This paper considers the problem of estimating the position of a scene point from its image projections onto generalized cameras, i.e., cameras that can be modeled by a spherical projection followed by a perspective one. The sought estimate is defined through a geometric criterion, specifically the minimization of the angles between the projections on the sphere of the available image points and the corresponding projections of the estimate. A solution based on convex optimization with linearmatrix inequalities (LMIs) is proposed for addressing this problem, which provides a candidate of the sought estimate. Moreover, a condition is provided for establishing exactness of the found candidate, i.e., establishing whether the found candidate is a minimizer of the considered geometric criterion.