Model curves that are linear:

Nonlinear:

Model curves that are open:

Closed:

Summary box:

A quadratic B-spline curve requires three control points:

A cubic B-spline curve requires four control points:

In general, a B-spline curve with degree d requires at least (d+1) control points:

With fewer control points, a lower-degree curve is generated:

A B-spline curve that is open:

Closed:

Knots can be specified to control the smoothness of a curve:

Weights can be specified per control point:

Colored curves:

B-spline curves with different thicknesses:

Thickness scaled relative to the PlotRange:

Thickness in printer's points:

Dashed curves:

Opacity determines the curve transparency:

EdgeForm can be used to specify the curve style when used as a boundary in a FilledCurve:

BSplineCurve can be used as the curve for an Arrow in 2D:

3D:

In 3D, BSplineCurve can be used as the curve for a Tube:

Tube with Arrow:

BSplineCurve can be used in GraphicsComplex:

By default, control points are assumed to be in world coordinates:

Use Scaled to specify control points relative to the PlotRange:

Use ImageScaled to specify control points relative to the whole image region in 2D:

Use Offset to apply an absolute offset to control points in 2D:

Control points can be Dynamic:

Embedding dimension:

Geometric dimension:

Point membership test:

Arc length:

Centroid:

Distance from a point:

Visualize equidistance contours:

Signed distance from a point:

A B-spline curve is bounded:

Calculate its bounds:

By default, a BSplineCurve with 4 or more control points will use a degree of 3:

With fewer control points, a lower degree is used:

Use SplineDegree to specify that a lower degree should be used:

A higher degree:

By default, knots are generated in such a way that the curve is smooth overall:

By repeating knots, you can introduce tangent discontinuities:

"Clamped" generates knots such that the curve interpolates the first and last control points:

For a degree-d curve, this corresponds to the first and last knot values being repeated d+1 times:

"Unclamped" generates uniform knots, causing the curve to not interpolate the endpoints:

For a degree-d curve with n control points, this corresponds to a consecutive sequence of length n+d+1:

Unclamped knots combined with SplineClosed will make a uniform periodic B-spline curve:

By default, all the control points have equal weights:

By giving more weight to a control point, the curve will be attracted to that point:

By default, the curve is open:

Use SplineClosed to close the curve: