Abstract: In this paper we describe the development and comparison of interaction techniques for 3D direct manipulation on multi-touch enabled devices. The literature on this topic currently shows diverging arguments for what enables effective and/or intuitive interaction. We argue that the limiting problem is the projection from 3D to 2D in input and output; and in particular how transformations in 3D are mapped to the interaction surface. Not only does this argument explain the divergence in the literature -- it also leads to improved interaction metaphors, similar but not identical to widgets in other 3D interaction domains. We show in a controlled experiment that adapted interaction widgets are significantly superior to other approaches in the context of multi-touch interaction.