Related Experiment Video
Updated: Mar 7, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
A ray casting method for the computation of the area of feasible solutions for multicomponent systems: Theory,
Mathias Sawall1, Klaus Neymeyr2
1Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057, Rostock, Germany.
Abstract:
Multivariate curve resolution methods suffer from the non-uniqueness of the solutions. The set of possible nonnegative solutions can be represented by the so-called Area of Feasible Solutions (AFS). The AFS for an s-component system is a bounded (s-1)-dimensional set. The numerical computation and the geometric construction of the AFS is well understood for two- and three-component systems but gets much more complicated for systems with four or even more components. This work introduces a new and robust ray casting method for the computation of the AFS for general s-component systems. The algorithm shoots rays from the origin and records the intersections of these rays with the AFS. The ray casting method is computationally fast, stable with respect to noise and is able to detect the various possible shapes of the AFS sets. The easily implementable algorithm is tested for various three- and four-component data sets.
Related Concept Videos
Area Computation by the Alternative Coordinate Method
Area Problem
Area Between Curves: Integrating With Respect to y
Castigliano's Theorem: Problem Solving
Moments of Inertia for Composite Areas
The second moment of area, also known as the moment of inertia, measures a structure's resistance to bending. It is calculated by...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

