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.

随着高阶方法和高阶网格的使用不断增加，科学的可视化软件需要进行自我调整以可靠地呈现关联的网格和数值解。在本文中，一种基于OpenGL 4框架的新颖方法可以实现基于GPU的高阶网格渲染以及几乎像素精确的高阶解决方案渲染。OpenGL着色语言的多个方面，尤其是专用着色器（GPU程序）的使用，可以应对这一可视化挑战。片段着色器用于计算每个像素的精确解，这是通过将自由度和形状函数转移到带有纹理的GPU来实现的。镶嵌着色器，结合几何误差估计，通过直接在GPU上提供元素的自适应细分，允许我们渲染高阶曲面网格。描述了一种计算高阶解边界的便捷方法。使用Bézier基而不是Lagrange函数的兴趣在于使用de Casteljau算法对多项式函数进行快速而可靠的评估。得出了一种绘制具有所需厚度的高度非线性等值线和线框的技术。它基于在GPU上执行的有限差分方案。与标准技术相比，我们无需使用任何线性插值步骤，也无需生成 使用Bézier基而不是Lagrange函数的兴趣在于使用de Casteljau算法对多项式函数进行快速而可靠的评估。得出了一种绘制具有所需厚度的高度非线性等值线和线框的技术。它基于在GPU上执行的有限差分方案。与标准技术相比，我们无需使用任何线性插值步骤，也无需生成 使用Bézier基而不是Lagrange函数的兴趣在于使用de Casteljau算法对多项式函数进行快速而可靠的评估。得出了一种绘制具有所需厚度的高度非线性等值线和线框的技术。它基于在GPU上执行的有限差分方案。与标准技术相比，我们无需使用任何线性插值步骤，也无需生成先验固定细分网格。这样可以减少内存占用，提高渲染的准确性和速度。最后，用各种3D示例说明了该方法。