This paper addresses the computation of spheres, right-circular cylinders, and right-circular cones from a single view. Geometric information about these objects are known a priori, as this would be the case for model-based vision applications. The 3-D poses of these objects can be computed using elliptical projection from the sphere or elliptical projections from the circular surfaces of a cylinder or cone. For the cylinder and cone, their poses can also be computed form their linear extremal contours. This paper employs simple analytic geometric techniques that address uniqueness of the solutions as well as the geometric interpretations of the non-unique solutions. For the sphere, its pose can be uniquely determined by its elliptical projection. Using a planar circular surface from either the cone or the cylinder, two solutions to the position and orientation of the circle are possible. From the linear extremal contours of a cylinder, its pose can be computed uniquely if the junctions are visible in the image, otherwise the position has one degree of freedom along the cylinder axis. From the linear contours of a cone, its pose can also be solved uniquely unless the junctions are occluded. In that case there are two possible solutions for the orientation but the position has one degree of freedom along the line joining the projection center to the image apex position.