Pointer analysis or points-to analysis (PTA) is a static program analysis for variables in a program, which determines a set of heap objects that individual variables may refer to at run time. In the literature, various types of context-sensitive analyses have been applied to improve the precision of PTA. In this article, we propose a framework that unifies existing context-sensitive PTA methods, under which we further explore more efficient ways for points-to calculation. In particular, we propose a call-graph-based context generation algorithm that combines the object-sensitive PTA and parameter-sensitive PTA approaches, and we implement the algorithm in the Soot compiler framework. Our new algorithm generates contexts for methods in a more complete and effective way, and it has been shown to achieve better precision with fewer generated contexts and less execution time than some of the known state-of-the-art context-sensitive approaches for PTA when tested with a selection of benchmarks from the DaCapo suite.