GPU-Accelerated Post-Processing and Animated Volume Rendering of Isogeometric Analysis Results

Abstract

Introduction: Isogeometric analysis (IGA) [1] has enabled better CAD integration by using the same spline representations (Non-Uniform Rational B-Splines, NURBS) for modeling and analysis. Traditionally, the nite element analysis results are visualized by creating a texture map of the property of interest and superimposing them over the boundary representation (B-rep) model or the mesh. This technique cannot be directly used to render internal quantities of interest without computationally intensive sectioning and remapping of the textures, which does not allow for interactive interrogation of the analysis results. Ray-casting is usually used to render volume data and is computationally more intensive than rasterization. Performing ray casting with volumetric splines used in IGA is still computationally intensive to perform interactively. In this work, we rst voxelize the isogeometric mesh using a GPU-accelerated ray intersection algorithm for cubic-Bézier volumes to convert volumetric splines to time-varying voxelized data structures. We then use GPU ray casting to volume-render the time frames of the simulation. This approach leads to interactive volume rendering of the results of dynamic IGA simulations, allowing for real-time manipulation in the 3D environment. One of the early algorithms to compute ray intersection with surfaces can be found in [2], where they reduce the ray-surface intersection to computing roots of a polynomial. [4] presented the Newton iteration technique that uses subdivisions of a surface to compute all the roots for the ray-surface combinations. [3] developed a method to decompose the NURBS surfaces into Bézier patches and then perform the triangulation of the surface for rendering. However, most of these previous approaches were not fast enough for animated volume rendering or mainly rendered the analysis results on surfaces as textures. To voxelize the IGA models, we rst decompose the NURBS elements into Bézier elements by performing Bézier extraction. This is required to deal with the non-uniformity of the knot vector in a general NURBS element. We then perform a modi ed ray intersection test with the six Bézier surfaces of the element using a grid of rays. We then generate a variable density voxel model representing the analysis results using the intersection data, which is repeated for the di erent time frames of the analysis. The