Optimization and Visualization of the Algorithm for Constructing a Second-Order Surface Defined by Nine Points

The paper focuses on the results of the experimental implementation of the historical problem of constructing a second-order surface (quadric) defined by nine points. The problem is based on the well-known Engel's algorithm (Engel J. H., 1889). The paper presents a block diagram of the algorithm. The software is additionally tested on the example of a new quadric. The algorithm is implemented by means of the basic geometric constructions, from setting nine points to the construction of a quadric surface. The software implementation proves to be of high accuracy. The designed visual model illustrates the function of the algorithm.