There are three ways of modeling objects using current modeling techniques: surface-base modeling, voxel-based modeling and image-base modeling. Traditional graphics use surfaces to model objects. To be consistent with our terrain model and to incorporate amorphous phenomena, we choose the voxel-based modeling to represent the objects put on top of the terrain: vehicles, buildings, planes, and such. This provides a seamless integration of our voxel-based terrain model, and other objects together.
Volume graphics is an emerging subfield of computer graphics. It consists synthesis, modeling, manipulation and rendering of volumetric geometric objects. Volumetric geometric objects are stored in a volume buffer. There are several ways to get volumetric data sets. In medical imaging, CT and MRI provide medical volume datasets of human bodies. Here we focus on sampled and computed data, where volume data are converted from surface representation to volume representation using a method called.
The fundamental idea of voxelization is to model and visualize according to scale.
Voxelization has been implemented mainly by software. Recently, several new approaches
have been proposed for voxelization of 3D synthetic objects. Some algorithms making use of
current graphics hardware have also been proposed, such as the polygon-based geometry
engine and frame buffer operations. We will discuss two closely related voxelization
techniques---binary voxelization and filtered voxelization. Then we give a survey of
algorithms for voxelizing various geometric objects.
Different approaches have been proposed by researchers. Kaufman et. al use a straight forward super-sampling. It is based on a scan-plane method. The scan plane is translated to sub-voxel positions and intersected with the grid. The values of each pixel in the scan-plane are then accumulated to obtain the anti-aliased scan-plane. An alternative method is to translate the entire grid to sub-voxel positions and then do the scan-plane intersection. Multiple passes for the entire gird is done for the required number of sub-voxel sample points.
Distance field techniques are another way of voxelization. All voxels of a scene are assigned their distance to the nearest surface point of the object. A certain value, typically 0, is assigned to the point on the surface. The distances are in general unbounded and the distance field of an object embodies the whole scene, which means that the traditional notion of spatially localized objects is violated. Object interior and background are usually distinguished by a different sign of the distance.
Some other researchers choose to use low-pass sampling filters. Wang and Kaufmandescribe a volume sampling technique. His method estimates the density contribution of geometric objects to the voxels. The density of a voxel is attenuated by Bartlett function---a super cone filter function. This function weights the density of a voxel linearly by the distance between the center of the voxel and the object surface in three dimension. To speed up computation, pre-computed lookup tables are made for a set of predefined geometric primitives. The index of the look up table is the distance of a voxel to the primitive surface to be voxelized.
Milos Sramek et. al. show that voxelization filters should be associated with visualization rendering filters to achieve best voxelization results. As we know, reconstruction of a continuous function and its derivative from sampled data is a complex problem, yet important for rendering. If center-difference method is used for gradient estimation and trilinear interpolation method is used for iso-surface rendering, the oriented box filter, which is a 1D box filter along the normal of object surface should be used for voxelization. Another filter he uses is oriented gaussian filter, which works well with tricubic interpolation and Gabor filter as reconstruction filters. His experiments show very good normal estimation of both filters on specific filter prameters with the corresponding reconstruction filters. Later, he further emphasizes that the voxelization model with a Gaussian surface density profile combined with tricubic interpolation and Gabor derivative reconstruction outperforms his previously published technique with a linear density profile.
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