### Table 1: Summary of applications of various configurations of conics

2004

"... In PAGE 6: ... The algorithms are simple and do not require correspondences of a large number of conics or the solution of multivariate polynomial equations. A summary of the results is shown in Table1 . Extensions to these methods which handle over determined sets of equations, obtained due to the presence of more than two coplanar conics, need to be explored.... ..."

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### Table 5: The reconstruction results of the three conics of the wooden house images.

1995

"... In PAGE 18: ... The raw entries correspond to the conics of the rst image and the column entries to those of the second image. The reconstruction results are illustrated in Table5 . To have an idea of the reconstruction results, each plane equation is put under the form (nT; ?d) where nT is the unit normal direction vector of the plane and d is the distance of the origin to the plane.... ..."

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### Table 2 We see that the direct computation of the optimal control via the subspace yields much smaller relative errors than the solution via the Riccati equation. Note that the subspace method always computed the Riccati solution to high relative accuracy.

### Table 1: The Primary Intersections

"... In PAGE 7: ... For convenience, we label all points, even though some of them are in the lower half-plane for some parameter values. The list is in Table1 ; a sketch in Figure 3 identi es the points. Remark: It is clear that intersections of one shock with another, or of a shock with the wall, generate new waves.... In PAGE 24: ...11) and v(u2) lt; 0 if I gt; u2=2. Checking the value of I in Table1 shows that this is indeed the case. This construction can also be used to estimate the values of vm and um.... In PAGE 31: ... This requires the two conditions 1 gt; 0 (so that 1 exists) and a gt; I(b), so that I is not admissible. The rst condition, from Table1 , is a lt; 1=p2. We describe the following reduction of the problem to a degenerate el- liptic equation.... ..."

### Table 2.3 shows the model statistics and the solutions obtained via both the approaches. As expected, the size of the OOA control problem is very large (in terms of the number of variables and equations) in comparison to the SRA control problem and thus needs much

### Table 1. Average computation time required by the naive algorithm per pair of conics.

2002

"... In PAGE 9: ... The example on the left also contains intersection points with equal x-coordinate. Table1 shows that, as one would expect, running time increases when degeneracies are present and also when the input precision is increased to represent nearly degenerate cases. However, the increase is not unreasonable.... In PAGE 11: ... Examples similar to the ones shown in Figure 2 with 30 and 60 conic segments require, respecitvely, 19 seconds and 49 seconds using our current implementation. Table1 indicates that, as one would expect, running time degrades when degeneracies are introduced. However, with the application of appropriate filtering techniques in our predicate implementations we are confident that the running times for conic segments will come in line with those for circular arcs.... ..."

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### Table 1. Average computation time required by the naive algorithm per pair of conics.

2002

"... In PAGE 9: ... The example on the left also contains intersection points with equal x-coordinate. Table1 shows that, as one would expect, running time increases when degeneracies are present and also when the input precision is increased to represent nearly degenerate cases. However, the increase is not unreasonable.... In PAGE 11: ... Examples similar to the ones shown in Figure 2 with 30 and 60 conic segments require, respecitvely, 19 seconds and 49 seconds using our current implementation. Table1 indicates that, as one would expect, running time degrades when degeneracies are introduced. However, with the application of appropriate filtering techniques in our predicate implementations we are confident that the running times for conic segments will come in line with those for circular arcs.... ..."

Cited by 18