This paper describes a C++ class hierarchy of implicit objects for geometry modeling and processing. This class structure provides a software kernel for integrating many various models and methods found in current implicit modeling areas. The software kernel includes primitive objects playing a role of unit element in creating a complex shape, and operator objects used to construct more complex shape of implicit object formed with the primitive objects and other operators. In this paper, class descriptions of these objects are provided to better understand the details of the algorithm or implementation, and its instance examples to show the capabilities of the object classes for constructive shape geometry. In addition, solid modeling system shown as an application example demonstrates that the proposed implicit object classes allow us to carry out modern solid modeling techniques, which means they have the capabilities to extend to various applications.