Related Experiment Video
Updated: May 29, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
Published on: March 18, 2019
Two-dimensional critical point configuration graphs
1IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598.
Abstract:
The configuration of the critical points of a smooth function of two variables is studied under the assumption that the function is Morse, that is, that all of its critical points are nondegenerate. A critical point configuration graph (CPCG) is derived from the critical points, ridge lines, and course lines of the function. Then a result from the theory of critical points of Morse functions is applied to obtain several constraints on the number and type of critical points that appear on cycles of a CPCG. These constraints yield a catalog of equivalent CPCG cycles containing four entries. The slope districts induced by a critical point configuration graph appear useful for describing the behavior of smooth functions of two variables, such as surfaces, images, and the radius function of three-dimensional symmetric axes.
Related Concept Videos
Graphs of Equations in Two Variables
Graphical Representation of Inequalities
Phase Diagrams of Ternary Systems
Two Components: Liquid–Liquid Systems
pV-Diagrams
Phase Diagrams
