Model rectangular surfaces that are flat:

Curved:

Twisted:

Model tubular surfaces that are straight:

Curved:

Closed:

Irregular:

Model surfaces of revolution:

BSplineSurface can represent topological disks:

Cylinders:

Spheres:

Tori:

Summary box:

A biquadratic B-spline patch requires a 3×3 array of control points:

A bicubic B-spline patch requires a 4×4 array of control points:

In general, a simple B-spline patch with degree d requires a (d-1)×(d-1) array of control points:

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

An open B-spline surface:

Closed:

Mixed:

Colored surfaces:

Different properties can be specified for the front and back of surfaces using FaceForm:

EdgeForm can be used to specify the style of the boundary edges of a surface:

Edges are not drawn for closed boundaries:

Surfaces with different specular exponents:

Opacity specifies the face transparency:

Glow specifies the color of the surface independent of any Lighting:

Use it with Lighting to create subtle shading:

Apply a Texture to a surface:

Draw surfaces with non-photorealistic shading:

Use MaterialShading to draw surfaces with physically based materials:

BSplineSurface 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:

Coordinates can be Dynamic:

Embedding dimension:

Geometric dimension:

Point membership test:

Area:

Centroid:

Distance from a point:

Visualize equidistance contours:

Signed distance from a point:

A B-spline surface is bounded:

Calculate its bounds:

By default, a BSplineSurface with 4×4 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:

Specify separate degrees per direction:

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

By repeating knots, you can introduce tangent discontinuities:

"Clamped" generates knots such that the surface interpolates the corner control points:

For a degree-d surface, 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 corner control points:

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

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 boundaries of a surface are open:

Close the surface along a single direction:

Close the surface in both directions:

Model a simple control cage for a section of pipe:

Use the cage along with knots and weights to specify a B-spline surface for the pipe:

Render the surface:

Model a chess pawn:

Model a chalice:

Plot interpolated data:

Increasing the SplineDegree results in a smoother fit to noisy data: