The paper introduces the concept of the primary set of characteristic vies for general quadric- surfaced solids. A characteristic view (CV) is a representative view of a characteristic-view domain (CVD). The CVDs represent a partitioning of the viewing space of a solid based on the isomorphism of the labeled line-junction graphs of perspective-projection views. The primary set of CVs is a minimal subset of the set of CVs that is sufficient to represent all object surfaces and their relationships to each other in the most general viewing positions. Results indicate that the primary set of CVs can be used for efficiently guiding object recognition based on CV modeling. This paper discusses a scheme for computing some practical viewing constraints, describes the method for determining the primary set of CVs, and outlines a procedure for using the primary set of CVs for efficient object recognition.