A geometrical method is provided to locate all kinds of azeotropes, i.e., nonreactive, kinetic, and reactive azeotropes, in homo- and heterogeneous ternary systems. The mass balance conditions of azeotropes are geometrically demonstrated as reaction kinetic surface (RKS), which can be further generalized as the potential singular point surface (PSPS). The azeotropes can be directly located by two sets of RKS's based on different components. However, it is more convenient to use PSPS with one set of RKS due to its important property; i.e., the PSPS consists of all kinds of azeotropes and all pure components such that the PSPS can be predicted starting from pure components. A continuation method is used to determine the PSPS and the RKS. Several nonreactive and reactive systems with homogeneous and heterogeneous liquid mixtures are illustrated.