### Table 1. P-field construction time for Puget Sound Terrain range image. The resolu- tion is represented by the size of the evenly- distributed sample rays and the maximum distance between nearby sample rays on the far plane (shown in parenthesis).

"... In PAGE 5: ...64. Table1 shows the p-field construction times for the range image with 265, 386 sample points at different reso- lutions. Except for the two lowest resolutions, the construc- tion times also include about 3.... ..."

### Table 10 Checking the density of the seeds: on a ray of 8-centres.

### Table 1: Step size statistics for rays that hit the iso-

"... In PAGE 6: ...igure 5: The hierarchical Lipschitz-based ray traversal algorithm. Figures 1 through 4 illustrate cases A-D. Figure 6: Rendered image of the lobster 5.2 Analysis Table1 lists the average distance between samples for both hit and miss rays. Even for highly detailed volumes such as the lobster, the average step size between samples is well over cell size.... In PAGE 6: ...Table 1: Step size statistics for rays that hit the iso- surface and rays that miss the iso-surface. tween samples for the images of Table1 . Because of the clipping to octree-cell boundaries, the step sizes tend to be at powers of two.... In PAGE 6: ... 5.3 Discussion The step sizes in Table1 show the average Lipschitz- octree algorithm step sizes beat the unit step sizes of ray marching. Moreover, the Lipschitz-octree structure combines the bene#0Cts of both the min-max octree and the distance transform, with the expectation that it can outperform both methods individually.... ..."

### Table 1. Random sphere reconstruction error metrics. A relatively high resolution Marching Cubes reconstruction is compared to our algorithm. The number of cross sections and the resolution of the distance field reconstruction were varied for our algorithm. The RMS error of the surfaces reconstructed from our algorithm approaches that of Marching Cubes applied directly to the implicit function.

"... In PAGE 8: ... We compute the RMS error of a reconstructed surface from the implicit function value at each vertex of the surface mesh. Table1 presents the value of the error metric for the reference surface and for several surfaces computed by our method. As the table and Figure 7 show, our reconstructions improve as either the number of cross sections increases or the distance field resolution increases.... ..."

### Table 1: The effect of grid resolutions on the accuracy and performance (in seconds) of a distance field amp; partial update computations

2001

"... In PAGE 12: ... In fact, fast marching level-set methods runs in a0a2a1 a139 a3 a130 a7 worst-case time using the narrow band approach [19], given the grid resolution of a3 x a3 x a3 and a139 is the number of cells in the narrow band. Table1 gives an example of the computation time using different grid resolutions a3 x a3 x a3 on a sphere of a67 a30a165a30a52a30 triangles with the correct distance value of 1.0 at the center of the sphere for the entire distance field vs.... In PAGE 13: ... 6.3 Partial Update of Internal Distance Fields Table1 also illustrates the performance gain in computing partial updates of the dis- tance field over the recalculation of the entire distance field. The last two columns of Table 1 give the computation time (in seconds) required for computing the entire distance field of the sphere vs.... In PAGE 13: ...3 Partial Update of Internal Distance Fields Table 1 also illustrates the performance gain in computing partial updates of the dis- tance field over the recalculation of the entire distance field. The last two columns of Table1 give the computation time (in seconds) required for computing the entire distance field of the sphere vs. updating only a67a8a170a100a171 of its distance field.... ..."

Cited by 20

### Table 1: The effect of grid resolutions on the accuracy and performance (in seconds) of distance field amp; partial update computations

"... In PAGE 6: ... In fact, fast marching level-set methods runs in a2a4a3 a123 a5 a113 a9 worst-case time using the nar- row band approach [20], given the grid resolution of a5 x a5 x a5 and a123 is the number of cells in the narrow band. Table1 gives an example of the computation results using different grid resolu- tions on a sphere of a69 a29a121a29a121a29 triangles with the correct distance value of 1.0 at the center of the sphere.... In PAGE 6: ... 6.3 Partial Update of Distance Fields Table1 also illustrates the performance gain in computing par- tial update of the distance field over the recalculation of the entire distance field. The last two columns of Table 1 give the computa- tion time (in seconds) required for computing the entire distance field of the sphere vs.... In PAGE 6: ...3 Partial Update of Distance Fields Table 1 also illustrates the performance gain in computing par- tial update of the distance field over the recalculation of the entire distance field. The last two columns of Table1 give the computa- tion time (in seconds) required for computing the entire distance field of the sphere vs. updating only a69a70a151a31a152 of its distance field.... ..."

### Table 1: The effect of grid resolutions on the accuracy and performance (in seconds) of distance field amp; partial update computations

"... In PAGE 8: ... In fact, fast marching level-set methods runs in a1a3a2 a180 a4 a161 a8 worst-case time using the narrow band approach [18], given the grid resolution of a4 x a4 x a4 and a180 is the number of cells in the narrow band. Table1 gives an example of the computation results using different grid resolutions on a sphere of a68 a30a179a30a55a30 triangles with the correct distance value of 1.0 at the center of the sphere.... In PAGE 8: ... 6.3 Partial Update of Internal Distance Fields Table1 also illustrates the performance gain in comput- ing partial update of the distance field over the recalcula- tion of the entire distance field. The last two columns of Table 1 give the computation time (in seconds) required for computing the entire distance field of the sphere vs.... In PAGE 8: ...3 Partial Update of Internal Distance Fields Table 1 also illustrates the performance gain in comput- ing partial update of the distance field over the recalcula- tion of the entire distance field. The last two columns of Table1 give the computation time (in seconds) required for computing the entire distance field of the sphere vs. updating only a68a9a197a199a198 of its distance field.... ..."