# EFSAT - An Exact and Efficient Triangle Intersection Test Hardware

### Andreas Raabe, Jan Tietjen, Joachim K. Anlauf

#### 2009

#### Abstract

Software implementations that test two triangles for intersection often favour speed over exact calculation. They leave it to the user to choose an exact or a fast test depending on the domain of application. Hardware implementations can not opt to make this distinction since users will always expect an accelerator hardware to be applicable in all possible settings. This paper introduces a novel approach towards exact intersection testing of triangles. It is based on the separating axes test and lends itself well to hardware implementation. To be integrable into a hierarchical collision detection design this test needs to be extremely resource efficient. Thus, it does not iterate until an exact solution is found, but instead categorises results as correct and possibly incorrect. It is implemented using 18-bit fixed-point numbers, while still maintaining resolutions that can keep up with double-precision floating-point implementations. The proposed test is integrated into a hierarchical collision detection FPGA-design accelerating collision queries by an order of magnitude. In a realistic benchmark less than 0:9% of possibly incorrect results are reported without impairing system performance.

#### References

- Held, M. (1996). ERIT - A collection of efficient and reliable intersection tests. Technical Report, University at Stony Brook.
- Karamcheti, V., Li, C., Pechtchanski, I., and Yap, C. (1999). A core library for robust numeric and geometric computation. In SCG 7899, New York, USA. ACM.
- Mehlhorn, K. and Schirra, S. (2001). Exact computation with leda real - theory and geometric applications. In Symbolic Algebraic Methods and Verification Methods, pages 163-172.
- MÃ¶ller, T. (1997). A Fast Triangle-Triangle Intersection Test. journal of graphics tools, 2(2):25-30.
- Plante, E., Cani, M.-P., and Poulin, P. (2001). A layered wisp model for simulating interactions inside long hair. In Computer Animation and Simulation 2001, Computer Science.
- Raabe, A., Hochgurtel, S., Zachmann, G., and Anlauf, J. K. (2006). Space-Efficient FPGAAccelerated Collision Detection for Virtual Prototyping. In Design Automation and Test (DATE), pages 206211, Munich, Germany.
- Raabe, A., Nett, A., and Niers, A. (2008). A Refinement Case-Study of a Dynamically Reconfigurable Intersection Test Hardware. In ReCoSoc08.
- Robbins, S. and Whitesides, S. (2003). On the reliability of triangle intersection in 3d. In ICCSA (3), pages 923- 930.
- Shewchuk, J. R. (1997). Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete & Computational Geometry, 18(3):305-368.
- Weller, R., Klein, J., and Zachmann, G. (2006). A model for the expected running time of collision detection using aabb trees. In Eurographics Symposium on Virtual Environments (EGVE), Lisbon, Portugal.
- Woulfe, M., Dingliana, J., and Manzke, M. (2007). Hardware accelerated broad phase collision detection. In SIGGRAPH 2007, New York, USA. ACM SIGGRAPH.

#### Paper Citation

#### in Harvard Style

Raabe A., Tietjen J. and K. Anlauf J. (2009). **EFSAT - An Exact and Efficient Triangle Intersection Test Hardware** . In *Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)* ISBN 978-989-8111-67-8, pages 355-360. DOI: 10.5220/0001775203550360

#### in Bibtex Style

@conference{grapp09,

author={Andreas Raabe and Jan Tietjen and Joachim K. Anlauf},

title={EFSAT - An Exact and Efficient Triangle Intersection Test Hardware},

booktitle={Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)},

year={2009},

pages={355-360},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001775203550360},

isbn={978-989-8111-67-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)

TI - EFSAT - An Exact and Efficient Triangle Intersection Test Hardware

SN - 978-989-8111-67-8

AU - Raabe A.

AU - Tietjen J.

AU - K. Anlauf J.

PY - 2009

SP - 355

EP - 360

DO - 10.5220/0001775203550360