No abstract

In this article, we address the problem of computing, storing and sorting, at an interactive rate, all of the intersections between millions of triangles (a 3D scene) and millions of rays starting from the same point. In this paper we focus on the fast GPU construction of a grid in projective space referencing the triangles of a 3D scene. We introduce a fast GPU algorithm used to build a grid of the rays constituting the scene, in the same projective space. This ray-based grid is computed during the initialization of the scene, which allows us to achieve higher performance, and to construct the triangle-based grid in distinct passes for very large scenes, without having to manage memory transfers between CPU and GPU. This algorithm works the same way for both static and dynamic scenes, allowing us to achieve interactive processing of complex and dynamic scenes. These optimizations are used to speed up the geometrical computations used in the nuclear field to evaluate the impact of radiative sources on an operator. These geometrical computations are similar to those of traditional ray tracing, except that only highly coherent rays are thrown in our application, and that we are looking for all intersections along each ray.

Finding efficient and physically based methods to interactively simulate deformable objects is a challenging issue. The most promising methods addressing this issue are based on finite elements and multigrid solvers. However, these multigrid methods still suffer, when used to simulate large deformations, from two pitfalls, depending on the kind of grids hierarchy used. If embedded grids are used, approximating complex geometries becomes difficult, whereas when unstructured grids hierarchy is used, solving speed-up is reduced by the necessity to update coarser levels stiffness matrices. We propose a framework that combines embedded grids solving with fast remeshing. We introduce a new hierarchical mesh generator which can build a hierarchy of topologically embedded grids approximating a complex geometry. We also show how to take advantage of the knowledge of the stiffness matrix sparsity pattern to efficiently update coarse matrices. These methods are tested on interactive simulation of deformable solids undergoing large deformations.