### Table 5: Mesh quality improvement for rand1 with both swapping and smoothing An important question in any local smoothing algorithm is the number of smoothing passes required to improve the mesh to the point where further improvement is negligible. Table 6 shows the e ect of various numbers of smoothing passes with the maxmin sine criterion on rand1. Similar results for rand2 with the maxmin angle criterion can be found in Appendix A. In both cases swapping was used before smoothing. In each case, mesh quality improves only negligibly after the fourth or fth smoothing pass. We conclude this subsection with a comparison of the computational e ciency of the various mesh improvement techniques. Table 7 compares timings for mesh improvement using swapping, smoothing, and a combination of the two for rand2 on a 110 MHz SPARC 5. The times for the swapping-only cases indicate that edge swapping, while very bene cial,

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"... In PAGE 15: ...20 0.017 0 0 Table 4: Comparison of the e ectiveness of smoothing for four di erent swapping options (mesh rand1, edge swapping enabled, maxmin sine smoothing) Table5 shows the results for rand1 using the local reconnection procedure given in Recommendation 3 followed by each of the eight smoothing options discussed in the preceding section. The distribution of dihedral angles for each random mesh improves signi cantly regardless of the choice of smoothing criterion.... ..."

Cited by 55

### Table 4 Swap Regressions

"... In PAGE 24: ... 22 4.1 Swap Regression Results Table4 presents our results from estimating interest rate swap regressions. In each specification, in addition to the structural variables we include a linear control for the time period--the month and year (1993 or 1994) in which the firm apos;s balance sheet and derivative position is observed.... ..."

### Table 12: Distributed Algorithms Speedups - No Swapping Uniform Mesh

"... In PAGE 23: ....3.2 Distributed Algorithm Performance - No Swapping In general, the results of the runs agree favorably with the predicted performance on a machine where swapping does not occur. Table12 summarizes the speedups for the uniform and non-uniform meshes. For the uniform mesh, the results are very consistent.... ..."

### Table 1: Number of unique tetrahedra and possible configurations for edge swapping (taken

"... In PAGE 8: ... Fortunately, when a60 is large, the number of unique tetrahedra is much smaller than the number of configurations times the number of tetrahedra since many tetrahedra appear in more than one configuration. This is shown in Table1 (taken from [3]) and means that the cost of performing a local mesh optimization is not quite as high as (6) initially suggests.... ..."

### Table 4. Results of the Rank-Based Proximity Swap Test

"... In PAGE 18: ... Expect P(a) to be a worse approximation of interval length for MAINTAIN than for TAXES. Table4 confirms this. Suppose one desires a target correlation of the swapped to the unswapped value of 0.... In PAGE 20: ... Recall that K is the average percentage change induced by the rank swap. Table4 shows that 0 the theory provides good predictions for the relationship between K and P(a). Again, the 0 distribution of each swapping interval is assumed to be approximately uniform.... In PAGE 20: ... Compare values (within each field) of 0 the quot;PCT OF RECORDS IN SWAPPING INTERVAL quot; column with the quot;AVERAGE ABSOLUTE PCT CHANGE/ OBS. quot;column from Table4 . The columns are almost directly linearly correlated.... In PAGE 20: ... When P(a) doubles, the observed value of K approximately doubles. 0 Also use Table4 to confirm the inverse relationship between the observed correlation, R(a, a apos;) and the corresponding observed value of K . This is a logical consequence of the validity of 0 Theorems 3 and 4.... In PAGE 22: ...fficient code could be written in another environment (Unix, C, etc.). The programming code exists which is easy to use and modify. Does this code execute in a relatively short amount of time? Table4 shows the CPU time required to execute the swap (Module 5).... In PAGE 42: ... When implemented on 1993 Annual Housing Survey data, the above estimate proved amazingly accurate in spite of all the ideal assumptions (uniform distributions, independent variables, and constants instead of expectations). Table4 shows the results.... ..."

