Abstract
Chemists often come across triangle domains – usually with the basic simplex in ℜ2. A smooth surface is needed for approximating the chemical properties between the measured data for solving some model (differential) equations numerically.
Our research group has been working on approximating ternary chemical surfaces of two special fields by smooth functions (vapour – Liquid equilibrium data and explosion-limit surfaces of ternary gas systems).
A mathematical solution was given in both fields by special spline surfaces, and for visualization, our own software (TRIGON) was used. In this paper the summarized chemical background of each problem is provided, the mathematical solutions, the newest theoretical developments and their results are discussed.