## Publica

Hier finden Sie wissenschaftliche Publikationen aus den Fraunhofer-Instituten. # Efficient Streaming Sample-based Surface Triangulation of Voxel Data

Effiziente Sample-basierte Triangulation von Oberflächen in gestreamten Voxeldaten

**Abstract**

Voxel-based discrete representations of 3-dimensional data are widely used in several fields of graphical computing, for instance in the 3D printing driver Cuttlefish. For commonly used techniques, such as the marching cubes algorithm, the creation of a polygonal/polyhedral mesh representation of the used voxel data at high resolutions can become time-consuming and result in meshes with excessive numbers of vertices, which nonetheless introduce "staircase" artifacts relative to the desired geometry. It is then often necessary to use additional post-processing steps, such as mesh decimation, at the expense of additional computational effort and possible inaccuracies regarding the representation of the original shape. The goal of this thesis is to simultaneously address all three of these issues, proposing an efficient technique to generate low-polygon meshes, which accurately represent the object’s shape. The intended technique is based on sampling the surface at regions of high curvature using, for example, an importance sampling technique, although different techniques will be explored. A comparison will be made between per-slice and per-chunk sampling (i.e. consider only a single slice or a whole chunk of slices when deciding where to place samples). The samples are to be mapped to a parametric, planar space, allowing to efficiently triangulate the sampled points. The necessity of additional post-processing steps in the parametric or reprojected object space will be assessed. The developed techniques will be implemented, integrated into Cuttlefish and evaluated based on comparisons to standard techniques such as marching cubes or Marching Tetrahedra using the above three measures: efficiency (time and memory), number of polygons in the output, and accuracy. Defining a measure of the accuracy of the output and computing it is a further aspect of the thesis, where at least the Hausdorff distance and collinearity of the surface normals will be measured in order to quantify the mesh quality.