# Cube UPD

The engine, though designed for simplicity and elegance as opposed to feature & eyecandy checklists, still competes nicely thanks to its novel "6-directional heighfield deformable cube octree" world structure that is the basis for its in-game editing. Occlusion culling, pixel & vertex shaders, very accurate lightmapping, robust custom physics system, network system, models, sound, scripting...

## Cube

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Extracts the n-th coordinate of the cube, counting in the following way: n = 2 * k - 1 means lower bound of k-th dimension, n = 2 * k means upper bound of k-th dimension. Negative n denotes the inverse value of the corresponding positive coordinate. This operator is designed for KNN-GiST support.

In addition to the above operators, the usual comparison operators shown in Table 9.1 are available for type cube. These operators first compare the first coordinates, and if those are equal, compare the second coordinates, etc. They exist mainly to support the b-tree index operator class for cube, which can be useful for example if you would like a UNIQUE constraint on a cube column. Otherwise, this ordering is not of much practical use.

In addition, a cube GiST index can be used to find nearest neighbors using the metric operators , , and in ORDER BY clauses. For example, the nearest neighbor of the 3-D point (0.5, 0.5, 0.5) could be found efficiently with:

The > operator can also be used in this way to efficiently retrieve the first few values sorted by a selected coordinate. For example, to get the first few cubes ordered by the first coordinate (lower left corner) ascending one could use the following query:

Makes a new cube from an existing cube, using a list of dimension indexes from an array. Can be used to extract the endpoints of a single dimension, or to drop dimensions, or to reorder them as desired.

Increases the size of the cube by the specified radius r in at least n dimensions. If the radius is negative the cube is shrunk instead. All defined dimensions are changed by the radius r. Lower-left coordinates are decreased by r and upper-right coordinates are increased by r. If a lower-left coordinate is increased to more than the corresponding upper-right coordinate (this can only happen when r 0), then extra dimensions are added to make n altogether; 0 is used as the initial value for the extra coordinates. This function is useful for creating bounding boxes around a point for searching for nearby points.

In all binary operations on differently-dimensioned cubes, I assume the lower-dimensional one to be a Cartesian projection, i. e., having zeroes in place of coordinates omitted in the string representation. The above examples are equivalent to:

The LifeSaver Cube was designed to store and carry dirty water. We recommend storing dirty water, either in the cube or in other storage containers, and filtering through the cube as and when clean water is required, to prevent recontamination of previously filtered water.

The online cube builder helps students develop many different skills including spatial reasoning, creativity, problem-solving, and an understanding of 3D objects. Using the 3D cube builder is easy after you experiment with it for a bit. This key will help you:

The Cube offers drone services to groups or individuals for academic projects. Drones can add a unique perspective to your projects with their high-resoultion cameras and additional sensors. Our drones have been used to support projects involving cinematography, photography, measurement of landscape, architectural recreation using photogrammetry, and topological reconstruction from surface photography. If you would like help with your project using our drone services, please schedule a consultation time or email __cube@pacific.edu__.

There are many situations where it would be useful to be able topublishmulti-dimensional data, such as statistics, on the web in such a waythat it can be linked to related data sets and concepts. The Data Cubevocabulary provides a means to do this using the W3C RDF(Resource Description Framework) standard. The model underpinning theData Cube vocabulary iscompatible with the cube model that underlies SDMX (Statistical Dataand Metadata eXchange), an ISO standard for exchanging and sharingstatistical data and metadata among organizations. The Data Cubevocabulary is a core foundation which supports extensionvocabularies to enable publication of other aspects ofstatistical data flows or other multi-dimensional data sets.

At the heart of a statistical dataset is a set of observed valuesorganized along a group of dimensions, together with associated metadata.The Data Cube vocabulary enables such information to be representedusing the W3C RDF(Resource Description Framework) standard and published following theprinciples oflinked data.The vocabulary is based upon the approach used by the SDMX ISO standardfor statistical data exchange. This cube model is verygeneral and so the Data Cube vocabulary can be used for other data setssuch as survey data, spreadsheets and OLAP data cubes [OLAP].

