### Table 1: Geometric Structure.

2007

"... In PAGE 6: ...BACKGROUND 3 2.1 Conformal Geometry Theory The geometric information of a surface has many layers, as shown in Table1 . Higher struc- tures determine lower structures.... ..."

### Table 2. Geometric Constraints.

2004

"... In PAGE 5: ... They specify rela- tions between geometric objects of the B-rep model, and the auxiliary objects. Any regularities between geometric objects which can be expressed by con- straint types in Table2 can be handled by our system. Note that we do not allow topological changes of the model in this paper|such changes will be considered in a separate paper.... In PAGE 25: ... It may be possible to modify the solvability test to create a decomposition plan for a symbolic constraint solver [7]. The constraint system contains equations of the types in Table2 . We also add one equation per direction vector to ensure that it is a unit vector.... ..."

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### Table 4: Geometric queries.

2008

"... In PAGE 42: ...ithout the overhead of the graphic interface. All the queries (i.e., using Piet, PostGIS and aR-tree) were ran 10 times, and we report the average execution times. Table4 shows the expressions for the geometric queries. Figure 19 shows the execution times for the set of geometric queries.... ..."

### Table 2. Geometric constraints.

2002

"... In PAGE 2: ... Furthermore, auxiliary objects (planes, cylinders, lines, di- rections, positions, lengths, angles) are used to express cer- tain regularities with simple constraints. The geometric constraints are represented as equations listed in Table2 . We require all direction vectors to be nor- malized.... ..."

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### Table 3: Geometric attacks

"... In PAGE 10: ... We construct such attacks by watermarking the shapes and then applying random translations, scalings and rotations on each of the objects (same geometric transformation on each one of them). The experiment is repeated 100 times and in Table3 we report the average false positive/negative... ..."

### Table 1: Geometrical Settings

"... In PAGE 3: ... Model Measurements were performed on a McDonnell Douglas Aerospace (now Boeing) 30P30N, high-lift configuration. Geometrical settings associated with this configuration are listed in Table1 . This particular geometry has been used in studies by Klausmeyer16 to examine separation control using micro-vortex generators on the flap and by Paschal17 to characterize unsteadiness in the slat wake.... ..."

### Table 2. Geometric Parameters

"... In PAGE 5: ... The parameters related to the fluid ERF LID 3354, shown in Table 1, have been determined from the manufacturer apos;s specifications [6]. The default geometric parameters of the ECS element shown in Table2 , have been determined from the dimensions of commercially available sensors and electronic equipment that will be used for measuring and actuating the device and also by manufacturing and machinability constraints. In the first prototype, that is presented in this work (see Section 4), no effort for miniaturization was made since the goal was to prove the concept that ERFs can be used to create haptic feedback.... ..."

### Table 1: Geometric information

"... In PAGE 20: ... e = QG gt;(G gt;QG) 1e fforcing the constraint G gt; e = eg x01 = 0; x02 = 0; x03 = e fchoose the initial guessg b1 = g; b2 = d = f B gt; e; b3 = 0 fcompute right hand sideg d = K3x0 b fcompute the defectg r0 = D3 ^ L 1 3 d fapply the transformationg p0 = w0 = D 1 3 r0 fpreconditioningg 0 = (w0; r0) for n = 0 step 1 until n quot; 0 do vn = D3 ^ L 1 3 K3pn fmatrix vector multiplication and transformationg = (vn; pn) = n+1= xn+1 = xn pn fupdate the iterateg rn+1 = rn vn fupdate the defectg wn+1 = D 1 3 rn+1 fpreconditioningg n+1 = (wn+1; rn+1) = n+1= n pn+1 = wn+1 + pn fupdate of the search directiong end for Figure 1: Domain decomposition with 8 subdomains In Table1 , the geometric informations about the domain decomposition and the discretization are listed for the re nement levels L used. Starting from the coarsest grid with 192 triangles for the whole domain , the re ned meshes are recursively constructed by subdividing each triangle into four smaller similar triangles.... In PAGE 21: ...Table 1: Geometric information In all following tables, a uni ed notation is used. L again denotes the re nement level and Table1 gives the corresponding information of the grids. t1 and t2 are the measured times in seconds for setting up the corresponding system of linear equations and for their solution.... ..."

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