# Replacing geometry of a polygon using the geometry of a polygon from another layer

I am trying to update a polygon shapefile by redoing the geometry on certain polygons to match the geometry of polygons in a separate, more accurate shapefile. Some of these polygons are extremely complex, and the replace geometry tool is taking much too long.

Is there a tool or method that would allow me to alter a polygon to match exactly the geometry of a polygon in a separate layer while retaining the attributes of the original polygon?

I vaguely recall doing this in ArcMap, but ArcGIS Pro is throwing me for a loop.

Select the polygon and copy it (either via the clipboard, Ctrl + V , or right click and copy) and Paste Special. You will then have the option to what layer you paste it to (like in ArcMap) and can also select if you want to copy attributes or not.

## GEOMTRANSFORM - Geometry Transformations¶

Geometry transformations return a new geometry. The purpose of a geometry transformation can be to achieve special effects for symbol rendering and labeling.

Geometry transformation is available at the LAYER level and the STYLE level. At the LAYER level (since 6.4), the original vector geometry (“real world” coordinates) is used. At the STYLE level, pixel coordinates are used.

It may be useful to apply pixel values also at the LAYER level, and that is possible. If UNITS is defined in the LAYER , the [map_cellsize] variable can be used to convert to pixel values at the LAYER level:

We only need to rely on the following four statements:

The sign of the 2D analog of the vector cross product indicates whether the second vector is clockwise (positive) or counterclockwise (negative) with respect to the first vector, in a standard right-handed coordinate system.

If the 2D analog of the vector cross product is zero, the two vectors are collinear.

If the 2D analog of the vector cross product between consecutive pairs of edge vectors in a polygon has differing signs (ignoring zeroes, as if they had no sign), the polygon must be concave.

If we examine the signs of the $x$ and $y$ components of the edge vectors, (again ignoring zeroes as if they had no sign), consecutively along the polygon, as a circular list, there must be exactly two sign changes, or the polygon is concave.

Statements 1, 2 and 3 are known from basic vector algebra.

Statements 3 and 4 combined, is equivalent to calculating the angle between each pair of consecutive edges in the polygon, and verifying that they are all in the same orientation (counterclockwise or clockwise), and that the sum of the angles is 360° (so that we can correctly detect self-intersecting polygons), except that we only consider four separate directions (the four quadrants in a standard coordinate system).

In pseudocode, the testing algorithm is as follows:

where != is the not-equal operator. This approach considers vertex lists with less than three vertices concave, but as this is determined by the very first If clause, you can change it to suit yourself. Degenerate polygons with at least three points, so either all the same point, or collinear, are considered convex by this approach.

Note that because this implementation does only two multiplications, and a number of additions, subtractions, and comparisons per polygon edge, it should be extremely efficient approach in most programming languages.

In a practical implementation, you might wish to replace > 0 with > eps , < 0 with < eps , x == 0 with x >= -eps && x <= eps , and x != 0 with x < -eps || x > eps , to account for rounding errors with floating-point numbers. I'd use an eps about one quarter to one sixteenth of the smallest meaningful change in either $x$ or $y$ coordinates.

## Looking for references about a tessellation of a regular polygon by rhombuses.

A regular polygon with an even number of vertices can be tessellated by rhombii (or lozenges), all with the same sidelength, with angles in arithmetic progression as can be seen on figures 1 to 3. Fig. 1 Fig. 2 Fig. 3

I had already seen this kind of tessellation, and I met it again in a recent question on this site (Tiling of regular polygon by rhombuses).

Let the polygon be $n$ -sided with $n$ even. The starlike pattern of rhombii issued from the rightmost point, that we will call the source, can be seen as successive ''layers'' of similar rhombii. A first layer $R_1$ with the most acute angles (they are $m:=dfrac<2>-1$ of them), then moving away from the source, a second layer $R_2$ with $m-1$ rhombii, etc. with a grand total of $dfrac<2>$ rhombii.

It is not difficult to show that rhombii in layer $R_p$ are characterized by angles $pdfrac.$

In fact (I had no idea of it at first), the rhombii pattern described above is much less mysterious when seen into a larger structure such as shown in figure 4. The generation process is simple: a regular polygon with $m$ sides is rotated by successive rotations with angle $dfrac$ around one of its vertices.

• where can I find some references?

• are there known properties/applications?

