Abstract
Clifford algebra formalism has been used recently in combination with standard term-rewriting techniques for proving many nontrivial geometric theorems. The key issue in this approach consists in verifying whether two Clifford expressions are equal. This paper is concerned with the generalization of the work to 3D geometric problems. A rewriting system is proposed and its theoretical properties are investigated. Some examples and potential applications are also presented.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Ablamowicz, R., Lounesto, P., Parra, J. M.: Clifford algebras with numeric and symbolic computations. Birkhäuser, Boston (1996). 131
Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated production of traditional proofs for theorems in Euclidian geometry-II. The volume method. Tech. Rep. WSUCS-92-5, Department of Computer Science, Wichita State University, USA (1992). 152
Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Machine proofs in geometry.World Scientific, Singapore (1995). 130
Dershowitz, N., Jouannaud, J.-P.: Rewrite systems. In: Handbook of theoretical computer science, vol. B (J. van Leeuwen, ed.), Elsevier, Amsterdam, pp. 243–320 (1990??). 138
Fèvre, S., Wang, D.: Proving geometric theorems using Clifford algebra and rewrite rules. In: Proc. CADE-15 (Lindau, Germany, July 5–10, 1998), LNAI 1421, Springer, Berlin Heidelberg, pp. 17–32. 130, 131, 146, 148
Fèvre, S., Wang, D.: Combining algebraic computing and term-rewriting for geometry theorem proving. In: Proc. AISC’ 98 (Plattsburgh, USA, September 16–18, 1998), LNAI 1476, Springer, Berlin Heidelberg, pp. 145–156. 130, 146, 147, 148, 150
Li, H.: Vectorial equations-solving for mechanical geometry theorem proving. J. Automat. Reason. (to appear). 130, 146, 147, 149
Li, H., Cheng, M.-t.: Proving theorems in elementary geometry with Clifford algebraic method. Adv. Math. (Beijing) 26: 357–371 (1997). 130, 146
Maybank, S. J.: Applications of algebraic geometry to computer vision. In: Computational algebraic geometry (F. Eyssette and A. Galligo, eds.), Birkhäuser, Boston, pp. 185–194 (1993). 154
Wang, D.: Geometry machines: From AI to SMC. In: Proc. AISMC-3 (Steyr, Austria, September 23–25, 1996), LNCS 1138, Springer, Berlin Heidelberg, pp. 213–239. 130
Wang, D.: Clifford algebraic calculus for geometric reasoning with application to computer vision. In: Automated deduction in geometry (D. Wang, ed.), LNAI 1360, Springer, Berlin Heidelberg, pp. 115–140 (1997). 130, 146, 147, 148, 150
Wu, W.-t.: Mechanical theorem proving in geometries: Basic principles. Springer, Wien New York (1994). 130
Yang, H., Zhang, S., Feng, G.: Clifford algebra and mechanical geometry theorem proving. In: Proc. 3rd ASCM (Lanzhou, China, August 6–8, 1998), Lanzhou Univ. Press, Lanzhou, pp. 49–63. 130, 147, 153
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de la Tour, T.B., Fèvre, S., Wang, D. (1999). Clifford Term Rewriting for Geometric Reasoning in 3D. In: Automated Deduction in Geometry. ADG 1998. Lecture Notes in Computer Science(), vol 1669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47997-X_8
Download citation
DOI: https://doi.org/10.1007/3-540-47997-X_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66672-1
Online ISBN: 978-3-540-47997-0
eBook Packages: Springer Book Archive