Privacy-preserving computational geometry
Privacy-preserving computational geometry is the research area on the intersection of the domains of secure multi-party computation (SMC) and computational geometry. Classical problems of computational geometry reconsidered from the point of view of SMC include shape intersection, private point inclusion problem, range searching, convex hull, and more.
The problems use the conventional "Alice and Bob" terminology. In all problems the required solution is a protocol of information exchange during which no additional information is revealed beyond what may be inferred from the answer to the required question.
- Point-in-polygon: Alice has a point a, and Bob has a polygon B. They need to determine whether a is inside B. 
- Polygon pair intersection: Alice has a polygon A, and Bob has a polygon B. They need to determine whether A intersects B. 
- Kaitai LIANG, Bo YANG, Dake HE, Min ZHOU, Privacy-Preserving Computational Geometry Problems on Conic Sections, Journal of Computational Information Systems 7: 6 (2011) 1910–1923
- Atallah M J, Du W. Secure Multiparty Computational Geometry. In Proc. Algorithms and Data Structures: 7th International Workshop, WADS 2001, Lecture Notes in Computer Science, LNCS 2125, Providence, RI, USA, pages 165–179, August, 8–10, 2001. (As cited by Liang et al. 2011)
- Li S D, Dai Y Q. Secure two-party computational geometry. Journal of Computer Science and Technology, 20(2): pages 258–263, 2005.
- Luo Y L, Huang L S, Zhong H. Secure two-party point-circle inclusion problem. Journal of Computer Science and Technology, 22(1): pages 88–91, 2007