Common Forms for Complex Hierarchical and Relational Data Structures.
Overview
The goal of silicate is to bridge planar geospatial data types with flexible mesh data structures and visualization.
We aim to provide
- a common-form for representing hierarchical data structures
- a universal converter between complex data types
- topological primitives for analysis and exploration.
The core of silicate are worker functions that are generic and work with any kind of data that has hierarchical structure. These functions work on models, that include various formats (sf, sp, trip) and also on silicate models themselves.
Functions
We have the following worker verbs, designed to work with many spatial data formats and with silicate’s own structures.
sc_object()- highest level properties, the “features”sc_coord()- all instances of coordinates, labelled by vertex if the source model includes themsc_vertex()- only unique coordinates (in some geometric space)sc_path()- individual paths, sequential tracessc_edge()- unique binary relations, unordered segments (segments and edges are currently under review, and may change)sc_segment()- all instances of edgessc_arc()- unique topological paths, arcs either meet two other arcs at a node, or include no nodessc_node()- unique nodes
The idea is that each function can return the underlying entities of a data object, no matter its underlying format. This interoperability design contrasts with major spatial packages that require format peculiarities in order to work, even when these details are not relevant.
Models
Silicate defines a number of key models to represent various interpretations of hierarchical (usually spatial) data. These are SC, PATH, ARC and TRI. Most models have a counterpart structurally-optimized version with a similar name: SC0, PATH0, TRI0. Other models are possible, and include DEL in the in-development anglr package that extends TRI.
Each model is composed of a type of primitive, and each provides a normalization (de-duplication) of geometry for efficiency and or topology. Silicate quite deliberately separates the concepts of geometry and topology completely. Primitives define the topology (edges, paths, arcs, or triangles) and the vertex table defines the geometry. We reserve the names x_, y_, t_ (time) and z_ (elevation) for the usual geometric dimensions, and these are treated specially by default. No limit is put geometric dimension however, it’s possible to store anything at all on the vertex table. Some models include an object table, and this represents a higher level grouping of primitives (and corresponds to features in SF).
The most general model is SC, composed of three tables vertex, edge and object and all entities are explicitly labelled. Indexes between tables are unique and persistent and arbitrary, they can be arbitrarily accessed. This is closely related to the more bare-bones SC0 model, composed of only two tables vertices, and objects. These are related structurally by nesting the relations within the object table. Here the relations are not persistent, so we can subset the objects but we cannot change the vertex table with updating these indexes.
SC0 can deal with 0-dimensional topology types (points) as well as 1-dimensional types (edges), but SC is strictly for edges.
Further models PATH, ARC, and TRI cover a broad range of complex types, and each is fundamental and distinct from the others. SC can be used to represent any model, but other models provide a better match to specific use-cases, intermediate forms and serve to expand the relationships between the model types.
SCis the universal model, composed of binary relationships, edges defined by pairs of vertices (a structural primitive model)TRIalso a structural primitive model, for triangulationsPATHa sequential model, for the standard spatial vector types, shapes defined by pathsARCa sequential model, for arc-node topology a shared-boundary decomposition of path modelsSC0is a stripped down structural model analogous toSC, there are only implicit relations of object to vertices, with a nested list of edge indexes
The models PATH0 and ARC0 are in-development. By analogy to SC0 they will be composed of two tables, object and vertex with nested structural-index tables on object holding the path and arc indexes that are row numbers of vertex. It’s not clear yet if this vertex table should be de-duplicated.
Earlier versions included a mix of these models, and the definitions have changed many times. Still a work-in-progress.
An extension of the TRI model DEL is provided in anglr which builds high-quality triangulations, but the structural representation is the same.
Each model is created by using a set of generic verbs that extract the underlying elements of a given model. This design means that the models themselves are completely generic, and methods for worker verbs can be defined as needed for a given context. Our ideal situation would be for external packages to publish methods for these verbs, keeping package-specific code in the original package. We think this provides a very powerful and general mechanism for a family of consistent packages.
There is another important function unjoin() use to normalize tables that have redundant information. The unjoin() isthe opposite of the database join, and has a nearly identical counterpart in the dm package with its decompose_table(). Unjoin is the same as tidyr::nest() but returns two tables rather than splitting one into the rows of other.
The unjoin is a bit out of place here, but it’s a key step when building these models, used to remove duplication at various levels. It’s the primary mechanism for defining and building-in topology, which is precisely the relationships between entities in a model. This function is published in the CRAN package unjoin.
Arbitrarily re-composable hierarchies
The common “well-known” formats of encoding geometry (WKB/WKT for binary/text) represent (pre-)aggregated data, yet the input levels of aggregation are often not directly relevant to desired or desirable levels of aggregation for analysis. A key stage in many GIS analyses is thus an initial disaggregation to some kind of atomic form followed by re-aggregation.
We propose a common form for spatial data that is inherently disaggregated, that allows for maximally-efficient on-demand re-aggregation (arbitrarily re-composable hierarchies), and that covers the complexity of geometric and topological types widely used in data science and modelling. We provide tools in R for more general representations of spatial primitives and the intermediate forms required for translation and analytical tasks. These forms are conceptually independent of R itself and are readily implemented with standard tabular data structures.
There is not one single normal form that should always be used. There is one universal form that every other model may be expressed in, but also other forms that are better suited or more efficient for certain domains. We show that conversion between these forms is more straightforward and extensible than from SF or related types, but is also readily translated to and from standard types. The most important forms we have identified are “universal” (edges and nodes), “2D primitives” (triangles), “arcs” (shared boundaries), and “paths” (normalized forms of SF types).
