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Mathematica > Data Manipulation > Numerical Data > Curve Fitting & Approximate Functions > Splines >

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Built-in Mathematica Symbol

SplineClosed

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

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->{c₁, c₂, ...}, the boundaries are connected in directions i for which c_i is True.

Generally, B-spline curve is open and passing through the first and last control points.

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

B-spline closed in v-direction:

Generally, B-spline curve is open and passing through the first and last control points.

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

B-spline closed in v-direction:

B-spline surface closed in both directions:

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

The basis functions differ by their indices:

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

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