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Unless the targeted mesh is developable, metric distortion is inevitable during the process of surface mesh parameterization, thus one important objective of all involved parametric studies is to reduce the metric distortion. In order to further reduce area and angle distortion, a novel method of boundary-free mesh parameterization is presented in the paper. Firstly, the initial boundary-fixed conformal parameterization from 3D surface mesh patch to a plane is performed in the method. Then, based on the initial parameterization, the iterations of boundary-free quasi-harmonic parameterization are developed, where the tensor field is updated in each iterative step and the principal curvature direction is utilized to terminate the iteration. The solution of the novel method is convenient to calculate since it involves a series of linear systems. In our novel parameterization method, lower metric distortion and considerable efficiency have been obtained in experiments.

Background It has been well established that theoretical kernel for recently surging genome-wide association study (GWAS) is statistical inference of linkage disequilibrium (LD) between a tested genetic marker and a putative locus affecting a disease trait. However, LD analysis is vulnerable to several confounding factors of which population stratification is the most prominent. Whilst many methods have been proposed to correct for the influence either through predicting the structure parameters or correcting inflation in the test statistic due to the stratification, these may not be feasible or may impose further statistical problems in practical implementation. Methodology We propose here a novel statistical method to control spurious LD in GWAS from population structure by incorporating a control marker into testing for significance of genetic association of a polymorphic marker with phenotypic variation of a complex trait. The method avoids the need of structure prediction which may be infeasible or inadequate in practice and accounts properly for a varying effect of population stratification on different regions of the genome under study. Utility and statistical properties of the new method were tested through an intensive computer simulation study and an association-based genome-wide mapping of expression quantitative trait loci in genetically divergent human populations. Results/Conclusions The analyses show that the new method confers an improved statistical power for detecting genuine genetic association in subpopulations and an effective control of spurious associations stemmed from population structure when compared with other two popularly implemented methods in the literature of GWAS.