### Table 2: Benchmarks for Delaunay triangulation in R3 and T3.

### Table 4-7: Finite Element. Delaunay triangulation. Gridding effect. 83 control points.

1996

"... In PAGE 30: ... RMSE for 83 control points and 27 check points for polynomials or orders one to ten. Table4 -1 shows the RMSE for the control points. Higher order polynomials result in a lower RMSE, but not necessarily a better distortion model.... In PAGE 30: ... Higher order polynomials result in a lower RMSE, but not necessarily a better distortion model. This is not merely conjecture as shown by Table4 -2. The excursions which characterize polynomials are minimal with low order polynomials, but increase in magnitude as the polynomial order increases.... In PAGE 31: ...0 0.299 1.554 1.582 Table4 -1: Polynomial registration. 83 control points Polynomial RMSE -- Check Points Degree x y total 1 22.... In PAGE 31: ...0 10.323 68.148 68.925 Table4 -2: Polynomial registration. 27 check points.... In PAGE 32: ....3.2.1 Greedy Triangulation Table4 -3 shows the results from using the Greedy triangulation and three different grid resolutions. The most obvious result is surprising.... In PAGE 32: ... Another interesting observation is with respect to the gridding effect. It is quite evident if the grid is not dense enough as shown in Table4 -4. The transformed image will appear even less smooth than a standard piecewise linear model over triangles.... In PAGE 32: ...788 5.434 Table4 -3: Finite element.... In PAGE 32: ...139 1.177 Table4... In PAGE 33: ....236 0.992 1.019 Table4 -5: Finite element.... In PAGE 33: ....681 1.787 5.010 Table4 -6: Finite element Delaunay triangulation. 83 control points and 27 check points.... In PAGE 33: ... An unexpected outcome from the gridding process is its potential usefulness for distortion diagnostics. The gridding effect, see Table4 -7, is highly local and given a large RMSE, indicative of the need to collect additional control points for linear piecewise warping. Table 4-8 lists the RMSEs using all of the... In PAGE 33: ... The gridding effect, see Table 4-7, is highly local and given a large RMSE, indicative of the need to collect additional control points for linear piecewise warping. Table4 -8 lists the RMSEs using all of the... In PAGE 34: ....135 0.628 0.643 Table4 -8: Finite Element.... In PAGE 34: ...222 2.773 Table4 -9: Multiquadric method.... In PAGE 35: ...089 2.806 Table4 -10: MQ (no polynomial precision), MQ (linear precision) and TPS (linear precision by default). 83 control points and 27 check points.... ..."

Cited by 1

### Table 8: Statistics for 2D divide-and-conquer Delaunay triangulation of several point sets.

1997

"... In PAGE 48: ... (I have also tried perfect lattices with 53-bit integer coordinates, but ORIENT3D and INSPHERE never pass stage B; the perturbed lattices are preferred here because they occasionally force the predicates into stage C or D.) The results for 2D, which appear in Table8 , indicate that the four-stage predicates add about 8% to the total running time for randomly distributed input points, mainly because of the error bound tests. For the more difficult point sets, the penalty may be as great as 30%.... ..."

Cited by 86

### Table 8: Statistics for 2D divide-and-conquer Delaunay triangulation of several point sets. Timings are

1997

"... In PAGE 50: ... (I have also tried perfect lattices with 53-bit integer coordinates, but ORIENT3D and INSPHERE never pass stage B; the perturbed lattices are preferred here because they occasionally force the predicates into stage C or D.) The results for 2D, which appear in Table8 , indicate that the four-stage predicates add about 8% to the total running time for randomly distributed input points, mainly because of the error bound tests. For the more difficult point sets, the penalty may be as great as 30%.... ..."

Cited by 86

### Table 8: Statistics for 2D divide-and-conquer Delaunay triangulation of several point sets.

1997

"... In PAGE 48: ... (I have also tried perfect lattices with 53-bit integer coordinates, but ORIENT3D and INSPHERE never pass stage B; the perturbed lattices are preferred here because they occasionally force the predicates into stage C or D.) The results for 2D, which appear in Table8 , indicate that the four-stage predicates add about 8% to the total running time for randomly distributed input points, mainly because of the error bound tests. For the more difficult point sets, the penalty may be as great as 30%.... ..."

