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This impact is on society, culture and creativity. Series and Schleimer from Warwick's Geometry and Topology group have produced attractive visualisations and physical realisations of mathematical objects arising in their research. These have elicited a wide response from members of the public, with designs being creatively used for commercial, aesthetic and educational purposes.
Series popularised a novel form of fractal art, based on the geometry of iterated Möbius maps, in her book Indra's Pearls. This has inspired many artists working in a variety of media ranging from posters to quilts. Schleimer designs elegant yet mathematically accurate realisations of three and four dimensional figures, such as knots and related surfaces, suitable for 3D printing. These are being commercially manufactured, sold and displayed publically.
Research at the University of Cambridge Department of Engineering on computer vision tracking led to the creation of Extra Reality Limited in 2010, which was subsequently acquired by a new company called Zappar Limited in May 2011. Zappar employs 17 staff and had revenue of GBP612k in the financial year 2012/13, an increase of 35% on the previous year.
Over 50 different brands have used Zappar's augmented reality application across more than 300 offerings in over 17 countries to deliver entertainment-based marketing interactions from 2011 to 2013. [text removed for publication] Examples of partners include Disney, Warner Brothers and Marvel. Zappar has changed attitudes in the media sector by showing that "augmented reality is finally ready for prime time" (President, Creative Strategies Inc, Time Online, 2012).
3D scanning technology has enabled multiple opportunities for innovation in diverse areas such as manufacturing, design, and the arts. However, full utilisation of this technology requires not just the scanning hardware, but accompanying software that can build meaningful, editable models. This development has been pioneered by research conducted in the School of Computer Science and Informatics, at Cardiff University. Innovative algorithms for reverse engineering and digital shape reconstruction were devised that enabled the reconstruction of complex computer aided design (CAD) models from data captured by 3D scanners. The algorithms have been endorsed by Geomagic Inc, a market leading American software corporation (recently acquired by 3D Systems), that has subsidiaries in Europe and Asia and global distributors, and incorporated into their software product suite. This is accessed by nearly 10,000 licensed users worldwide, who have applied the product for industrial applications including aerospace and automotive engineering, product design, cultural heritage preservation, and healthcare. Accordingly, the impacts claimed are twofold: a) economic gain manifesting in the benefits to Geomagic and a plethora of end users who have utilised the software, b) impact on practitioners and professional services in diverse domains.
The Boujou special effects software was developed from research carried out at the Department of Engineering Science. It enables sophisticated computer generated imagery (CGI) to be quickly and easily added to `real' film footage, facilitating the visual effects that feature so importantly in films such as Harry Potter and X-Men. The software has become an essential tool used by film-makers, TV advert producers, and video game manufacturers, and for instance played a pivotal role in helping `The Curious Case of Benjamin Button' win the 2009 Oscar for Best Visual Effects. Between 2008 and 2013, sales of Boujou totalled £1.37 million and this software boosted productivity and profitability right across the global digital entertainment industry.
A new company, Geomerics, was created as a spin-out from the Cavendish Laboratory. Geomerics now employs 22 full time staff, with offices in Cambridge, UK and Vancouver, Canada. Geomerics has pioneered a new business sector in selling lighting middleware technology, based on Cambridge research, to games developers. Customers include Electronic Arts, Square Enix and Take 2 (three of the five largest publishers) and licenses have been sold in Europe, North America, Japan and Korea. In 2011 the first game released using Geomerics software, Battlefield 3, became the fastest selling game in Electronic Arts' history, having sold nearly 20M copies.
Research at the University of Cambridge Department of Engineering (DoEng) since 1997 created methods for reconstructing a three-dimensional (3D) model of an object from a single two-dimensional photograph. Metail, a company founded in 2008, sponsored further research at the DoEng and commercialised the results in an online fashion retailing application. Metail enables customers to select an item of clothing and see how they would look wearing it from a variety of angles, having entered just one photograph of themselves and a few basic body measurements. Metail attracted over GBP3.5M investment. Its application is used by Shop Direct, Tesco, Warehouse, Zalando and Dafiti. Sales data shows that the Metail application increases the propensity of customers to buy and reduces the proportion of goods returned.
In the late 1990s, a significant barrier to the adoption of virtual reality software was the expense of manually creating models of real-world scenes. To address this, between 1998 and 2004, the ICARUS software system was developed, which enabled the creation of structured, 3D geometric models from a sequence of images or video. The system also pioneered improved methods of camera tracking. ICARUS was subsequently licensed and developed commercially, and became the foundation for video and film post-production products that are used worldwide in the film (e.g. Universal Pictures, Warner Bros, Paramount Pictures) and television (e.g. BBC) industries, underpinning a company with an annual turnover in excess of £1m.
Research on the optimal arrangements of soap bubbles and soap films has been used as a vehicle for public engagement in mathematics. Presentations and demonstrations have been given in both Welsh and English at various events. These have had an impact on the awareness and interest of school children in geometry and mathematics.
The Centre for Sports Engineering Research (CESR) has developed new methods to allow accurate 3D measurement. These methods have evolved from lab-based to in-situ systems allowing real world measurements using multi-camera systems, object tracking, signal processing and planar calibration. This research has had four main types of impact:
This case study describes the impact of research at Loughborough University from 2009-2012 into the mathematical modelling of the dynamics of ions using perturbation theory of Hamiltonian systems of equations. Outcomes from this research have been incorporated into software used for the performance modelling of a series of high-precision Fourier Transform Mass Spectrometers manufactured by Thermo Fisher Scientific GbmH and branded as OrbitrapTM with an average price $0.5 million. The derived methodology reduces the time of numerical modelling of the behaviour of charged particles in an OrbitrapTM instrument by a factor of 100 to 1000. This reduction is of significant benefit to the Life Science Mass Spectrometry, Scientific Instrumentation Division of Thermo Fisher Scientific and indirectly the users of the instrument.