The purpose of this paper is to introduce a new kind of microarchitectured material that utilizes active control to alter its bulk shape through the deformation of its compliant elements. This new kind of microarchitectured material achieves its reconfigurable shape capabilities through a new control strategy that utilizes linearity and closed-form analytical tools to rapidly calculate the optimal internal actuation effort necessary to achieve a desired bulk surface profile. The kind of microarchitectured materials introduced in this paper is best suited for high-precision applications that would benefit from materials that can be programed to rapidly alter their surface or shape by small repeatable amounts in a controlled manner. Examples include distortion-correcting surfaces on which precision optics are mounted, airplane wings that deform to increase maneuverability and fuel efficiency, and surfaces that rapidly reconfigure to alter their texture. In this paper, the principles are provided for optimally designing 2D or 3D versions of the new kind of microarchitectured material such that they exhibit desired material property directionality. The mathematical theory is provided for modeling and calculating the actuation effort necessary to drive these materials such that their lattice shape comes closest to achieving a desired profile. Case studies are provided to demonstrate the utility of this theory and finite-element analysis (FEA) is used to verify the results.