Graphics using Implicit Surfaces with Interval Arithmetic based Recursive Voxelization

N. Stolte (Singapore)


Voxel, Voxelization, 3D Visualization, Interval Arithmetic, Implicit Surfaces


Interval arithmetic is a powerful, convenient and efficient tool to solve graphics problems. However, the number of research papers concerning this subject has been consid erably small even though the advantages of interval arith metic overweigh their disadvantages. This work shows a collection of techniques successfully implemented using intervals that deal with graphics based on recursive voxeli sation. Voxelization is seen here as a generic tool to harness intervals which can be extended to other applications. Voxelization is the transformation of a continuous sur face into voxels. Intervals allow the voxelization to be done recursively, since interval arithmetic guarantees that the zero of an implicit function, which describes the sur face to be voxelized, cannot occur into a three-dimensional region. This allows the elimination of the whole region from subsequent analysis allowing an efficient time recur sive subdivision. Even though voxelization is used here for high quality interactive display of implicit surfaces, it could also be used in other rendering algorithms (such as ray tracing), in trans formation of implicit surfaces to polygons (using marching cubes algorithm), or for other more generic tasks such as calculation the volume inside an implicit surface.

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