@inprocedings{den-08-aa-geom,
  author = {Denner-Broser, Britta},
  title = {An Algorithm for the Tracing Problem using Interval Analysis},
  journal = {Proceedings of the ACM Symposium on Applied Computing (SAC)},
  year = 2008,
  location = {Fortaleza, BR},
  pages = {1832–1837},
  month = mar,
  doi = {10.1145/1363686.1364127},
  comment = {Says that AA should be used to reduce uncertainty but does not use it. Dynamic Geometry is interactive programs such as CABRI that simulate geometric constructions using intersection and interpolation of lines, circles, etc..  Problem (NP-hard) is detecing singular events such as 2 circles becoming tangent or coincident when centers are dragged with mouse.  These critical events are avoided by using complex straight lines (2 dim instead of 1 dim) so that the path may detour around singularities.},
  abstract = {We give an algorithm for the Tracing Problem in Dynamic Geometry that uses interval arithmetic. In this work, we focus on an algebraic model. Here the objects are real or complex numbers with the operations $+$, $-$, $\times$, $/$, and $\sqrt{}$. Originally, geometric objects like points, lines, or circles have been considered.  Our algorithm proceeds stepwise and detects (potential) critical points in advance. For each step, the algorithm computes a steplength that is small enough to handle the ambiguity of the root function. This is achieved by using interval arithmetic. After the detection of a critical point, the singularity is avoided by a detour through the complex plane $\mathbb{C}$.},
  url = {{\url{https://dl.acm.org/doi/abs/10.1145/1363686.1364127?casa_token=K62Z9u9ppx0AAAAA:_7XtOP4NKMlQOHRN7yK4vuAPjZyWjFe2BRTsqfV1qTM6W3df0j0HSzCmjsWcaJ8VNhY_s_uDiNs}}},
  quotes = {... The usage of affine arithmetic might reduce this problem [3]. ... comments and for pointing out the relation to affine arithmetic. ... Affine arithmetic: Concepts and applications. Numerical ...}
}