Published in Volume XX, 2010, pages 33-52

**Authors:** E. Bartocci, D.R. Cacciagrano, M.R. Di Berardini, E. Merelli, and L. Tesei

### Abstract

The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel that models naturally binding sites on the surface of shapes. In this paper, the full formal timed operational semantics of the calculus is provided, together with examples that illustrate the use of the calculus in a well-known biological scenario. Moreover, a result of well-formedness about the evolution of a given network of well-formed 3D processes is proved.

Full Text (PDF)### References

[1] E. Bartocci, D. R. Cacciagrano, M. R. Di Berardini, E. Merelli, and L. Tesei. Shape Calculus: Timed Operational Semantics and WellFormedness. Available at http://arxiv.org/abs/1011.2488, Technical Report, 2010.

[2] E. Bartocci, F. Corradini, M. R. Di Berardini, E. Merelli, and L. Tesei. Shape Calculus. A Spatial Mobile Calculus for 3D shapes. Scientic Annals of Computer Science, 20:1-31, 2010.

[3] C. Ericson. Real-time collision detection. Elsevier North-Holland, Inc., 2005.

[4] C. Hecker. Physics, part 3: Collision response. Game Developer Magazine, pages 11-18, 1997.

### Bibtex

@article{sacscuza:bartocci2010tosawosc, title={Timed Operational Semantics and Well-Formedness of Shape Calculus}, author={E. Bartocci and D.R. Cacciagrano and M.R. Di Berardini and E. Merelli and L. Tesei}, journal={Scientific Annals of Computer Science}, volume={20}, organization={``A.I. Cuza'' University, Iasi, Romania}, year={2010}, pages={33--52}, publisher={``A.I. Cuza'' University Press} }