"... In PAGE 29: ...eshes using the technique described in Section 5.1. The octree examples that were shown for comparison of the octree and kd-tree based hierarchies have been constructed using the same data structure but with a simple octree subdivision rule. Table1 shows the times required to construct the adaptive grids and to extract the isosurfaces from those grids using our adaptive iso- surface extraction algorithm described in Section 3. In addition, it contains the number of polygons of the used input meshes, the maximum depth of the generated kd-trees, and the number of triangles generated by the extraction algorithm.... ..."

"... In PAGE 7: ... Our algorithm culls away invisible isosurfaces effectively with the help of nVidia occlusion extensions. Table1 com- pares the size of the visible isosurfaces extracted by our al- gorithm with the size of the whole isosurfaces for the UNC brain dataset. Three test iso-values were used.... ..."

"... In PAGE 7: ... Our algorithm culls away invisible isosurfaces effectively with the help of nVidia occlusion extensions. Table1 com- pares the size of the visible isosurfaces extracted by our al- gorithm with the size of the whole isosurfaces for the UNC brain dataset. Three test iso-values were used.... ..."

"... In PAGE 12: ...eshes using the technique described in section 5.1. The octree examples that were shown for comparison of the oc- tree and kd-tree based hierarchies have been constructed us- ing the same data structure but with a simple octree subdi- vision rule. Table1 shows the times required to construct the adaptive grids and to extract the isosurfaces from those grids using our adaptive isosurface extraction algorithm de- scribed in section 3. In addition, it contains the number of polygons of the used input meshes, the maximum depth of the generated kd-trees, and the number of triangles gener- ated by the extraction algorithm.... ..."

"... In PAGE 6: ... However, even with a high resolution of lattice subdivision we still had about 50% sav- ing in storage; for the smaller resolutions of lattice subdivision, we achieved about 75% ? 90% space savings. Table6 shows the performance of isosurface extraction using the temporal hierarchical index tree for the F-18 data set. We also show the performance of the regular Marching Cubes algorithm (denoted as MCs), the Interval Tree method (denoted as Int.... ..."

"... In PAGE 6: ... Extraction time, generated triangles and image quality will be of interest. Considering the triangle generation speed with respect to the number of tetrahedra shown in Table2 , we see that the extraction time is nearly constant. An optimal algorithm would just inspect those tetrahedra, that contribute to the iso-surface.... In PAGE 6: ...7, Threshold = 0:2 exhibit constant behavior, but the decay is quite low which means, that the triangulation of the volume implicitly results in an effective processing of the generated tetrahedra. As we can see in Table2 the time needed to generate the tri- angles is decreasing significantly compared to the standard march- ing cubes algorithm. Looking especially at Head 1 we see, that the number of triangles is about a half and the processing time is about 6 times faster.... ..."

"... In PAGE 6: ... However, even with a high resolution of lattice subdivision we still had about 50#25 sav- ing in storage; for the smaller resolutions of lattice subdivision, we achieved about 75#25 , 90#25 space savings. Table6 shows the performance of isosurface extraction using the temporal hierarchical index tree for the F-18 data set. We also show the performance of the regular Marching Cubes algorithm (denoted as MCs), the Interval Tree method (denoted as Int.... ..."

"... In PAGE 9: ...(a) Level 6, 58,491 vertices (b) Level 7, 80,111 vertices (c) Level 8, 89,505 vertices Figure 2: Mesh of an iso-surface from the spherical harmonic data set at different levels of resolution in the images appearing as shadows, because the normals used for shading do not correspond to the normals of the tri- angles at coarser levels. In Table3 we give timing results for the iso-surface ex- traction and for the iso-surface refinement algorithm for the spherical harmonic data set. Together with the time informa- tion we include the number of triangles in the iso-surface at each level of resolution.... ..."