Generate Basis Functions for Cubic B-Spline Surfaces

Tensor product B-spline functions can be easily built up using the multiplication of the basis functions.

In[1]:=

knots = {0, 0, 0, 0, 1, 1, 1, 1};

GraphicsGrid[

 Table[Plot3D[

   BSplineBasis[{3, knots}, i, x] BSplineBasis[{3, knots}, j, y], {x, 

    0, 1}, {y, 0, 1}, PlotRange -> All, Mesh -> 3, Axes -> False, 

   Boxed -> True, 

   PlotLabel -> 

    TraditionalForm[

     BSplineBasis[{3, knots}, i, u] BSplineBasis[{3, knots}, j, 

       v]]], {i, 0, 3}, {j, 0, 3}], ImageSize -> {500, 500}]

Out[1]=