Distance-based triangulation is a fundamental technique for localization and mapping in two-dimensional spaces. Potential applications include wireless sensor networks, mobile robotics, and mapping systems, where real-time and reliable two-dimensional localization is essential. In addition to the usual triangulation algorithms, physics also uses its development, the so-called causal dynamic triangulation, which connects quantum geometry with the concepts of space and time. In it, significant results were achieved in modeling black holes and cosmological conditions, in which conventional triangulation methods make it possible to understand what the plane of the event horizon may consist of. In real-world applications, however, sensor measurements are often corrupted by noise and unpredictable errors, making it infeasible to reconstruct the true coordinates of points directly from raw distances. Classical optimization-based approaches to restore the coordinates of the entire set of points can mitigate noise but usually incur high computational costs, as they attempt to minimize global error measures. To balance computational efficiency and reconstruction accuracy, we introduce a heuristic algorithm for planar point coordinate recovery. The method is amenable to parallel computation and is able to return solutions of acceptable quality within practical time limits. The experimental methods proposed in this paper and their corresponding estimates show that the proposed approach makes it possible to reliably reconstruct the configurations of flat points, despite noisy distance data.