### Table 4. Results of the Rank-Based Proximity Swap Test

"... In PAGE 19: ... Expect P(a) to be a worse approximation of interval length for MAINTAIN than for TAXES. Table4 confirms this. Suppose one desires a target correlation of the swapped to the unswapped value of 0.... In PAGE 21: ... Recall that K is the average percentage change induced by the rank swap. Table4 shows that 0 the theory provides good predictions for the relationship between K and P(a). Again, the 0 distribution of each swapping interval is assumed to be approximately uniform.... In PAGE 22: ...of the quot;PCT OF RECORDS IN SWAPPING INTERVAL quot; column with the quot;AVERAGE ABSOLUTE PCT CHANGE/ OBS. quot;column from Table4 . The columns are almost directly linearly correlated.... In PAGE 22: ... When P(a) doubles, the observed value of K approximately doubles. 0 Also use Table4 to confirm the inverse relationship between the observed correlation, R(a, a apos;) and the corresponding observed value of K . This is a logical consequence of the validity of 0 Theorems 3 and 4.... In PAGE 24: ...The programming code exists which is easy to use and modify. Does this code execute in a relatively short amount of time? Table4 shows the CPU time required to execute the swap (Module 5).... In PAGE 45: ... When implemented on 1993 Annual Housing Survey data, the above estimate proved amazingly accurate in spite of all the ideal assumptions (uniform distributions, independent variables, and constants instead of expectations). Table4... ..."

### Table 3: Evaluation of merged x-coordinate assignment and edge crossing reduction approach to x-placement. Name Simple Uniform Linear Programming

"... In PAGE 7: ... In Table 2 for each benchmark we give the time for layer assignment and the number of layers, the time for edge crossing reduction and the number of edge crossings, and the time, width of the layout and the total weighted edge length for x-coordinate assign- ment using the linear programming approach, and the iterative x-coordinate assignment. Table3 evalu- ates merged x-assignment and edge crossing reduction approaches. The first approach does not use vertex swapping while the second does.... ..."

### Table 2 The number of edges removed by the edge-insertion algorithm when it computes MV from either

"... In PAGE 13: ... It is interesting to note that the amountofwork needed to construct MV is far less for points in a square than for points near a circle. Table2 shows the number of edges removed during the construction of MV . While the di erence between the twopoint distributions is striking, the choice of the initial triangulation seems to have far less in uence on the running time of the edge-insertion algorithm.... ..."

### Table 1: Statistics of metamorphosis examples: The number of edge swaps required for connectivity transformation is quite smaller than the edge count of an in-between mesh. The small heights of the dependency graph implies that many edge swaps can be performed simultaneously in connectivity interpolation.

"... In PAGE 5: ... For ex- ample, in [LDSS99], the triangle count of a metamesh is five to ten times larger than the bigger one of input meshes. In contrast, Table1 shows that the vertex count of an in- between mesh is less than the sum of the vertex counts of input meshes. Fig.... In PAGE 5: ...nput meshes. Fig. 6 demonstrates that the proposed tech- nique generates visually pleasing metamorphoses with the smaller numbers of vertices. Table1 summarizes the statistics of the morphing exam- ples. For each example, feature vertices were specified by the user to establish the feature correspondence between input meshes.... In PAGE 5: ... For each example, feature vertices were specified by the user to establish the feature correspondence between input meshes. In Table1 , the size of an in-between mesh does not include the vertices temporarily introduced for geomorphs. In Table 1, we can see that the number of edge swaps re- quired for connectivity transformation is quite smaller than the edge count of an in-between mesh.... In PAGE 5: ... In Table 1, the size of an in-between mesh does not include the vertices temporarily introduced for geomorphs. In Table1 , we can see that the number of edge swaps re- quired for connectivity transformation is quite smaller than the edge count of an in-between mesh. Note that the edge swaps are applied to the converted source and target meshes, Mprime S and Mprime T, which have the same number of edges as an c... In PAGE 6: ... When we compare the results with the re- lated work [LL04], we can see that our approach generates smaller number of edge swaps. In Table1 of this paper, the number of edge swaps is about a half of the edge count of the bigger input mesh. In Table 1 of [LL04], the edge swap count is similar to the bigger edge count.... In PAGE 6: ... In Table 1 of this paper, the number of edge swaps is about a half of the edge count of the bigger input mesh. In Table1 of [LL04], the edge swap count is similar to the bigger edge count. Table 1 also shows the height of a dependency graph con- structed for connectivity interpolation described in Sec.... In PAGE 6: ... In Table 1 of [LL04], the edge swap count is similar to the bigger edge count. Table1 also shows the height of a dependency graph con- structed for connectivity interpolation described in Sec. 4.... ..."

### Table 4: Summary of the results obtained for the first test problem without edge/face swapping (the global energy minimum is BHBCBMBCBCBCBC).

"... In PAGE 13: ... This may be demonstrated, for example, by contrasting the results of Table 2 with those obtained for the same test problem but without the connectivity optimization step included in Figure 1. Such modified results are presented in Table4 and clearly demonstrate the limitations of the adaptive algorithm when edge/face swapping is neglected.... ..."