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I3D 2016, Pascal Lecocq, Arthur Dufay, Gael Sourimant, Jean-Eudes Marvie Detailed version of SIGGRAPH 2015 talk. We introduce analytic approximations for accurate real-time ren- dering of specular surfaces lit by area light sources. Our solution leverages the Irradiance Tensors developed by Arvo for the ren- dering of Phong surfaces lit by a polygonal light source. Using a reformulation of the 1D boundary edge integral, we develop a general framework for approximating and evaluating the integral in constant time using simple peak shape functions. To overcome the Phong restriction, we propose a low cost edge splitting strategy that accounts for the spherical warp introduced by the half vector parametrization. Thanks to this novel extension, we accurately ap- proximate common microfacet BRDFs, providing the first practi- cal method producing specular stretches that closely match ground truth image references in real-time. Finally, using the same approxi- mation framework, we introduce support for spherical and disc area light sources, based on an original polygon spinning method sup- porting non-uniform scaling operations and horizon clipping. Im- plemented on a GPU, our method achieves real-time performances without any assumption on area light shape nor surface roughness, with a quality close to the ground truth.