The different figures have been produced by Matlab programs. The program that has generated Fig. 2 is given below it uses complex numbers, especially apt to render angular relationships:

Edit : I am indebted to @Ethan Bolker for attracting my attention to zonohedra (or zomes, as some architects call them), a 3D extension of Fig. 4 (or an equivalent one with less or more circles) by 3D extension, we mean a polyhedron made of (planar) rhombic facets whose projection on $xOy$ plane is the initial figure, as shown on Fig. 5. The idea is simple (we refer here to the two left figures in Fig. 6): the central red "layer" (with the thinnest rhombi) is "lifted" as an umbrella whose highest point, the apex of the zonohedra, say at height $z=1$ , with the bottom of the $n$ ribs of the umbrella at $z=1-a$ . Let us denote by $V_k, k=1, cdots n$ with components $left(cos( frac<2 pi k>),sin( frac<2 pi k>), -a ight)$ the (3D) vectors issued from the apex. Layer $1$ rhombi have sides $V_k$ and $V_$ by the very definition of a rhombus, layer $2$ (yellow) rhombi have sides $V_k$ and $V_$ , etc. Note that Fig. 6, unlike Fig. 5, displays a closed zonohedron obtained by gluing 2 identical zonohedra. The right part of Fig. 6 displays the same zonohedron colored in a spiraling way.

Let us remark that there is a degree of freedom, i.e., the way the initial "umbrella" with ribs $V_k$ is more or less open, i.e., $a$ can be chosen.

Fig. 5 : The upper part of a regular zonohedron and its projection onto the horizontal plane.

Fig. 6 : A typical regular zonohedron generated by Minkowski addition of vectors $(cos(2k pi/n), sin(2k pi/n),1)$ for $k=1,2. n$ with $n=15$ .

Fig. 7 : A rhombic 132-hedron (image borrowed to the Wikipedia article).

See the very educational page on S. Dutch's site : (https://www.uwgb.edu/dutchs/symmetry/zonohedra.HTM) (sorry: broken link)

Have a look at the article (https://en.wikipedia.org/wiki/Zonohedron) which enlarges the scope I have isolated the picture of the rhombic 132-hedron (Fig. 7).

A general definition of zonotopes (general name for zonohedra) is as a Minkowski addition of segments. See (http://www.cs.mcgill.ca/

A funny article about zomes (http://archive.bridgesmathart.org/2012/bridges2012-545.pdf). "Bridges Organization" promotes connections between mathematics and arts, in particular graphical arts.

The rhombic dodecahedron is a zonohedron that can tessellate the 3D space.

A very interesting 19 pages article by Sandor Kabai in the book entitled "Homage to a Pied Puzzler" Ed. Pegg Jr, Alan H. Schoen, Tom Rodgers Editors, AK Peters, 2009 (this book is a tribute to Martin Gardner).

## Replacing geometry of a polygon using the geometry of a polygon from another layer - Geographic Information Systems

Tableau evolves rapidly with new features. Plotting data on a map is one of those coolest features. This blog will show you a short history of how Tableau’s data mapping has developed over the last few years.

Geographic roles and polygons, version 9.0

Mapping requires location data – a position on a map is determined by a set of coordinates which can originate in your data. Alternatively, Tableau can geocode geographies into latitude and longitude. For a complete list of geographic role types that Tableau can geocode visit here

This is a simple method until you have locations that Tableau cannot localise on map. This was the case for UK local authorities until 2015, a key geography boundary affecting many types of analysis including the distribution of public funding. An alternative method then was to blend pre-made extracts of map polygons, which were readily available thanks to the Tableau community.

Figure 1. Polygon data extract of Local Authorities in England and Wales.

Mapbox integration, version 9.2

Adding flair to your geographic data became possible with Mapbox integration. It gave users the ability to fully customise their background map style. Either by building the entire map to branding guidelines or even better, to answer landscape-dependent questions which need markers such as streetlights or mountains on a map. These can be imported into Tableau using Mapbox bringing a new layer to your organisation’s data.

Custom territories, version 10.0

Tableau brought in custom territories to visualise new areas that exist outside of your data. This may be necessary in planning a business where geographic areas are constantly changing. By clicking, you can create regions on the fly by selecting marks on a map and group them to quantify your data to another level.

Figure 2 Custom territory of sub-regions in Europe.

Shapefiles, version 10.2

The next big thing of mapping in Tableau is to be able to connect directly to geospatial files, replacing the need to transform data for polygon maps. Yes, that’s right, reading your own custom Shapefiles from ESRI and GIS. Shapefiles contain data of polygons, lines or points for example for sales areas, delivery routes or stores and you can use directly them in Tableau.

