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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>An MAT seminar of interest on Friday at 1pm, about the mathematics of spherical imaging:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> mat-announce-bounces@lists.mat.ucsb.edu [mailto:mat-announce-bounces@lists.mat.ucsb.edu] <b>On Behalf Of </b>mat-announce@lists.mat.ucsb.edu<br><b>Sent:</b> Tuesday, January 17, 2017 11:14 AM<br><b>To:</b> mat-announce@lists.mat.ucsb.edu<br><b>Subject:</b> [MAT-announce] [ Henry Segerman | MAT - Seminar Series - Friday January 20 . 1pm - ELINGS 1601 ]<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><img width=840 height=512 style='width:8.75in;height:5.3333in' id="_x0038_7FACB3C-7056-4E17-9CA7-5AEF2C35635A" src="cid:image001.jpg@01D270B5.FDD3BFB0"><o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><b><span style='font-size:13.5pt;font-family:"Arial",sans-serif;color:#C84677;background:white'>Mathematical transformation of spherical images and video</span></b><span style='font-family:"Myriad Pro",sans-serif;color:#BF1656;background:white'> </span><o:p></o:p></p><div><p class=MsoNormal style='background:white'><span style='font-size:9.5pt;font-family:"Myriad Pro",sans-serif;color:#222222'>by</span><o:p></o:p></p></div><div><p class=MsoNormal style='background:white'><b><span style='font-size:10.0pt;font-family:"MyriadPro-Semibold",serif;color:#222222'>Henry Segerman</span></b><o:p></o:p></p></div><div><p class=MsoNormal style='background:white'><b><span style='font-size:10.0pt;font-family:"MyriadPro-Semibold",serif;color:#222222'><br><br></span></b><o:p></o:p></p></div><div><p class=MsoNormal style='background:white'><b><span style='font-size:10.0pt;font-family:"MyriadPro-Semibold",serif;color:#222222'>| FRIDAY January 20 | 1:00pm | ELINGS 1601 |</span></b><o:p></o:p></p></div><div><p class=MsoNormal style='background:white'><b><span style='font-size:10.0pt;font-family:"MyriadPro-Semibold",serif;color:#222222'><br><br></span></b><o:p></o:p></p></div><div><div><p class=MsoNormal style='background:white'><b><span style='font-size:10.0pt;font-family:"MyriadPro-Semibold",serif;color:#222222'>______________</span></b><span style='color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><b><span style='font-size:10.5pt;font-family:"Helvetica",sans-serif;color:#333333'><br><br></span></b><span style='color:black'><o:p></o:p></span></p></div><div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:#222222'>Spherical (or "360 degree") still and video cameras capture light from all directions, producing a sphere of image data. What kinds of post-process transformations make sense for spherical photographs and video? We can rotate the sphere, but is there an analogue to zoom in flat video? </span><span style='color:#222222'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='color:#222222'><o:p> </o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:#222222'>By viewing the sphere of image data as the Riemann sphere, we can use complex numbers to describe the positions of the pixels. By scaling the complex plane, we get something like a zoom effect, with which we can make a spherical version of the Droste effect. By applying other complex functions, we can "unwrap" the sphere, producing other Escher-like impossible images and video.</span><span style='color:#222222'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='color:#222222'><o:p> </o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Arial",sans-serif;color:#222222'>The code to generate these effects is written in Python, and much of it is available on GitHub.</span><span style='color:#222222'><o:p></o:p></span></p></div></div><div><p class=MsoNormal style='background:white'><b><span style='font-size:10.5pt;font-family:"Helvetica",sans-serif;color:#BF1656'><br><br></span></b><span style='color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><b><span style='font-family:"MyriadPro-Semibold",serif;color:#222222'>______________</span></b><span style='color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='color:black'><o:p> </o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='color:black'><o:p> </o:p></span></p></div><div><p class=MsoNormal style='background:white'><span class=il><span style='font-size:9.5pt;font-family:"Arial",sans-serif;color:#C84677'>Henry</span></span><span style='font-size:9.5pt;font-family:"Arial",sans-serif;color:#C84677'> Segerman is a mathematician, working mostly in three-dimensional geometry and topology, and a mathematical artist, working mostly in 3D printing. He is an assistant professor in the Department of Mathematics at Oklahoma State University, and author of the new book "Visualizing Mathematics with 3D Printing</span><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:#C84677'>”</span><span style='font-size:9.5pt;font-family:"Arial",sans-serif;color:#C84677'>.</span><o:p></o:p></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:9.5pt;font-family:"Arial",sans-serif;color:#C84677'><br><br></span><o:p></o:p></p></div><div><p class=MsoNormal style='background:white'><img width=841 height=252 style='width:8.7604in;height:2.625in' id="_x0030_9DC4957-9EBB-4D9D-83E1-BC43337474EB" src="cid:image002.jpg@01D270B5.FDD3BFB0"><o:p></o:p></p></div></div></div></div></body></html>