library(silicate)

Implicit and explicit topology

Topology is the inherent underlying shape structure of data and silicate is clear on the distinction. There are two kinds of data structures that are abandoned by geospatial vector formats: surfaces and ordered linear paths. This might sound controversial but really is not, it’s a trivial phrasing of what is in the simple features standard. This is why silicate treats “spatial polygons” as PATH forms, because they are inherently linear structures and any surface interpretation is purely implicit (winding or even-odd rule). For an explicit surface, silicate requires a truly surface-based form, with triangular primitives.

Silicate itself only inclues ear-clipping triangulation, a relatively cheap method suitable for implicit surfaces using closed paths. A more sophisticated meshing triangulation is available in the anglr package. The anglr package is less strict than silicate, and will happily treat many path-based data structures as implicit surfaces, and so we can plot3d() or as.mesh3d() a polygon or line layer and it will do its best to generate a true explicit surface. We can otherwise use the silicate model TRI() or TRI0() or the anglr models DEL() or DEL0() to actually work with the data structure in use (not just a visual side-effect).

It’s important to know what is the simplest vs more complex ways of creating surfaces. In general, TRI0() is cheapest, and DEL() is most expensive - but the former requires paths, and the latter works with edges. The cheapest one, is TRI0(). TRI() is next expensive (adds visible property, and native orientation, and arbitrary subsetting) … but cheap triangles, next is DEL0() (control over area, angle, Steiner points, Delaunay constraint, etc), then DEL().

• DEL must be composed from edges, and edges can come from any model
• TRI must be composed from close paths, there’s no path in SC, ARC or TRI
• DEL0 should exist, and be the default workhorse
• TRI cannot be set-vectorized, we have to call earcut for each POLYGON
• DEL is set-vectorized, classify all triangles by intersection with input paths (or holes)
• triangles in DEL that fall in holes are not visible, but don’t need to be removed
• if we DEL a TRI we could test triangle inclusion to classify the triangles that are in holes