The quality of images produced by Discrete Ray‐Tracing voxel spaces is highly dependent on 3d grid resolution. The huge amount of memory needed to store such grids often discards discrete Ray‐Tracing as a practical visualization algorithm. The use of an octree can drastically change this when most of space is empty, as such is the case in most scenes. Although the memory problem can be bypassed using the octree, the performance problem still remains. A known fact is that the performance of discrete traversal is optimal for quite low resolutions. This problem can be easily solved by dividing the task in two steps, working in two low resolutions instead of just one high resolution, thus taking advantage of optimal times in both steps. This is possible thanks to the octree property of representing the same scene in several different resolutions. This article presents a two step Discrete Ray‐Tracing method using an octree and shows, by comparing it with the single step version, that a substantial gain in performance is achieved.

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Abstract.A new approach to ray tracing implicit surfaces based on recursive space subdivision is presented in this paper. Interval arithmetic, already used to calculate intersections in ray tracing and ray casting (numerically or subdividing 1D or 2D spaces), is now used here to implement a ray tracing based on reliable rays traversals into a potentially infinite octree-like subdivided space, eliminating explicit intersections. Novel, robust and efficient algorithms for ray voxelization and BSP octant ordering are used to recursively traverse rays through the space. Implicit surfaces are robustly voxelized and hierarchically stored into an octree to a certain given level. During rendering, the subdivision based voxelization of surfaces and rays continues further down until a resolution near the discrete domain of the floating point numbers is acquired. To guarantee robustness of the ray voxelization, interval arithmetic with calculations performed under appropriate rounding modes in Pentium-4 x87 and SSE2 FPUs respectively is applied. The major advantage is that the traversal algorithm is guaranteed to find reliable intersections between the rays and the scene without any explicit intersection calculation, solving a known precision problem of the ray traversal in a previous approach, used here for comparison. The precision of the traversal can be arbitrarily increased within the limitation of the floating point representation.

Polygon temperature computation in 3D virtual scenes is fundamental for JR image simulation. This article describes in detail the temperature calculation software and its current extensions, briefly presented in [1J. This software, called MURET, is used by the simulation workshop CHORALE of the French DGA. MURET is a one-dimensional thermal software, which accurately takes into account the material thermal attributes of the three-dimensional scene and the variation of the environment characteristics (atmosphere) as a function of the time. Concerning the environment, absorbed incident fluxes are computed wavelength by wavelength, for each half an hour, during 24 hours before the time of the simulation. For each polygon, incident fluxes are composed of : direct solar fluxes, sky illumination (including diffuse solar fluxes). Concerning the materials, classical thermal attributes are associated to several layers, such as conductivity, absorption, spectral emissivity, density, specific heat, thickness and convection coefficients are taken into account. In the future, MURET will be able to simulate permeable natural materials (water influence) and vegetation natural materials (woods). This model of thermal attributes induces a very accurate polygon temperature computation for the complex 3D databases often found in CHORALE simulations. The kernel of MURET consists of an efficient ray tracer allowing to compute the history (over 24 hours) of the shadowed parts of the 3D scene and a library, responsible for the thermal computations. The great originality concerns the way the heating fluxes are computed. Using ray tracing, the flux received in each 3D point of the scene accurately takes into account the masking (hidden surfaces) between objects. By the way, this library supplies other thermal modules such as a thermal shadow computation tool.