### Table 2: Intersect() Semantics (Partial)

2003

"... In PAGE 10: ... Recall that the idea is to try to find out if there is some value for x that can satisfy both (x op1 a) and (x op2 b). Table2 shows some examples for pairs of operators; the values of a and b are assumed arbitrary. The first row, for example, says that (x, =, a) intersects (x, op2, b) is true if (a op2 b) is true; this is because the only possible value that can satisfy both is a.... ..."

### Table 1 Number of intersection Subcase of intersection Intricacy

### Table 1. Minkowski functionals of a single ball B of radius r and of an intersection B \ Bx of two balls separated by a distance x = 2rd (0 d 1).

"... In PAGE 7: ... As shown in Appendix A this formula can be generalized for arbitrary point processes, if the V (B) are replaced by a series V containing the complete hierarchy of correlation functions. Truncating Equation (A12) after the rst two terms we have V = V (B) ? 2 Z d3x (x)V (B \ Bx) : : : (2) In Table1 we summarize the Minkowski functionals V (B) of a single ball B of radius r and of an intersection B\Bx of two balls separated by a distance x = 2rd (0 d 1). Note, that all Minkowski functionals of the empty intersection x gt; 2r become zero.... ..."

### Table 1. Line intersections

2005

"... In PAGE 7: ... Line estimation improvement by using Image/text areas removal. All possible line intersections (see Table1 ) are detected progressively according to the following algorithm. First, we detect all intersections with IDs 1-4.... ..."

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### Table 3: Intersection Operators

"... In PAGE 3: .... Specialisation Operators: this group consists of two operators: Intersect and Intersect1. They integrate a set of overlapping local classes by generating a common subclass. Table3 shows the effects of each of this group of operators. 4.... ..."

### Table 2. Intersection Results

"... In PAGE 8: ... Therefore we select a high-precision strategy and use the intersection of two results with different seed vector numbers to further improve the precision. The results in Table2 show that the precision is improved greatly and able to achieve at 97% with combination strategy. When the searching ... ..."

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### Table 1. The Primary Intersections

"... In PAGE 4: ... These are S1 \ S2, Si \ W and Si \ Pi for i = 1 and 2. We name these points in Table1 , for reference. Remark: It is clear that intersections of one shock with another and of shocks with the wall generate new waves.... In PAGE 7: ... 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 shall call this... ..."