Figure 3. Geometry field for point geometries of navigable rivers in Peru

After 10.2 release, Craig (CTO) transformed the repository of tablemapping.bi into a web data connector. What does this mean? You can directly connect to (online) geographic data in your workbook. Preview mapping layers at https://www.tableaumapping.bi.

Live and dual-axis, version 2018.1

The ability to connect directly to spatial data in SQL is fairly new. There is no need to download data or lose the live feed that drives real-time decision-making such as those coming from the smart grid or emergency services.

To provide flexibility, also in this version, Tableau released dual-axis mapping allowing users to visualise multiple mapping layers.

Spatial joins, version 2018.2

The latest new feature in Tableau is to combine topologically-related data using a spatial join. In essence if you have two spatial files comprising of polygon or points, you can combine them.

Figure 4. Spatial join of wild-life crossings and conservation land in Vermont.

Three years ago, what first attracted me to Tableau was the ability of mapping data. I was able to see the distributing of agricultural land across the UK. However, there were limits to geocoding, and it was tricky to blend geographic data. Since then Tableau has made big strides introducing new features in a very short time. The Tableau community continually contributes with ideas, such as of hexbin mapping for density plots or using viz in tooltips as a loupe. It would not have been possible without you, Tableau users, so thank you. Collectively you have made mapping even more user-friendly, flexible and seamless.

## Introduction

A wide range of human activities is concentrated within settlements. This makes urban areas primary consumers of natural resources. With regard to planning for sustainability, decision-makers need detailed information of the built environment as well as urban greenery, the two main components of the settlement structure. Furthermore, the functions of housing, employment, education, supply and recreational use, which are concentrated in urban areas, can boost sustainability if the spatial mix is intelligently planned (EU 2007, 4). This can also be ensured by the careful delineation of urban areas.

The cartographic representation of any administrative reference unit will contain polygons of the urban area as well as open space. Such delineation of the urban area can be realised using basic topographic geodata. Clearly, this entails the spatial identification of the interior vs. the exterior, i.e. the creation of an urban mask for geospatial analysis and evaluation of the settlement structure. In international studies, the analysis of urban spaces frequently considers only built-up structures. The term “urban mask” is used in this narrow sense, for example in the context of the two global geo-databases Global Urban Footprint (GUF) and Global Human Settlement Layer (GHSL) (Minghini et al. 2017). Both sets of geodata, which are derived from remote-sensing data, are grid-oriented and focus on built-up areas while ignoring urban green. A rural–urban mask derived from CORINE Land Cover (CLC) 2012 is provided by the Copernicus Climate Change Service as an additional data source for 100 European city regions to calculate urban heat islands (Copernicus Climate Change Service 2019). The minimum mapping unit in the CLC data and consequently in the rural–urban mask is 25 ha. Unfortunately, this primarily rural–urban delineation does not provide a suitable geometry for detailed analyses. A comparable urban mask is not yet publicly available for the thematic context and scale of the European Urban Atlas, i.e. minimum mapping unit: 0.25 ha (EU 2016).

In Germany, an urban mask geometry is included as an object type in the official topographical basic geodata (ATKIS): the so-called Ortslage (AdV 2018, 224). This object type, which has been translated as “urban site”, Footnote 1 has a minimum size of 10 ha. It encompasses built-up areas and urban green spaces within the administrative city area. The urban mask is already recognised as an important reference unit for urban, regional and environmental planning. Depending on the availability of data, urban masks can describe the spatial extent of settlements as well as their characteristic features, thereby assisting in a wide range of strategic planning tasks at small and medium scales as well as relevant scientific studies. This is demonstrated by many examples in planning and research that use the geometry of the ATKIS urban site.

