### Table 1. Mapping to geometric solutions.

2006

"... In PAGE 5: ... This provides a framework in which to handle these problems in a clean and uniform way by considering their geometric meaning. Table1 shows a number of distributed systems problems and their mapping to geometric techniques. Note that there are geometric solutions that do not correspond immediately to networking problems.... ..."

Cited by 5

### Table 1: The 3D geometric data types

"... In PAGE 35: ...:100,000 {road, river, buildine, ..., lot} Table1 : Default settings for scale ranges and preferred image sources for geographic... In PAGE 75: ...topological projective exception German English German Enelish German English an at hinter behind zwischen between bei near links left fern far neben besid,e NN xn rechts right nahe close to iiber aboae unter below aor in front of Table1 : German spatial relations and their English counterparts 2. COMPUTING THE ELEMENTARY SPATIAL RELATIONS Following [Landau amp; Jackendoff 93], people do not account for every detail of the ob- jects involved when they apply spatial relations.... In PAGE 75: ...e.g., at and near), the projective relations (e.g., in front of , right, and below), and the relation between, which takes an exceptional position in the group of spatial relations.r Table1 shows the 13 different German spatial relations and their English counterparts considered at the moment. lln the sequel only the English expressions for the German prepositions are used.... In PAGE 101: ...einand, A., Gamma, E., amp; Marty, R. (1989). Design and Implementation of ETt*: A searnless Object-Oriented Application Framework. Structured Programming, 10(2),63-87 apos; APPENDIX A: 3D SPATIAL ADT FUNCTIONS This appendix contains the functions specific for one of the following 3D spatial data types: POINT3, POLYLINE3, POLYGON3, and POLYHEDRON3; see Table1 . In Tables 2, 3, 4, and 5, the in- and output functions are omitted.... In PAGE 109: ... The difference with geographic data is that the candidate cells can be based on either the spatial data, the attribute data or a combination of both. Table1 gives an example of primary candidate partitionings in which the predicate is based on some spatial or nonspatial property of the entity. Table 1: Primary Candidate Partitioning Table Entity Predicate a) mapsheet mapsheet_name : apos;Laverton apos; mapsheet_name : apos;Albany apos; mapsheet_name c apos;Laverton apos;, apos;Al- bany apos; b) mlne status : apos;Developing apos; status : apos;Abandoned apos; c) mlne Y-coordinate lt;: 32 Y-coordinate gt; 32... In PAGE 109: ... Table 1 gives an example of primary candidate partitionings in which the predicate is based on some spatial or nonspatial property of the entity. Table1 : Primary Candidate Partitioning Table Entity Predicate a) mapsheet mapsheet_name : apos;Laverton apos; mapsheet_name : apos;Albany apos; mapsheet_name c apos;Laverton apos;, apos;Al- bany apos; b) mlne status : apos;Developing apos; status : apos;Abandoned apos; c) mlne Y-coordinate lt;: 32 Y-coordinate gt; 32... ..."

### Table 3. Execution times and relative speedup. Geometric means do not include raytrace (rt), the single-threaded version of mtrt.

"... In PAGE 6: ...able 3. Execution times and relative speedup. Geometric means do not include raytrace (rt), the single-threaded version of mtrt. Although the focus of this work is in demonstrating the utility of SableSpMT as a research and analysis framework, measurable speedup remains the ultimate goal of any speculative system, and we provide overall performance data in Table3 . We compare our multithreaded results against executions where SpMT failure is ar- tificially forced at every join point, and are thus able to provide a dynamic upper bound on speedup by factoring out overhead con- cerns.... ..."

### 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.... ..."

Cited by 9

### 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.... ..."

Cited by 3

### 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.... ..."