This tutorial describes how to model functionally defined geometric objects using HyperFun. Although HyperFun Polygonizer is referenced throughout the tutorial, any other available viewer of HyperFun models can be used for exercises.

HyperFun is a simple geometric modeling language for F-rep objects. F-rep stands for function representation. In F-rep, objects are described using a single real continuous function F(x1, x2, x3, …, xn) >= 0.

Since F-rep models are more general than traditional skeletal implicit surfaces, convolution surfaces, distance-based models, CSG (Constructive Solid Geometry), sweeps, and voxel models, HyperFun can deal with all these geometric models (see F-Rep page for more details about F-rep).

In HyperFun, F-rep objects are described using assignments, conditional selections, and iterations as in traditional programming languages. In addition to arithmetic and relational operators, HyperFun has built-in set-theoretic operators such as union, intersection, subtraction, and so on. Some predefined library primitives and operators are available in HyperFun. Using these functionalities, quite complex objects can be modeled.

You can freely download HyperFun tools. Now, HyperFun Polygonizer and HyperFun for POV-Ray are available on-line. These tools can run under Windows, Linux and Unix, but only Windows versions are ready.