• DOI:10.1145/513400.513416
Corpus ID: 6655454

Incidences between points and circles in three and higher dimensions

@inproceedings{Aronov2002IncidencesBP,
  title={Incidences between points and circles in three and higher dimensions},
  author={B. Aronov and V. Koltun and M. Sharir},
  booktitle={SCG '02},
  year={2002}
}

• B. Aronov, V. Koltun, M. Sharir
• Published in SCG '02 2002
• Computer Science, Mathematics

(MATH) We show that the number of incidences between <i>m</i> distinct points and <i>n</i> distinct circles in $\reals^3$ is <i>O</i>(<i>m</i> ^4/7 <i>n</i> ^17/21+<i>m</i> ^2/3 <i>n</i> ^2/3+<i>m</i>+<i>n</i>); the bound is optimal for <i>m n</i> ^3/2. This result extends recent work on point-circle incidences in the plane, but its proof requires a different analysis. The bound improves upon a previous bound, noted by Akutsu et al. [2] and by… Expand