1.Représentations

Bézier surfaces are special types of rational surfaces, which use Bernstein bases to represent the polynomial functions. Several types of Bézier surfaces exist.

1.1.Tensor product Bézier surfaces

A rectangular or tensor product Bézier parametric surface is the image of a map of the form

where are the control points, and , are the Bernstein basis elements of degree for the interval .

A rational tensor-product Bézier surface is constructed as follows:

where are the weights of the control points (usually ).

The bidegree of the parametrisation is .

1.2.Simplex Bezier surfaces

A triangular or simplex Bézier parametric surface is the image of a map of the form

where is the triangle defined by the points , are the control points, and , are the barycentric coordinates of with respect to ().

A rational triangular Bézier surface is constructed similarly as for rectangular surfaces:

where are the weights of the control points (usually positive).

2.Example

Here is the well-known example of a teapot model made of 32 pieces of tensor product Bézier surfaces of bidegre :