Direct Isosurface Ray Casting of NURBS-Based Isogeometric Analysis

In NURBS-based isogeometric analysis, the basis functions of a 3D model's geometric description also form the basis for the solution space of variational formulations of partial differential equations. In order to visualize the results of a NURBS-based isogeometric analysis, we developed a novel GPU-based multi-pass isosurface visualization technique which performs directly on an equivalent rational Bézier representation without the need for discretization or approximation. Our approach utilizes rasterization to generate a list of intervals along the ray that each potentially contain boundary or isosurface intersections. Depth-sorting this list for each ray allows us to proceed in front-to-back order and enables early ray termination. We detect multiple intersections of a ray with the higher-order surface of the model using a sampling-based root-isolation method. The model's surfaces and the isosurfaces always appear smooth, independent of the zoom level due to our pixel-precise processing scheme. Our adaptive sampling strategy minimizes costs for point evaluations and intersection computations. The implementation shows that the proposed approach interactively visualizes volume meshes containing hundreds of thousands of Bézier elements on current graphics hardware. A comparison to a GPU-based ray casting implementation using spatial data structures indicates that our approach generally performs significantly faster while being more accurate.