GRAPE is a GRAphics Programming Environment to understand, explore and solve mathematical problems from differential geometry and continuum mechanics, two of the main research areas of the Sonderforschungsbereich 256 (SFB) for Nonlinear Partial Differential Equations at the University of Bonn. It has been developed by students and staff members of the SFB in Bonn since 1987, but now also receives much impetus from groups in Berlin and Freiburg.

GRAPE has an object-oriented kernel written in standard C and uses a device independent approach for interactive graphic visualization. Therefore it runs on a variety of computers - available drivers currently many systems including Silicon Graphics, Sun, X-window standard, PostScript, Softimage and others. The system offers a class and method library for mathematical applications and objects for interactive control to be used in C programs. Additionally, it includes an interactive visualisation and programming environment. GRAPE is an open system with easy extension of existing classes, inclusion of new methods, and adaptation of the graphics interface. GRAPE allows nearly all geometric objects including their mathematical data to be time-dependent.

We support among others different kinds of curves, surfaces and volumes in three space and hierarchies of data. Geometric objects may carry additional information as for example an n-dimensional finite element function or describe maps between surfaces. Various mathematical algorithms from differential geometry and finite element theory as well as numerous visualisation tools are available including for example local refinement, extraction of level sets, reflection operations, calculation of particle traces or deformations of surfaces in flow fields. The driver concept allows display and modification of objects e.g. in hyperbolic space.

The GRAPE software is non-commercial. Scientific sites may obtain it on request from the SFB in Bonn for free.

Bonn, 24. May 1994

Konrad Polthier