The first author has previously developed a third degree polynomial co
ordinate transformation which improves the accuracy of numerical quadr
ature schemes typical of boundary element implementations. This transf
ormation is now extended to include additional integrand variations an
d kernels of order ln(1/r),1/r,1/r2 and 1/r3 are discussed. The optimi
zed parameter which governs the transformation is presented in tabular
form for several source to element minimum distances.