One important use of the urban site is in the assessment of infill development potential (BBSR 2013, 2014). Such assessment entails analysing existing basic geodata to determine gaps between buildings as well as the potential for redensification, leading to the establishment of potential land registers of infill potential, e.g. at the level of the federal states (Hintzen and Petersen 2016). Further, parameters of settlement structure at spatial resolution considerably below the municipal level are needed to conduct intelligent strategic settlement and infrastructure planning. This can be usefully supported by the ATKIS urban site (Schiller and Bräuer 2013). Other researchers use the basic geometry of the urban site to distinguish between urban and extra-urban areas to pinpoint potential areas for future settlement development (MWEKL 2011). In the analysis of urban sprawl, the calculation of dispersion (according to the Swiss measurement concept) can be based on the settlement area boundaries of the urban site (Schwarzak et al. 2014). This ATKIS object type is also an important intersection geometry in analyses of urban greenery: Increased surface temperatures have been found in less greened urban site areas as compared to the respective administrative city area (Frick et al. 2020). When regional authorities are planning sites for wind farms, the visual impact and pressure of wind turbines on settled areas is often insufficiently taken into consideration. Taeger and Ulferts (2017) present a GIS-based approach to identify and assess potential conflicts between proposed wind farm sites and settlements at regional level using the ATKIS urban site. Such considerations are already included in regional planning documents (Regionalplanung Thüringen 2020). When planning efficient NGA (Next Generation Access) network extensions, it can be helpful to focus on settlement areas so as to significantly reduce costs and achieve a high level of development (Fornefeld et al. 2015). Here too the tool of urban sites can be helpful. The Southern Upper Rhine Regional Association uses the delimitation of urban sites to map and evaluate so-called biotope complex types while considering the factors of usage and nature conservation (Regionalverband Südlicher Oberrhein 2010). Walz et al. (2011) and LIKI (2019) consider urban site polygons as fragmentation elements when developing indicators on landscape fragmentation. Such indicators measure the extent to which the landscape is fragmented by technical elements thereby, disturbing the local nature and wildlife as well as recreational activities.

Deilmann et al. (2017) discuss various aspects of the balance between compactness, efficiency and the environmental quality of settlement areas. They claim that the built environment and urban greenery should be explicitly linked in spatial terms, arguing that the delineation of an urban mask from open space in the surrounding area is necessary for the geospatial analysis of settlement structures. Such an urban mask refers to the urbanised areas of a city within its administrative boundaries, containing the contiguous built-up area as well as the spatially- and functionally-related areas of transport, recreation, vegetation and water.

These examples of the various applications in Germany of the geometry of an urban mask illustrate its manifold potential for urban, regional and landscape planning as well as research tasks. Therefore, it would be useful to have such an urban mask at European level, especially as a layer of the Urban Atlas within the framework of the Copernicus Land Monitoring Service (EU 2016). This paper presents a GIS-supported algorithm to generate such a layer from Urban Atlas data. We will demonstrate the method on 30 European cities that cover a wide range of urban structures. Further, the physical shape of the ATKIS urban site will be compared with that of the urban mask, here in the case of Leipzig, Germany. Subsequently, one basic urban metric (shape complexity of the urban space) will be presented and discussed as representative of a number of urban planning tasks which could potentially benefit from the tool of the urban mask. Furthermore, we address the question of a mixed automated-manual technology in the delineation of the urban mask.

Generally, graphics primitives like Polygon , Triangle , Disk and MeshRegion -related functions such as RegionDifference and RegionUnion may help you.

As a starting point for you, here is example D:

I suggest to look up the used symbols in the documentation. Moreover, each documentation page has links to further related symbols. See also Graphics for setting up scenes (including axes, coloring, filling style etc.)

Like Henrik says, it is possible to use the region functionality in Mathematica to define those regions using unions and complements. Another way to define regions is by specifying their boundaries. To this end, Mathematica has a function called FilledCurve :

To get the curved shapes, you may use graphics primitives such as BezierCurve and BSplineCurve .

Even if you choose to work with unions and complements you may want to use FilledCurve to create regions that you can work with. For example, there is no primitive that will allow you create those curved regions directly, but you can easily create them by combining e.g. BezierCurve and FilledCurve .

(Being able to use segments like BezierCurve is also one of the reasons why FilledCurve is preferred over Polygon the simple example in this post could also be created using Polygon but it only works so long as the boundary consists of straight lines.)

This approach also handles geometries with holes in them, but I refer to the documentation for the details on that.

## Supported Features of Nanite

The following sections outline how best to work with Nanite in your project in Unreal Engine 5 Early Access.

### Geometry

Nanite can be enabled on Static Meshes and Geometry Collections .

A mesh with Nanite enabled can be used with the following Component types:

Hierarchical Instanced Static Mesh

Nanite is currently limited to rigid meshes. These represent greater than 90% of the geometry in any typical scene for projects and is the initial focus of Nanite development. Nanite supports dynamic translation, rotation, and non-uniform scaling of rigid meshes, but does not support general mesh deformation, whether it is dynamic or static. This means any position of a Nanite mesh in a way that is more complex than can be expressed in a single 4x3 matrix multiply applied to the entire mesh.

Deformation not supported includes, but is not limited to:

World Position Offset in materials

Nanite meshes also do not currently support:

Vertex painting on instances

This specifically means per-instance painted colors using the editor's Mesh Paint mode.

