Finding Derivatives of Bezier Curves

Generalizing Swept and Skinned Shapes

I made a point of modeling surfaces of revolution as a control net for the sake of flexibility. Then, I turned around and introduced custom code for swept and skinned surfaces. These forms are not as flexible. For instance, you might want to transform the spring into a snake by expanding the end into a head and perhaps produce a rattle on the tail. This is not easy with the current form.

If you want to create a more flexible shape, you can do so by defining a surface with three different parametric curves. In this case, u and v would be the surface as you saw with surfaces of revolution and a new w curve could be the path shape. You could model the shape by combining the pieces you already have. First, use the skinning/sweeping code to position uv control points along the w path instead of vertices. Then, use the uv calculations to create the actual vertices. This might sound complex, but you have all the basic pieces at your fingertips.

Remember that such a representation can be heavier than the simple path and cross section method. The spring, for example, would require many more control points if modeled this way. For simple skinned or swept shapes, the code provided on the CD will be quite adequate. However, if you feel comfortable with the material, you might want to implement the other method as an exercise.