### Table 1.Correspondence between STC and mesh entities.

"... In PAGE 1: ... INTRODUCTION The whisker weaving algorithm produces the Spatial Twist Continuum data for an all- hexahedral mesh [1] [2]. The whisker weaving algorithm constructs and represents STC entities in its datastructure that are the dual of all-hex mesh entities; these entities are shown in Table1 . This information represents connectivity of an all-hex mesh only, and contains * This work was supported by the U.... ..."

### Table 1 Input to DRAMA: mesh speci ed by element number, element connectivity and element type information. The notation nk (i;j) refers to the kth node of the element with the index pair (i; j)=(local element index, processor number). ^ N(ue) is the number of nodes for an element of type ue and Nj is the number of elements owned by processor j. The variable nk (i;j) itself is the index pair (local node index, processor number).

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"... In PAGE 6: ... For each element, the element type, which determines the associated costs, is also given. Table1... ..."

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### Table 3: Input to DRAMA: mesh speci ed by element number, element connectivity and element type information. The notation nk (i;j) refers to the kth node of the element with the index pair (local element index, processor number)=(i; j). ^ N(ue) is the number of nodes for an element of type ue and N l j is the number of elements owned by processor j. nk (i;j) itself is the index pair (local node index, processor number).

in Dynamic Re-Allocation of Meshes for parallel Finite Element Applications ESPRIT LTR Project 24953

### Table 3: Input to DRAMA: mesh speci ed by element number, element connectivity and element type information. The notation nk (i;j) refers to the kth node of the element with the index pair (local element index, processor number)=(i; j). ^ N(ue) is the number of nodes for an element of type ue and N l j is the number of elements owned by processor j. nk (i;j) itself is the index pair (local node index, processor number).

### Table 2: Comparison of compressed le sizes in bytes. The second column is the list of original le sizes; The third column lists the GZIP results; the fourth column gives the costs of connectivity coding; the last two columns present the costs of geometry coding with two di erent quantization bits per vertex (bpv) where the numbers in parenthesis are geometry error. Besides the ability of handling any kind of triangular meshes, our layering compression scheme also cherishes a blocking feature that makes it particularly suitable for both incremental transmission/display and error resilient streaming [1]. 7 Conclusion We have described a space e cient encoding for both a lossless and an error-bounded lossy compression scheme for triangular meshes. The compression is achieved by capturing the redundant information in both the topology (connectivity) and geometry, and possibly property attributes. Error-bounded lossy geometry 8

"... In PAGE 7: ... The geometric error bewteen A and B is de ned as E(A; B) = 1 n Pn?1 i=0 min0 j lt;n jjPi ? Qjjj2 where Pi(0 i lt; n) and Qj(0 j lt; n) are the vertex positions of A and B respectively, and A is normalized such that its bounding box diameter is 100. This geometric error is used for results in Table2 where our results are compared with... ..."

### 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 2: Connection Information

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"... In PAGE 4: ... With this connection in- formation, we exclude impossible connections of Korean characters and English phoneme se- quences. We can get the following connection information from #5Cdressing quot; example#28 Table2 #29. Table 2: Connection Information... ..."

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### Table 1. The connectivity relations of a k-simplex mesh.

"... In PAGE 6: ... The constant connectivity between vertices im- plies a simple relation between the number of ver- tices and the number of edges. Table1 sum- marizes the connectivity between vertices, edges, faces, and cells of a k-simplex mesh. If a k-simplex mesh is (k + 1)-connected, all (k + 1)-connected meshes are not necessary simplex meshes.... ..."

### Table 1: Results for mapping FEM graphs to mesh-connected systems

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"... In PAGE 5: ...Table 1: Results for mapping FEM graphs to mesh-connected systems Table1 compares some results of mapping a FEM- graph to different mesh-connected machines by Simulated Annealing and the Kohonen-process. We do not claim that the results achieved by SA are the best one can obtain using this method, but we actually put some effort into tuning the parameters of the algorithm.... ..."

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