Cited by 86

### Table 8: Statistics for 2D divide-and-conquer Delaunay triangulation of several point sets. Timings are

1997

"... In PAGE 50: ... (I have also tried perfect lattices with 53-bit integer coordinates, but ORIENT3D and INSPHERE never pass stage B; the perturbed lattices are preferred here because they occasionally force the predicates into stage C or D.) The results for 2D, which appear in Table8 , indicate that the four-stage predicates add about 8% to the total running time for randomly distributed input points, mainly because of the error bound tests. For the more difficult point sets, the penalty may be as great as 30%.... ..."

Cited by 86

### Table 4-6: Finite element Delaunay triangulation. 83 control points and 27 check points.

1996

"... In PAGE 30: ... RMSE for 83 control points and 27 check points for polynomials or orders one to ten. Table4 -1 shows the RMSE for the control points. Higher order polynomials result in a lower RMSE, but not necessarily a better distortion model.... In PAGE 30: ... Higher order polynomials result in a lower RMSE, but not necessarily a better distortion model. This is not merely conjecture as shown by Table4 -2. The excursions which characterize polynomials are minimal with low order polynomials, but increase in magnitude as the polynomial order increases.... In PAGE 31: ...0 0.299 1.554 1.582 Table4 -1: Polynomial registration. 83 control points Polynomial RMSE -- Check Points Degree x y total 1 22.... In PAGE 31: ...0 10.323 68.148 68.925 Table4 -2: Polynomial registration. 27 check points.... In PAGE 32: ....3.2.1 Greedy Triangulation Table4 -3 shows the results from using the Greedy triangulation and three different grid resolutions. The most obvious result is surprising.... In PAGE 32: ... Another interesting observation is with respect to the gridding effect. It is quite evident if the grid is not dense enough as shown in Table4 -4. The transformed image will appear even less smooth than a standard piecewise linear model over triangles.... In PAGE 32: ...788 5.434 Table4 -3: Finite element.... In PAGE 32: ...139 1.177 Table4... In PAGE 33: ....236 0.992 1.019 Table4 -5: Finite element.... In PAGE 33: ... An unexpected outcome from the gridding process is its potential usefulness for distortion diagnostics. The gridding effect, see Table4 -7, is highly local and given a large RMSE, indicative of the need to collect additional control points for linear piecewise warping. Table 4-8 lists the RMSEs using all of the ground control points.... In PAGE 33: ... The gridding effect, see Table 4-7, is highly local and given a large RMSE, indicative of the need to collect additional control points for linear piecewise warping. Table4 -8 lists the RMSEs using all of the ground control points. Finite Element RMSE -- Grid Points Grid x ytotal 30x30 1.... In PAGE 33: ....165 0.721 0.740 Table4... In PAGE 34: ....135 0.628 0.643 Table4 -8: Finite Element.... In PAGE 34: ...222 2.773 Table4 -9: Multiquadric method.... In PAGE 35: ...089 2.806 Table4 -10: MQ (no polynomial precision), MQ (linear precision) and TPS (linear precision by default). 83 control points and 27 check points.... ..."

Cited by 1

### Table 3: Statistics for 2D divide-and-conquer Delaunay triangulation of several point sets.

1996

"... In PAGE 10: ...lattices with 53-bit integer coordinates, but ORIENT3D and INSPHERE would never pass stage B; the perturbed lattices occasionally force the predicates into stage C or D.) The results for 2D, outlined in Table3 , indicate that the four-stage predicates add about 8% to the total running time for randomly distributed input points, mainly because of the errorboundtests. Forthe more difficult point sets, the penalty may be as great as 30%.... ..."

Cited by 47

### Table 1: The run time of parallel Delaunay triangulation using ParLeda (second)

### Table 3.2: Delaunay Triangulation: running time in secs; 400000 random points, 32{128 bit

in Combinatorial Curve Reconstruction and the Efficient Exact Implementation of Geometric Algorithms