The curvilinear coordinates’ approach to the smart-designs generation problem

Purpose: The aim of this paper is to present an alternative approach to the problem of accuracy estimation for smartdesigns’ class (also named space-filling or intelligent design) by making use of the design’s geometrical properties. Design/methodology/approach: The assumed topographical condition: ‘all design cases have to be on the defined surface’ is reversed into a curvilinear coordinate system mapped on this surface. Then a sequence of irregular experimental designs is generated on the surface with various descriptive parameters and sampling from testing function is taken. Next, the identification of a general linear-quadratic model is conducted and various accuracy measures in comparison to a test function are calculated. At last the monotonic correlation analysis between accuracy measures and the design’s geometrical properties is conducted. Findings: Significant and strong correlation between the accuracy measures and some of the geometrical properties has been found. Research limitations/implications: The correlations found are a strong suggestion for further research. The future investigations should be provided with various and more complicated testing functions and different topographical conditions. The relations between geometrical properties and accuracy measures need to be identified and their distributions and confidence intervals need to be determined. Practical implications: The results obtained outline the method of the approximation accuracy estimation from geometrical properties of the design. Originality/value: Worked out formulas may be of a significant value for those conducting data mining in technological data warehouses.