OpenGL 4 with GLSL shading language have become a standard on many common architectures (Mac, Linux, Windows, , ...) from a couple of years. In the mean time, high-order methods (for flow solution and for meshing algorithm) are emerging. Many of them have proven their abilities to provide accurate results on complex (3D) geometries. However, the assessment of a particular meshing algorithm or of a high-order numerical scheme strongly relies on the capacity to validate and inspect visually the current mesh/solution at hand. However, having at the same time, an accurate and interactive visualization process for high-order mesh/solution is still a challenge as complex process are usually involved in the graphic pipeline: non linear root finding, ray tracing, GPU programming,. .. . In this paper, we discuss the current status and issues of using the (raw) OpenGL 4 pipeline to render curved high-order entities, and almost pixel-exact solutions. We illustrate this process on meshes and solutions issued from high-order curved from CAD and with high-order interpolated solutions.
With the increasing use of high-order methods and high-order meshes, scientific visualization software need to adapt themselves to reliably render the associated meshes and numerical solutions. In this paper, a novel approach, based on OpenGL 4 framework, enables a GPU-based rendering of high-order meshes as well as an almost pixel-exact rendering of high-order solutions. Several aspects of the OpenGL Shading Language and in particular the use of dedicated shaders (GPU programs) allows to answer this visualization challenge. Fragment shaders are used to compute the exact solution for each pixel, made possible by the transfer of degrees of freedom and shape functions to the GPU with textures. Tessellation shaders, combined with geometric error estimates, allow us to render high-order curved meshes by providing an adaptive subdivision of elements on the GPU directly. A convenient way to compute bounds for high-order solutions is described. The interest of using Bézier basis instead of Lagrange functions lies in the existence of fast and robust evaluation of polynomial functions with de Casteljau algorithm. A technique to plot highly nonlinear isolines and wire frames with a desired thickness is derived. It is based on a finite difference scheme performed on GPU. In comparison with standard techniques, we remove the use of any linear interpolation step and the need to generate a priori a fixed subdivided mesh. This reduces the memory footprint, improves the accuracy and the speed of the rendering. Finally, the method is illustrated with various 3D examples.
To cite this version:Rémi Feuillet, Adrien Loseille, David Marcum, Frédéric Alauzet. Connectivity-change moving mesh methods for high-order meshes: Toward closed advancing-layer high-order boundary layer mesh generation.Curved mesh generation starting from a P 1 mesh and closed advancing-layer boundary layer mesh generation both rely on mesh deformation and mesh optimization techniques. The approach presented in this work is to generalize connectivity-change moving mesh methods to high-order meshes. This approach is based on a high-order linear elasticity solver for the mesh deformation and on high-order mesh optimization operators such as mesh smoothing and generalized swapping. Thanks to this method, P k meshes are generated from P 1 meshes and closed advancing-layer boundary layer mesh generation will soon be possible.
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