Vertex colors imported on the original mesh are supported.

The maximum number of instances that can be present in the scene is capped to two million instances. This includes all instances that are streamed in and not just ones enabled for Nanite. Only instances streamed in are counted. This is being actively improved for future releases of Unreal Engine.

Per vertex tangents are not stored from the Static Mesh when it is enabled for Nanite. Instead, tangent space is implicitly derived in the pixel shader. Tangent data is not stored in order to reduce data size. There is a difference in tangent space using this approach that could cause discontinuities at edges. However, this hasn't been shown to be a significant issue and supporting vertex tangent sis planned for a future release of Unreal Engine.

### Materials

The following materials, with the following settings cannot be assigned to Nanite meshes. They will either be disallowed or will have no effect on Nanite meshes if used.

Unsupported materials will use a default material and place a warning in the Output Log with additional details.

Any Blend Mode besides Opaque

This includes Masked and Translucent blend modes

For example, using a Nanite mesh for Mesh Decals

Decal meshes projected onto Nanite meshes is supported

Materials that use the following will not render correctly when applied to a Nanite mesh and may appear visibly broken.

### Rendering

The following rendering features are not currently supported:

View-specific filtering of objects using:

Anything filtered by FPrimitiveSceneProxy::IsShown()

Stereo rendering for Virtual Reality

Multisampling Anti-Aliasing (MSAA)

Raytracing against the fully detailed Nanite mesh

Ray Tracing features are supported but rays intersect the coarse representation (called a proxy mesh) instead of the fully detailed Nanite mesh

Some visualization view modes do not yet support displaying Nanite meshes

Use caution with some visualization modes in the Static Mesh Editor when viewing highly detailed geometry. Viewing Normals and UV can cause problems with editor performance.

### Supported Platforms

Nanite is currently supported on PlayStation 5, Xbox Series S|X, and PCs with graphics cards meeting these specifications, using the latest drivers with DirectX 11 or 12:

## 2.5 Spatial Index-Related Structures

This section describes the structure of the tables containing the spatial index data and metadata. Concepts and usage notes for spatial indexing are explained in Section 1.7. The spatial index data and metadata are stored in tables that are created and maintained by the Spatial indexing routines. These tables are created in the schema of the owner of the feature (underlying) table that has a spatial index created on a column of type SDO_GEOMETRY.

### 2.5.1 Spatial Index Views

There are two sets of spatial index metadata views for each schema (user): xxx_SDO_INDEX_INFO and xxx_SDO_INDEX_METADATA, where xxx can be USER, DBA, or ALL. These views are read-only to users they are created and maintained by the Spatial indexing routines.

#### 2.5.1.1 xxx_SDO_INDEX_INFO Views

The following views contain basic information about spatial indexes:

USER_SDO_INDEX_INFO contains index information for all spatial tables owned by the user.

ALL_SDO_INDEX_INFO contains index information for all spatial tables on which the user has SELECT permission.

DBA_SDO_INDEX_INFO contains index information for all spatial tables on which the user has SELECT permission if the user has the DBA role.

The USER_SDO_INDEX_INFO, ALL_SDO_INDEX_INFO, and DBA_SDO_INDEX_INFO views contain the same columns, as shown Table 2-3, except that the USER_SDO_INDEX_INFO view does not contain the SDO_INDEX_OWNER column. (The columns are listed in their order in the view definition.)

Table 2-3 Columns in the xxx_SDO_INDEX_INFO Views

Column Name Data Type Purpose
SDO_INDEX_OWNER VARCHAR2 Owner of the index (ALL_SDO_INDEX_INFO and DBA_SDO_INDEX_VIEWS only).
INDEX_NAME VARCHAR2 Name of the index.
TABLE_NAME VARCHAR2 Name of the table containing the column on which this index is built.
COLUMN_NAME VARCHAR2 Name of the column on which this index is built.
SDO_INDEX_TYPE VARCHAR2 Contains QTREE (for a quadtree index) or RTREE (for an R-tree index).
SDO_INDEX_TABLE VARCHAR2 Name of the spatial index table (described in Section 2.5.2).
SDO_INDEX_STATUS VARCHAR2 Contains DEFERRED if the index status has been set to deferred (using the index_status keyword with the ALTER INDEX statement) and VALID if the index status is not deferred.

USER_SDO_INDEX_METADATA contains index information for all spatial tables owned by the user. (USER_SDO_INDEX_METADATA is the same as SDO_INDEX_METADATA, which was the only metadata view for Oracle Spatial release 8.1.5.)

