Parametric shape optimization aims at minimizing a function f(x) where x ∈ X ⊂ Rd is a vector of d Computer Aided Design parameters, representing diverse characteristics of the shap e Ω x . It is common for d to be large, d & 50 , making the optimization diffcult, especially when f is an expensive black-b ox and the use of surrogate-based approaches [1] is mandatory. Most often, the set of considered CAD shapes resides in a manifold of lower dimension where it is preferable to perform the optimization. We uncover it through the Principal Comp onent Analysis of a dataset of n designs, mapped to a high-dimensional shape space via φ : X → Φ ⊂ R D , D d . With a proper choice of φ , few eigenshapes allow to accurately describ e the sample of CAD shap es through their principal comp onents α α α in the eigenbasis V = [ v 1 ,..., v D ] ...