### Table 2 Collision candidate distance field generation

### Table 2: Timing (in seconds) on partial update of the distance field vs. the recomputation of the entire distance field

2001

"... In PAGE 13: ... The timing (in seconds) for partial update vs. complete recomputation of the dis- tance fields for various models, including a torus, an apple and a deformed sphere is given in Table2 . Note that the torus model with more triangles and the same grid res- olution takes less time to compute than a simpler apple model with far less polygons.... ..."

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### Table 2: Timing (in seconds) on partial update of the dis- tance field vs. the recomputation of the entire distance field

"... In PAGE 8: ... complete recomputation of the distance fields for various models, in- cluding a torus, an apple and a deformed sphere (Fig. 7), is given in Table2 . Note that the torus model with more triangles and the same grid resolution takes less time to... ..."

### 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.... ..."

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### 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.... ..."

### Table 2 Collision candidate distance field generation Table 3 Real-time performance for sequence

"... In PAGE 6: ...onsists of 480 triangles. The hardware used throughout is an Intel P4 2.8GHz system with an nVidia Quadro4 900XGL graphics card. Times for distance field generation after voxelization for each collision candidate body part are shown in Table2 . The distance field is calculated for the whole voxel space, but Voronoi cell membership references are only propagated up to the outer offset surface 3 T =6 to conserve memory.... ..."

### Table 1. Time statistics for computing the cur- vature and the distance field. Time is mea- sured in seconds.

2004

"... In PAGE 5: ... The to- tal time does not include the time on pre- computation. Table1 gives the timing data for the preprocessing steps. Table 2 shows time and error statistics of SDM in comput- ing the three examples.... ..."

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### Table 4: Comparison on 67108864 byte CThead distance field using lossy and lossless compression techniques.

2004

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### Table 6. Accuracy of the various methods when compared to the true sub-voxel accurate distance field. (1 GHz Athlon).

2001

"... In PAGE 13: ...ig.13. Example of a problematic case for the hybrid method. We are now examining the use of a tie-list (which has been previously proposed for a related problem [24]) to solve this problem. Table6 shows the hybrid method, the EVDT applied to a binary segmentation and the 8VCVDT applied to a distance shell compared to the true sub-voxel accurate distance field. We can see that it is an order of magnitude more accurate, but without too much of a performance penalty.... In PAGE 14: ... The sub-voxel accurate distance shell is propagated using the most accurate 8 pass VCVDT, and then those vectors are used to direct a further pass through the data in order to calculate the distance to the correct sub-voxel surface. Table6 demonstrates that this method produces the correct distance for 90% of voxels, whereas the previous best (EVDT on binary segmented data) produces the correct distance to less than 1% of voxels. Section 5 shows how the new accurate distance field benefits our research in two main application areas.... ..."

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