We present a family of convected particle domain interpolations (CPDIs) within the framework of the material point method (MPM). That includes two dimensional triangular, quadrilateral, and polygonal CPDIs and three dimensional tetrahedron and polyhedron CPDIs. Theoretical derivations as well as computer implementation aspects are provided. A new perspective of CPDIs is given to link it to the recent works on the coupling of MPM and the finite element method. Numerical examples are given to demonstrate the performance of the proposed method. © 2016 Elsevier B.V.