Spatial transformations: from fundamentals to applications

  • Robert Foster, Patrick Grant, Yang Hao, Alastair Hibbins, Thomas Philbin, Roy Sambles
  • Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences, July 2015, Royal Society Publishing
  • DOI: 10.1098/rsta.2014.0365

Introduction to spatial transformations

What is it about?

This paper forms the introduction to this themed issue of Philosophical Transactions of the Royal Society A on ‘Spatial transformations’, arising from the Royal Society Scientific Discussion Meeting held in January 2015. The paper begins with a review of the concepts and history of spatial transformations, followed by a discussion of the contributions from the papers in this themed issue. A summary of the advantages and current limitations of spatial transformations concludes the paper, with the key challenges identified at the Scientific Discussion Meeting also given.

Why is it important?

This paper serves to set the various contributions to the themed issue of Phil. Trans. A in context, both in terms of a brief historical review of the concepts involved and also in how the work presented in the rest of the issue sits in relation to each other. Some key areas for further exploration of this exciting field are also highlighted.


Dr Robert N Foster
University of Birmingham

The spatial transformations paradigm is a powerful technique providing high degrees of control over wave propagation in many regimes, including electromagnetic/light waves, sound waves, seismic waves and thermal waves. Although the mathematical development can be traced back to the late 1800s, modern developments in computing and fabrication (such as 3D printing) offer new opportunities to take advantage of spatial transformations. However, there are still challenges to overcome before the full potential can be realised. In addition, there are new areas of physics and engineering where the spatial transformations approach is yet to be applied, where it could have significant impact. This paper seeks to capture these ideas in the context of the themed issue (for which it serves as an introduction), with other papers in the issue then giving greater detail and insight into specific aspects.

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The following have contributed to this page: Dr Robert N Foster