The present work investigates programmable auxetic surfaces and how they can be enabled to achieve a general surface shape upon external control. To actively generate target geometries from an initial geometry, a process of non-uniform
expansion or contraction as well as an alteration of local curvatures are necessary. This implies the alignment of a multiplicity of control factors. The present work suggests that auxetic mechanisms hold a high potential to achieve and
simplify such alignments. As a key principle for achieving defined target forms and the required shape transitions, the study identifies the modification of the local scaling factor and the Gaussian curvature of plane surfaces. Within this
work, such active surfaces are created utilizing multi-layered auxetic tessellations. To control the scaling factor and the curvature of the resulting structure, we propose different multi-layered auxetic structures comprising rotational
actuators. These concepts are demonstrated for the example of kagome tessellations but can easily be transferred to other auxetic tessellations.