An algorithm for the tracing problem using interval analysis
Britta Denner-Broser · 2008
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 +, --, .,/, and √. 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 C.