Model rectangular surfaces that are flat:

Curved:

Twisted:

Model tubular surfaces that are straight:

Curved:

Closed:

Irregular:

Model surfaces of revolution:

BezierSurface can represent topological disks:

Cylinders:

Spheres:

Tori:

Summary box:

A quadratic Bézier patch requires a 3×3 array of control points:

A cubic Bézier patch requires a 4×4 array of control points:

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

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

With more control points, a composite Bézier surface is generated:

An open Bézier 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:

BezierSurface 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 Bézier surface is bounded:

Calculate its bounds:

By default, a BezierSurface 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:

For a BezierSurface with n×n control points, specifying a degree d where d<n-1 will give a composite Bézier surface:

Specify separate degrees per direction:

By default, the boundaries of a surface are open:

Close the surface along a single direction:

Close the surface in both directions:

Boundaries are closed by copying the first row and/or column of the control point array to the end of the array:

Composite Bézier surfaces are made of multiple Bézier patches:

Show the individual patches that form the surface:

Model a discrete control cage for a chalice:

Define a smooth BezierSurface over the cage:

Render the surface:

Model an object with sharp edges using a composite BezierSurface:

Model a chess pawn: