**Dept. of Computer and Information science, Linköping University**

## IDA Technical Reports: abstract

*Generated: Sat, 20 Dec 2014 16:06:07 *

Fritzson, P., Fritzson, D., Viklund, L., and Herber, J. (1991).
**Transformation of Equation-Based Real-World Models to Efficient Code,
Applied to Machine Elements Geometry**.
Technical Report LiTH-IDA-R-91-38, Department of Computer and Information
Science, Linköping University, Sweden.
Also in Proceedings of the 1st National Swedish Symposium on Real-Time
Systems, Uppsala, August 19-20, 1991.
(bibtex),

**Abstract: **Software which deals with the real external
world usually includes a model of relevant aspects of this world. A high
level and concise way of expressing such models is through mathematics -
equations and formulae, which can model geometry and other properties.
However, software which interacts with the real world, usually real-time
software, is very dependent on efficient execution of the code which
implements the model. A typical example is a robot arm, where the software
must include a computationally efficient model of the arm geometry and
surroundings in order to precisely guide the arm movement.In our approach we
combine the advantages of both a high level abstract model representation and
execution of efficient code. This is achieved by providing symbolic
transformations of the model: i.e. to minimize the part which is solved
numerically and transform the model into a computationally efficient form. To
this end, we have designed and implemented a prototype object-oriented
programming environment to support the process. The environment can handle
realistic problems, since the user can supply expertise in terms of
transformations and simplifications of equations.An essential component in
this environment is a modeling and programming language called ObjectMath
(Object oriented Mathematical language for scientific computing). It is a
hybrid language that combines object oriented language features with a
computer algebra language, in this case Mathematica. Using ObjectMath, it is
possible to model classes of equation objects, and to support inheritance of
equations. Geometrical constraints are expressed through connection objects
and coordinate system objects, and through use of parametric surface
techniques. When necessary, equations can be transformed to C++ code for
efficient numerical solution. A prototype version of the environment is
currently being used for an example model of 200 equations describing a
rolling bearing in three dimensions.

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