ALL_SDO_INDEX_METADATA contains index information for all spatial tables on which the user has SELECT permission.

DBA_SDO_INDEX_METADATA contains index information for all spatial tables on which the user has SELECT permission if the user has the DBA role.

The USER_SDO_INDEX_METADATA, ALL_SDO_INDEX_METADATA, and DBA_SDO_INDEX_METADATA views contain the same columns, as shown Table 2-4. (The columns are listed in their order in the view definition.)

Table 2-4 Columns in the xxx_SDO_INDEX_METADATA Views

Column Name Data Type Purpose
SDO_INDEX_OWNER VARCHAR2 Owner of the index.
SDO_INDEX_TYPE VARCHAR2 Contains QTREE (for a quadtree index) or RTREE (for an R-tree index).
SDO_INDEX_NAME VARCHAR2 Name of the index.
SDO_INDEX_TABLE VARCHAR2 Name of the spatial index table (described in Section 2.5.2).
SDO_INDEX_PRIMARY NUMBER Indicates if this is a primary or secondary index. 1 = primary, 2 = secondary.
SDO_INDEX_PARTITION VARCHAR2 For a partitioned index, name of the index partition.
SDO_PARTITIONED NUMBER Contains 0 if the index is not partitioned or 1 if the index is partitioned.
SDO_TSNAME VARCHAR2 Schema name of the SDO_INDEX_TABLE.
SDO_COLUMN_NAME VARCHAR2 Name of the column on which this index is built.
SDO_INDEX_DIMS NUMBER Number of dimensions of the geometry objects in the column on which this index is built.
SDO_RTREE_HEIGHT NUMBER Height of the R-tree for an R-tree index.
SDO_RTREE_NUM_NODES NUMBER Number of nodes in the R-tree for an R-tree index.
SDO_RTREE_DIMENSIONALITY NUMBER Number of dimensions indexed for an R-tree index.
SDO_RTREE_FANOUT NUMBER Maximum number of children in each R-tree node for an R-tree index.
SDO_RTREE_ROOT VARCHAR2 Rowid corresponding to the root node of the R-tree in the index table for an R-tree index.
SDO_RTREE_SEQ_NAME VARCHAR2 Sequence name associated with the R-tree for an R-tree index.
SDO_RTREE_PCTFREE NUMBER Minimum percentage of slots in each index tree node to be left empty when an R-tree index is created.
SDO_LAYER_GTYPE VARCHAR2 Contains DEFAULT if the layer can contain both point and polygon data, or a value from the Geometry Type column of Table 2-1 in Section 2.2.1.
SDO_LEVEL NUMBER The fixed tiling level at which to tile all objects in the geometry column for a quadtree index.
SDO_NUMTILES NUMBER Suggested number of tiles per object that should be used to approximate the shape for a quadtree index.
SDO_MAXLEVEL NUMBER Maximum level for any tile for any object for a quadtree index. It will always be greater than the SDO_LEVEL value.
SDO_COMMIT_INTERVAL NUMBER Number of geometries (rows) to process, during index creation, before committing the insertion of spatial index entries into the SDOINDEX table.
SDO_FIXED_META RAW If applicable, this column contains the metadata portion of the SDO_GROUPCODE or SDO_CODE for a fixed-level index.
SDO_TABLESPACE VARCHAR2 Same as in the SQL CREATE TABLE statement. Tablespace in which to create the SDOINDEX table.
SDO_INITIAL_EXTENT VARCHAR2 Same as in SQL CREATE TABLE statement.
SDO_NEXT_EXTENT VARCHAR2 Same as in SQL CREATE TABLE statement.
SDO_PCTINCREASE NUMBER Same as in SQL CREATE TABLE statement.
SDO_MIN_EXTENTS NUMBER Same as in SQL CREATE TABLE statement.
SDO_MAX_EXTENTS NUMBER Same as in SQL CREATE TABLE statement.
SDO_RTREE_QUALITY NUMBER Quality score for an R-tree index. Do not attempt to interpret this value directly instead, use the SDO_TUNE.ANALYZE_RTREE procedure and the SDO_TUNE.QUALITY_DEGRADATION function, which are described in Chapter 16.
SDO_INDEX_VERSION NUMBER Internal version number of the index.
SDO_INDEX_GEODETIC VARCHAR2 Contains TRUE if the index is geodetic (see Section 4.1.4) and FALSE if the index is not geodetic.
SDO_INDEX_STATUS VARCHAR2 Contains DEFERRED if the index status has been set to deferred (using the index_status keyword with the ALTER INDEX statement) and VALID if the index status is not deferred.

