Summary: Quaternionic theory has greatly been developed in recent years. Thus, in our view, the study of trigonometric and logarithmic type quaternionic functions is important for the determination and realization of a hypercomplex theory. In this paper, we intend to give a geometrical foundation for both logarithmic and trigonometric hypercomplex functions based on the exponential function of quaternionic type recently introduced by M. F. Borges, J. A. Marão and J. M. Machado in their paper [Int. J. Pure Appl. Math. 48, No. 4, 495–500 (2008; Zbl 1177.30063)].