Installation
# Install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("hypertidy/silicate")
Usage
Convert a known external model to a silicate model.
library(silicate)
#>
#> Attaching package: 'silicate'
#> The following object is masked from 'package:stats':
#>
#> filter
x <- SC(minimal_mesh) ## convert simple features to universal form
y <- ARC(minimal_mesh) ## convert simple features to "arc-node" form
Obtain the elements of a known model type.
sc_vertex(x)
#> # A tibble: 14 × 3
#> x_ y_ vertex_
#> <dbl> <dbl> <chr>
#> 1 0 0 n88USC
#> 2 0 1 tQxSvg
#> 3 0.2 0.2 zpYYIG
#> 4 0.2 0.4 1qRN7h
#> 5 0.3 0.6 3FN2ty
#> 6 0.5 0.2 HInlqb
#> 7 0.5 0.4 KHLNO5
#> 8 0.5 0.7 gqkZ6j
#> 9 0.69 0 yJGoeK
#> 10 0.75 1 raggYW
#> 11 0.8 0.6 xekZyd
#> 12 1 0.8 XBwKMi
#> 13 1.1 0.63 9fpRi6
#> 14 1.23 0.3 0mxEDK
sc_edge(x)
#> # A tibble: 15 × 4
#> .vx0 .vx1 path_ edge_
#> <chr> <chr> <int> <chr>
#> 1 n88USC tQxSvg 1 mHkjqV
#> 2 tQxSvg raggYW 1 knBf33
#> 3 raggYW XBwKMi 1 NQVyd6
#> 4 gqkZ6j XBwKMi 1 avIufa
#> 5 gqkZ6j xekZyd 1 TCSls3
#> 6 yJGoeK xekZyd 1 AAMn9v
#> 7 n88USC yJGoeK 1 CwiGwr
#> 8 zpYYIG HInlqb 2 naREkh
#> 9 HInlqb KHLNO5 2 TptXFI
#> 10 3FN2ty KHLNO5 2 3nlZMA
#> 11 1qRN7h 3FN2ty 2 eXVs6C
#> 12 zpYYIG 1qRN7h 2 AwOvSP
#> 13 xekZyd 9fpRi6 3 gIpLK6
#> 14 9fpRi6 0mxEDK 3 OnFWZr
#> 15 yJGoeK 0mxEDK 3 q1WBzB
sc_node(y)
#> # A tibble: 2 × 1
#> vertex_
#> <chr>
#> 1 yUZl0a
#> 2 Z0xCkI
sc_arc(y)
#> # A tibble: 4 × 2
#> arc_ ncoords_
#> <chr> <int>
#> 1 bpKiyx 4
#> 2 oSxSsU 5
#> 3 q3ZSRx 7
#> 4 yUVgqO 2
silicate models
There are two kinds of models, primitive and sequential.
Primitive-based models are composed of atomic elements that may be worked with arbitrarily, by identity and grouping alone.
Sequential-based models are bound to ordering and contextual assumptions. We provide the PATH and ARC models as generic, relational forms that provide a convenient intermediate between external forms and primitives models. Further intermediate models exist, including monotone and convex decompositions of polygons.
There is one universal primitives-based model, an edge-only model with two tables at its core. Higher level structures are described by grouping tables, with as many levels as required. Any other model can be expressed in this form.
We also differentiate structural primitives, which are specializations that are more convenient or more efficient in certain cases. These include triangulations (2D primitives), and segment structures (1D primitives), and could provide higher dimensional forms (3D primitives, etc. ).
Currently, we provide support for the universal model SC, the sequential models PATH (simple features belongs here, amongst many others) and ARC (arc-node topology, TopoJSON-like, OpenStreetMap), and structural primitives TRI.
In practice a segment model is trivial to generate, “SEG” but we haven’t done that. This would be analogous to the format used by rgl::rgl.lines or spatstat::psp.
We take care to allow for labelling (identity) of component elements, without taking full responsibility for maintaining them. Random IDs are created as needed, but any operation that works with existing IDs should be stable with them.
Context, and some related projects
The spacebucket (arbitrary multi-layer polygonal overlays) and sphier (generic hierarchies from atomic forms) show two different approaches to the problem of hierarchical data and flexible representations.
The key difference between the silicate approach and simple features is the separation of geometry and topology. This allows for normalization (de-duplication) of the entities that are present or that can be identitied. Simple features has no capacity to de-duplicate or otherwise identify vertices, edges, paths or arcs, though tools that work with simple features do construct these schemes routinely in order to perform operations. When these richer, topological structures are built they are usually then discarded and the vertices are again de-normalized and again expressed explicitly without recording any of the relationships. In this sense, simple features can be described as an explicitly-stored PATH analogue, and is no different from the model used by shapefiles, binary blobs in databases, and many other spatial vector formats. There are a number of notable exceptions to this including TopoJSON, Eonfusion, PostGIS, QGIS geometry generators, Fledermaus, Mapbox, WebGL, Threejs, D3, AFrame, Lavavu but unfortunately there’s no overall scheme that can unify these richer structures.
The silicate family is composed of a small number of packages that apply the principles here, either to read from path forms or primitive forms. As work continues some of these will be incorporated into the silicate core, when that is possible without requiring heavy external dependencies.
Looking for a music reference? I always am: Child’s Play, by Carcass.
Please note that the ‘silicate’ project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.