This method uses cubic Hermite splines to build a mortality curve. Given a set of survival fractions \(\sfrac_i\) and person-years lived \begin{equation} \ssf_i=\int_0^{x_i} \sfrac(a) da \end{equation} at ages \(x_i\) for \(i=0,\ldots,n-1\) the value of \(\ssf(x)\) and \(\sfrac(x)\) at age \(x\in[x_i,x_{i+1})\) is \begin{eqnarray} \ssf(x)&=& A \ssf_i + B\ssf_{i+1} + C\sfrac_i+D\sfrac_{i+1}\\ \sfrac(x)&=& A' \ssf_i + B' \ssf_{i+1} + C' \sfrac_i + D' \sfrac_{i+1} \end{eqnarray} where \begin{eqnarray} A&=& 2t^3-3t^2+1,\\ B&=&-2t^3+3t^2,\\ C&=&(t^3-2t^2+t)(x_{i+1}-x_i),\\ D&=&(t^3-t^2)(x_{i+1}-x_i), \end{eqnarray} and \begin{equation} t=\frac{x-x_i}{x_{i+1}-x_i}. \end{equation}
Unlike other build methods this method requires both a frequency measure of mortality (death rate, death probability, survival fraction) and a duration measure (person-years lived, person-years lived after, life expectancy or separation factor). This extra information is necessary when one wants to reproduce both survival fraction and life expectancy data in a published life table or when one wants to convert death rates into death probabilities using a specified set of separation factors. The duration measure data is given in a RESULTS object. The name of the results object must be given in the build method extrainfo string.