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.

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 them`sc_vertex()`

- only unique coordinates (in some geometric space)`sc_path()`

- individual paths, sequential traces`sc_edge()`

- unique binary relations, unordered segments (segments and edges are currently under review, and may change)`sc_segment()`

- all instances of edges`sc_arc()`

- unique topological paths, arcs either meet two other arcs at a node, or include no nodes`sc_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.

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.

`SC`

is the universal model, composed of binary relationships, edges defined by pairs of vertices (a structural primitive model)`TRI`

also a structural primitive model, for triangulations`PATH`

a sequential model, for the standard spatial vector types, shapes defined by*paths*`ARC`

a sequential model, for*arc-node topology*a shared-boundary decomposition of path models`SC0`

is a stripped down structural model analogous to`SC`

, 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.

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).

```
# Install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("hypertidy/silicate")
```

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
```

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.

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.

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