x], {x, 3 / 4, 7 / 4}, PlotRange -> {0, 1}], Graphics[BSplineCurve[pts, SplineClosed -> True], Axes -> True]}

The basis functions are periodic. Thus they are of the same shape:

Wolfram Language code: Plot[Evaluate[cbasis], {x, 0, 10 / 4}]
Wolfram Research (2008), SplineClosed, Wolfram Language function, https://reference.wolfram.com/language/ref/SplineClosed.html.

Text

Wolfram Research (2008), SplineClosed, Wolfram Language function, https://reference.wolfram.com/language/ref/SplineClosed.html.

CMS

Wolfram Language. 2008. "SplineClosed." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SplineClosed.html.

APA

Wolfram Language. (2008). SplineClosed. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SplineClosed.html

BibTeX

@misc{reference.wolfram_2026_splineclosed, author="Wolfram Research", title="{SplineClosed}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/SplineClosed.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_splineclosed, organization={Wolfram Research}, title={SplineClosed}, year={2008}, url={https://reference.wolfram.com/language/ref/SplineClosed.html}, note=[Accessed: 13-June-2026]}