There has been a tendency in the last decade to transition from single-discipline to multi-disciplinary analysis and design; this trend has been hastened by the increased availability of analysis and optimization frameworks that manage the workflow. But one of the enabling technologies that is needed has not received much attention: that is, the need to transfer information from the surface of one representation to another, with particular emphasis on transferring the data conservatively. Described herein is a new method for performing such transfers. It is based upon two key technologies: a universal view of solver discretizations and a new optimization-enabled conservative fitting technique. The scheme is fully described and demonstrated in one dimension; then the extension to two dimensions is discussed along with results.