As a result, we have a method for rendering a parametric surface. Or, put it in another way, we have a method for generating a set of triangles that approximate the given parametric surface. This approximation may not be a good one because it could have too many triangles and some of these triangles may be in wrong positions or too small. An adaptive technique dynamically adjusts the sizes, the number and the positions of triangles. Implicit Surfaces Let us turn to implicit surfaces.
Implicit surfaces are very useful in modeling.
For example, suppose we are given two surfaces and want to find a third one that can smoothly joining the given surfaces together. This process is called blending and the third surface is a blending surface of the given surfaces. This blending surface is of course not unique and is usually in an implicit form. The blending surface provides a smooth transition from the green surface to the blue one. In addition to blending, many applications and computations such as offsetting naturally generate algebraic surfaces.