Skip to Main content Skip to Navigation
Journal articles

On pixel-exact rendering for high-order mesh and solution

Abstract : 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [54 references]  Display  Hide  Download
Contributor : Rémi Feuillet <>
Submitted on : Sunday, September 27, 2020 - 6:17:45 PM
Last modification on : Sunday, October 4, 2020 - 3:23:32 AM


Files produced by the author(s)




Rémi Feuillet, Matthieu Maunoury, Adrien Loseille. On pixel-exact rendering for high-order mesh and solution. Journal of Computational Physics, Elsevier, 2020, pp.109860. ⟨10.1016/⟩. ⟨hal-02950321⟩



Record views


Files downloads