A statistical data set comprises a collection of observations madeat some points across some logical space. The collection can be characterized bya set of dimensions that define what the observation applies to (e.g. time,area, gender) along with metadata describing what has beenmeasured (e.g. economic activity, population), how it was measured and how theobservations are expressed (e.g. units, multipliers, status). We canthink of the statistical data set as a multi-dimensionalspace, or hyper-cube, indexed by those dimensions. This space iscommonly referred toas a cube for short; though the name shouldn't be takenliterally, it is not meant to imply thatthere are exactly three dimensions (there can be more or fewer) northatall the dimensions are somehow similar in size.

It is frequently useful to group subsets of observations within adataset. In particular to fix all but one (or a small subset) of thedimensions and be able to refer to all observations with thosedimension values as a single entity. We call such a selection a slicethrough the cube. For example, given a data set on regional performanceindicators then we might group together all the observations about a given indicatorand a given region. Each such group would be a slice representing a time series of observed values.

In order to illustrate the use of the data cube vocabulary we willuse a small demonstrationdata set extracted fromStatsWales reportnumber 003311 which describes life expectancy broken down by region(unitary authority), age and time. The extract we will use is:

To support this reuse of general statistical concepts the data cube vocabulary provides the qb:concept property which links a qb:ComponentProperty to the concept it represents. We use the SKOS vocabulary [SKOS-PRIMER] to represent such concepts. This is very natural for those cases where the concepts are already maintained as a controlled term list or thesaurus. When developing a data structure definition for an informal data set there may not be an appropriate concept already. In those cases, if the concept is likely to be reused in other guises it is recommended to publish a skos:Concept along with the specific qb:ComponentProperty. However, if such reuse is not expected then it is not required to do so - the qb:concept link is optional and a simple instance of the appropriate subclass of qb:ComponentProperty is sufficient.

Both representation approaches require that, for every point in the space of dimensions for which there is an observation, a value must be given for every measure. In the case of multi-measure observations each measure must be present on each observation. In cubes which use a measure dimension there are sets of observations for each populated point in the cube and within each of those sets there must be an observation giving each measure.

This approach allows multiple observed values to be attached to an individual observation. It is suited to representation of things like sensor data and OLAP cubes. To use this representation you simply declare multiple qb:MeasureProperty components in the data structure definition and attach an instance of each property to the observations within the data set.

Note the duplication of having the measure property show up both as the property that carries the measured value, and as the value of the measure dimension. We accept this duplication as necessary to ensure the uniform cube/dimension mechanism and a uniform way of declaring and using measure properties on all kinds of datasets.

Slices allow us to group subsets of observations together. This is not intended to represent arbitrary selections from the observations but uniform slices through the cube in which one or more of the dimension values are fixed.

In some cases code lists have a hierarchical structure. In particular, this is used in SDMX when the data cube includes aggregations of data values (e.g. aggregating a measure across geographic regions).Hierarchical code lists SHOULD be represented using the skos:narrower relationship, or a sub-property of it,to link from the skos:hasTopConceptcodes down through the tree or lattice of child codes. In some publishing tool chains the corresponding transitive closure skos:narrowerTransitive will be automatically inferred. The use of skos:narrower makes it possible to declare new concept schemes which extend an existing scheme by adding additional aggregation layers on top.All items are linked to the scheme via skos:inScheme.

In normal form then the qb:Observations whichmake up a Data Cube have property values for each of the requireddimensions, attributes and measures as declared in the associated datastructure definition. This form for a Data Cube istermed normalized. It is a convenient format forquerying data and makes it possible to write uniform queries whichextract sets of observations, including from across multiplecubes. However, the verbosity of a fully normalized representationincurs overheads in transmission and storage of Data Cubes which maybe problematic in some settings. Note that abbreviated form is provided as an option and there is requirement that it be used. In many settings standard compression techniques can eliminate much of the overhead of normalized form. 041b061a72