Has Artificial Intelligence Learned to Solve Point-in-Polygon and Line-Segment–Polygon Intersection Problems

Abstract

Two years ago, we concluded that ChatGPT could not reliably solve the problems of determining the relationship between a point and a polygon or computing the intersections of a line segment with a polygon. To assess the progress of artificial intelligence, we presented the same tasks in 2026 to ChatGPT, Gemini, Grok, DeepSeek, and Perplexity. All five systems correctly determined the position of the points relative to the polygon, while four of the five tools (ChatGPT, Gemini, Grok, and DeepSeek) also correctly identified both intersection points between the line segment and the polygon; only Perplexity produced an incorrect result. Some of the tools also provided graphical illustrations and detailed mathematical explanations. The results indicate that artificial intelligence has made significant progress over the past two years in solving such geometric problems. Nevertheless, because of the possibility of errors and hallucinations, the results should still be critically verified.