### Table IV. Comparison of algorithms on the Vase example with translated initialization (+1000). Note the significant change in mean gradient error of the original Fast Marching Method with respect to Table II.

### Table IV. Comparison of algorithms on the Vase example with translated initialization (+1000). Pay attention to the sharp change in all measures of the original Fast Marching Method with respect to Table 5.2.

### Table 1 Fast marching algorithm

"... In PAGE 3: ...eodesic active contours as well (Caselles et al., 1997). In bors which have smaller values than u. (Cohen and Kimmel, 1997) and in our Appendix A is also The algorithm is detailed in 3D in the next section in mentioned how the curvature of the minimal path is now Table1 . The Fast Marching technique selects at each controlled by the weight term w.... ..."

### Table 1. Fast Marching algorithm

"... In PAGE 4: ... This technique of considering at each step only the necessary set of grid points was originally introduced for the construction of minimum length paths in a graph between two given nodes in [7]. The algorithm is detailed in Table1 . An example is shown in Figure 2.... ..."

### Table 4: Comparisons of marching directions.

"... In PAGE 7: ... It is expected that, in comparison with methods that trace along curves of degree 2, polynomial and helical tech- niques require less iterations for improving the coordinates of the the obtained points. For illustrative purpose we present in Table4 the number of iterations required for tracing the intersection of three given pairs of surfaces. It is noticeable the superiority of the Ye algorithm in handling transversal intersections that satisfy the condition expressed by Eq.... ..."

### Table 2: Computation time on a Pentium IV 1GHz with 1Gb of memory. Dist and March stand for the signed distance transform, and fast marching from its zero level set (in min- utes). Evolve include the LSM solver, Collide the collisions detection, Remesh the local remeshing and Fitting is the fi- nal MLS projection (in seconds).

"... In PAGE 7: ... As detailed in Table 1, unlike the other methods, we recover the correct topology in all cases, while maintaining a reasonable output size, and a high quality mesh (see Figure 10). Note in Table2 that the remeshing time is negligible. Figure 10: A side by side comparison with the PowerCrust reconstruction (left).... ..."

### Table 1 : Fast Algorithm

"... In PAGE 8: ...onstants c1 and c2; then, the solution of (3.4) and (3.6) needs O(n ln n) operations. The following tables give us the numerical results of the fast algorithm and the quadrature method, ( Table1 and Table 2, respectively) applied to equation (1.3) with k(x; t) de ned by (3.... ..."

### TABLE 1 Complexity of the fast multipole method

2004