HyperFun Project is a free software development project for functionally based shape and volume modeling, visualization, animation, and fabrication. The project is based on the Function Representation (FRep) of geometric objects and supporting software tools built around the HyperFun language.

In FRep, complex geometric objects are constructed using simple ones (primitives) and operations on them. Any object in three-dimensional space is defined by a continuous real function of point coordinates <m>F(x,y,z)</m>. This continuous real-valued function is positive inside the object, negative outside, and takes zero value on its surface. Similarly, a multidimensional object is defined by a function of several variables <m>F(x_1, x_2, x_3, …, x_n)</m>. For example, an object changing in time can be defined by <m>F(x,y,z,t)</m> with <m>t</m> representing time. Object’s attributes represent such properties as color, material density or temperature at any given point in the form <m>S_i = S_i(x_1, x_2, x_3, …, x_n)</m>, where <m>S_i</m> is an arbitrary function of point coordinates.

HyperFun is a simple volume modeling language. It was introduced for teaching and practical use of FRep modeling. This Web site will help you to learn and use HyperFun in production of original shapes, images, and animations. You may start from the informal HyperFun description. However, an easier way can be to go through the step-by-step HyperFun Tutorial. We also provide here software tools and exercises which can be freely installed and distributed. More details on the project motivation and software system architecture can be found in the project overview.

A great variety of shapes can be modeled using this approach. You can find many examples at the HyperFun Gallery and in the Applications section. If you have questions or comments, you may contact each of the team members personally or use this contact information to reach the entire development team.