Tensor product surfaces

Abstract

The easiest way to build a surface is to sweep a curve through space such that its control points move along some curves. The control points of these control curves control the surface. The surface representation by these control points has properties analogous to those of a univariate curve (e.g., Bézier or B-spline) representation. This is due to the fact that one can deal with these surfaces by applying just curve algorithms. Similarly, one can build multidimensional volumes by sweeping a surface or volume through space such that its control points move along curves. Again, one obtains control nets having properties analogous to those of the underlying curve representations.