### 2.5.2 Spatial Index Table Definition

The information in each quadtree spatial index table (each SDO_INDEX_TABLE entry as described in Table 2-4 in Section 2.5.1) depends on whether the index is an R-tree index or a quadtree index.

For an R-tree index, the spatial index table contains the columns shown in Table 2-5.

Table 2-5 Columns in an R-tree Spatial Index Data Table

Column Name Data Type Purpose
NODE_ID NUMBER Unique ID number for this node of the tree.
NODE_LEVEL NUMBER Level of the node in the tree. Leaf nodes (nodes whose entries point to data items in base table) are at level 1, their parent nodes are at level 2, and so on.
INFO BLOB Other information in a node. Includes an array of <child_mbr, child_rowid> pairs (maximum of fanout value, or number of children in each R-tree node, such pairs), where child_rowid is the rowid of a child node, or the rowid of a data item from the base table.

For a quadtree index, the spatial index table contains the columns shown in Table 2-6.

Table 2-6 Columns in a Quadtree Spatial Index Data Table

Column Name Data Type Purpose
SDO_CODE RAW Index entry for the object in the row identified by SDO_ROWID.
SDO_ROWID ROWID Rowid of a row in a feature table containing the indexed object.
SDO_STATUS VARCHAR2 Contains I if the tile is inside the geometry, or contains B if the tile is on the boundary of the geometry.
SDO_GROUPCODE RAW Index entry at level SDO_LEVEL (hybrid indexes only).

For a quadtree index, the SDO_CODE, SDO_ROWID, and SDO_STATUS columns are always present. The SDO_GROUPCODE column is present only when the selected index type is HYBRID.

### 2.5.3 R-Tree Index Sequence Object

Each R-tree spatial index table has an associated sequence object (SDO_RTREE_SEQ_NAME in the USER_SDO_INDEX_METADATA view, described in Table 2-4 in Section 2.5.1). The sequence is used to ensure that simultaneous updates can be performed to the index by multiple concurrent users.

The sequence name is the index table name with the letter S replacing the letter T before the underscore (for example, the sequence object MDRS_5C01$associated with the index table MDRT_5C01$).

## Working with Shape Layers in Adobe After Effects CC (2015 release)

After Effects includes five shape tools: Rectangle, Rounded Rectangle, Ellipse, Polygon, and Star. When you draw a shape directly in the Composition panel, After Effects adds a new shape layer to the composition. You can apply stroke and fill settings to a shape, modify its path, and apply animation presets. Shape attributes are all represented in the Timeline panel, and you can animate each setting over time.

The same drawing tools can create both shapes and masks. Masks are applied to layers to hide or reveal areas or as input into effects shapes have their own layers. When you select a drawing tool, you can specify whether the tool draws a shape or a mask.

### Drawing a shape

You’ll begin by drawing a rectangle with a fill and stroke.

1. Select the Rectangle tool ().
2. Choose Fit from the Magnification Ratio pop-up menu at the bottom of the Composition panel so that you can see the entire composition.

Using the Info panel to guide you, position the cursor at approximately 950, 540, which is near the center of the Composition panel. (You may need to widen the Info panel to see the X and Y coordinates.)

Select the Shape Layer 1 layer name, press Enter or Return, change the layer name to Spiral, and press Enter or Return to accept the change.

### Applying a fill and stroke

You can change the color of a shape by modifying its Fill settings in the Tools panel. Clicking the word Fill opens the Fill Options dialog box, where you can select the kind of fill, its blending mode, and its opacity. Clicking the Fill Color box opens the Adobe Color Picker if the fill is solid, or the Gradient Editor if the fill is a gradient.

Similarly, you can change the stroke color and width of a shape by modifying its Stroke settings in the Tools panel. Click the word Stroke to open the Stroke Options dialog box click the Stroke Color box to select a color.

Select Rectangle 1 in the Timeline panel.

### Twisting a shape

The rectangle is fine, but it isn’t very exciting. In After Effects, you can easily modify a basic shape into something more complex and interesting. You’ll use the Twist path operation to transform this rectangle into a spiral shape.

As you work with the Twist path operation, keep in mind that it rotates a path more sharply in the center than at the edges. Positive values twist clockwise negative values twist counterclockwise.

In the Timeline panel, open the Add pop-up menu next to Contents in the Spiral layer, and choose Twist.

Change the Angle to 220.

