## 7. Bezier surfaces

To create a Bézier surface, We blend a mesh of Bézier curves using the
blending function

where j and k are points in parametric space and represents the location of the knots in real space.
The Bézier functions specify the weighting of a particular knot. They
are the Bernstein coefficients. The definition of the Bézier functions is

where C(n,k) represents the binary coefficients. When u=0, the function is
one for k=0 and zero for all other points. When we combine two orthogonal
parameters, we find a Bézier curve along each edge of the surface, as
defined by the points along that edge. Bézier surfaces are useful for
interactive design and were first applied to car body design.

You can look at the Bezier surface
from a 3x3 mesh, or the Bezier
surface from a 4x4 mesh

### Further Information

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