### Table 2.1 summarizes the main features of out-of-core simplification techniques. For each method, we list: the type of input (Dataset); the type of space partition adopted (Partitioning); the type of approach (Simplification); the possibility to build a multi-resolution model based on the specific simplification technique (Multi-res); and the space requirements in main memory (Space). The algorithms by Hoppe [20], Prince [37] and Magillo and Bertocci [33] are designed for either regular or irreg- ular terrain data, while all the other technique can handle arbitrary triangle meshes describing the boundary of 3D objects. When applied to terrain simplification, al- gorithms based on space partitioning should be modified by replacing the octree which partitions 3D space with a simpler quadtree partition of the 2D domain of the TIN. Note that only methods based on space partitioning are suitable to build multi-resolution models.

### Table 1: Triangle Counts

"... In PAGE 6: ... We tested bending along the y-axis of the object and measured the amount of subdivision that occurred. The results are summarized in Table1 and are shown in Plate 1. The first two cases show the greatest amount of subdivision since the original mesh is composed of flat Triangle Count... ..."

### Table 1: The characteristics of the eight triangle meshes used in this study.

1998

"... In PAGE 5: ... These datasets vary widely in the numbers of vertices and triangles. Table1 shows the characteristics of the datasets. Our preprocessing algorithm performs breadth rst traversal of the triangle mesh to nd out the traversal order and the current and next frontier for each level.... ..."

Cited by 15

### Table 1: The characteristics of the eight triangle meshes used in this study.

1998

"... In PAGE 7: ... These datasets vary widely in the numbers of vertices and triangles. Table1 shows the characteristics of the datasets. Our preprocessing algorithm performs breadth rst traversal of the triangle mesh to nd out the traversal order and the current and next frontier for each level.... ..."

Cited by 15

### Table 3: List of triangles for the sample mesh shown in Figure 3

2001

"... In PAGE 9: ...late Voronoi polygon geometry quickly in response to node addition, deletion or movement. The list of triangles for a simple example mesh is given in Table3 . Depending on the application, additional geometric data for a triangle data class might include projected area, gradient, and gra- dient vector (cf.... ..."

Cited by 8

### Table 1: Number of vertices and triangles for our example meshes.

"... In PAGE 5: ... None of the source and target meshes in our examples share the same number of vertices, triangles, or connectivity. Table1 lists this geometric information about each model, and Table 2 gives timing results for each example. Our method is extremely fast.... ..."

### Table 1: The characteristics of the triangle mesh models used in our study.

"... In PAGE 6: ... 5 Performance Evaluation Based on a prototype implementation of the proposed compression-domain triangle mesh editor, we compare the peak memory requirement and edit performance of the CDE editor and a traditional mesh editor. The 3D models used in this study and their characteristics are shown in Table1 . All measurements are taken on a Pentium II 300-MHz machine with 320 MBytes of memory running Linux.... ..."

### Table 7: Results for adapted meshes with less triangles at the poles.

"... In PAGE 9: ... The only difference is that at the poles the number of triangles is reduced, see Figure 2b. The corresponding results are given in Table7 . Again, the number of iterations decreases and the errors increase compared to the reference values of Table 1.... ..."

### Table 1: Pseudo-code for recursive mesh refinement and triangle stripping.

"... In PAGE 6: ....1.3 Run-Time Refinement With all the necessary pieces in hand, we now summarize the al- gorithm for top-down refinement and on-the-fly triangle strip con- struction. Pseudo-code for these steps is listed in Table1 . The re- finement procedure builds a triangle strip V =(v0;v1;v2;:::;vn), that is represented as sequence of vertex indices.... In PAGE 7: ... construction is the same as in [17]. A vertex v is appended to the strip using the procedure tstrip-append ( Table1 ). Line 5 is used to turn corners in the triangulation by effectively swapping the two most recent vertices, which results in a degenerate triangle that is discarded by the graphics system [9].... ..."