The rectangle changes dramatically. Next, you’ll change the center point of the twist to create a larger spiral.

If the center of your spiral looks different from ours, you probably drew a slightly larger or smaller rectangle. You can delete what you have and start over with a fresh composition or try adjusting the x-axis value for Center.

In the Timeline panel, change the x-axis value for Center to .

The spiral is a bit thin. You’ll change the stroke width to thicken it.

Select the Spiral layer in the Timeline panel, and then change the Stroke Width value in the Tools panel to 20 px.

The center of the spiral has a rounded cap, but the end is square. You’ll change the end so that they match.

Choose Round Join from the Line Join menu.

The spiral looks great. Now you just need to center it, so that it looks natural when it rotates, and then you’ll set up its rotation and add motion blur.

Press A to reveal the Anchor Point property for the layer. Then adjust the x-axis and y-axis values until the anchor point is centered in the black center (negative space) of the spiral, just above the center end cap. (The exact values will vary depending on how you created the initial shape.)

Click the Motion Blur switch for the layer, and then click the Enable Motion Blur button () at the top of the Timeline panel.

## Working with Objects in Adobe InDesign CC (2014 release)

In this section, you’ll use various features that allow you to create nonrectangular frames. To begin, you’ll subtract the area of one shape from another. After that, you’ll create a polygon-shaped frame, and then you’ll add rounded corners to a frame.

### Working with compound shapes

You can change the shape of an existing frame by adding other shapes to or subtracting other shapes from its area. The shape of a frame can also be changed, even if the frame already contains text or graphics. Now you’ll subtract a shape from the green background on page 3 to create a white background for the article at the bottom of the page.

Using the Rectangle Frame tool (), draw a frame from where the right edge of the first column meets the horizontal guide at 46p6 on the vertical ruler, to the intersection of the bleed guides that meet outside the lower-right corner of the page.

Draw a rectangle, and snap to the bleed guide corner.

Choose Object > Pathfinder > Subtract to subtract the top shape (the new rectangle) from the green shape. The text frame at the bottom of the page is now on a white background.

A lock icon ( ) is displayed in the upper-left corner of a locked frame. Clicking the icon unlocks the frame.

### Creating polygons and converting shapes

You can use the Polygon tool () or the Polygon Frame tool () to create regular polygons with however many sides you want. You can also change the shape of an existing frame, even if the frame already contains text or graphics. You’ll try this out by creating an octagonal frame, placing a graphic within it, and then resizing the frame.

1. Click the Layers panel icon or choose Window > Layers to open the Layers panel.
2. Click the Graphics layer to select it.
3. Select the Polygon Frame tool () in the Tools panel. It’s grouped with the Rectangle Frame tool () and the Ellipse Frame tool ().

Click anywhere on page 3 to the left of the text “Wasting Time.” In the Polygon dialog box, change Polygon Width and Polygon Height to 9p, change Number Of Sides to 8, and then click OK.

With the polygon shape selected, choose File > Place, and select stopsign.tif in the Links folder in the Lesson04 folder. Click Open.

Using the Selection tool (), drag the midpoint handle on the top of the graphics frame downward until the edge of the frame is even with the top of the Stop sign. Drag the three other midpoint handles so that all of the surrounding area is cropped and only the red of the Stop sign is visible.

Choose View > Fit Page In Window, and then use the Selection tool () to move the frame so that its vertical center edge aligns with the top edge of the text frame to the right that contains the headline (a green Smart Guide is displayed), and its right edge is approximately one gutter width to the left of the right edge of the green background frame. Pause briefly before dragging to display the graphic as you drag.

### Adding rounded corners to frames

Next, you’ll modify a text frame by rounding its corners.

With the Selection tool () still selected, hold down the Z key to temporarily access the Zoom tool (), zoom in on the dark blue text frame on page 1, and then release the Z key to return to the Selection tool.

If the yellow square is not visible when selecting the frame, choose View > Extras > Show Live Corners. Also ensure Screen Mode is set to Normal (View > Screen Mode > Normal).

Select the dark blue text frame, then click the small yellow square that’s slightly below the resizing handle at the upper-right corner of the frame. Four small yellow diamonds replace the four resizing handles at the corners of the frame.

After you create rounded corners, you can Alt-click (Windows) or Option-click (Mac OS) any of the diamonds to cycle through several different corner effects.

Drag the diamond at the upper-right corner of the frame to the left and release the mouse button when the live radius (R:) value is approximately 2p0. As you drag, the other three corners change, too. (If you hold down the Shift key when dragging, only the corner you are working on changes.)