Successful morphogenesis on the scale of organs or organisms requires strict coordination between the constituent cells whose action on the local scale must be orchestrated accurately to achieve a functional shape on the global scale. We present a theoretical model in which morphogenetic information is encoded only through a locally preferred curvature, but with cell dynamics which simultaneously ensures that these interactions globally achieve morphogenesis and correct cell-neighbor exchanges to avoid cell stretches. This is achieved by a cell-cell interaction potential that drives correct cell intercalation to reorganize the cell sheet dynamically during the deformation processes. We demonstrate morphogenesis of simple three-dimensional shapes and study the effects of fixed cell neighbor connectivity and noisy cell division.