Lehtinen, Jaakko, Zwicker, Matthias, Kontkanen, Janne, Turquin, Emmanuel, Sillion, François X., Aila, Timo, Computer Science and Artificial Intelligence Laboratory [Cambridge] ( CSAIL ), Massachusetts Institute of Technology ( MIT ), Department of Computer Science and Engineering [San Diego] ( CSE-UCSD ), University of California [San Diego] ( UC San Diego ), TKK Helsinki University of Technology, Helsinki University of Technology ( TKK ) -TKK, Acquisition, representation and transformations for image synthesis ( ARTIS ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Laboratoire Jean Kuntzmann ( LJK ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Institut National Polytechnique de Grenoble ( INPG ), NVIDIA ( NVIDIA ), NVIDIA Corp., Publications in Telecommunications Software and Multimedia, Helsinki University of Technology, Computer Science and Artificial Intelligence Laboratory [Cambridge] (CSAIL), Massachusetts Institute of Technology (MIT), Department of Computer Science and Engineering [Univ California San Diego] (CSE - UC San Diego), University of California [San Diego] (UC San Diego), University of California (UC)-University of California (UC), TKK Helsinki University of Technology (TKK), Acquisition, representation and transformations for image synthesis (ARTIS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), NVIDIA (NVIDIA), Department of Computer Science and Engineering [San Diego] (CSE-UCSD), and University of California-University of California
We introduce a meshless finite element framework for solving light transport problems. Traditional finite element methods use basis functions parameterized directly on the mesh surface. The creation of suitable parameterizations or clusterings requires pre-processing that is difficult, error-prone, and sensitive to the quality of input geometry. The resulting light transport solutions still tend to exhibit discontinuities, necessitating heuristic post-processing before visualization. Due to these problems finite element methods are rarely used in production. The core idea of our approach is to use finite element basis functions induced by hierarchical scattered data approximation techniques. This leads to a mathematically rigorous recipe for meshless finite element illumination computations. As a main advantage, our approach decouples the function spaces used for solving the transport equations from the representation of the scene geometry. The resulting solutions are accurate, exhibit no spurious discontinuities, and can be visualized directly without post-processing, while parameterization, meshing and clustering problems are avoided. The resulting methods are furthermore easy to implement. We demonstrate the power of our framework by describing implementations of hierarchical radiosity, glossy precomputed radiance transfer from distant illumination, and diffuse indirect precomputed transport from local light sources. Moreover, we describe how to directly visualize the solutions on graphics hardware.