I?m still working on my package RCGAL, that I already present in a previous post.
This previous post was about the reconstruction of surfaces. Now I implemented the Boolean operations on meshes. Here are some simple examples.
Union of two cubes:
Intersection of two cubes (one rotated):
Difference of two cubes:
Intersection of a cube and a truncated icosahedron:
The code generating these plots is given in the RCGAL examples.
Now let?s turn to a more interesting example.
The compound of five tetrahedra
The compound of five tetrahedra is provided by RCGAL.
These are five tetrahedra in a pretty configuration, each centered at
the origin. You can get their meshes by typing
tetrahedraCompound. This is a list with two components: a
meshes providing for each tetrahderon its vertices
and its faces, and a field
rglmeshes, similar to
meshes but these meshes are ready for plotting with the
rgl package. Here it is:
library(RCGAL) library(rgl) rglmeshes <- tetrahedraCompound[["rglmeshes"]] open3d(windowRect = c(50, 50, 562, 562), zoom = 0.75) bg3d("#363940") colors <- hcl.colors(5, palette = "Spectral") invisible(lapply( 1:5, function(i) shade3d(rglmeshes[[i]], color = colors[i]) ))
I wondered for a long time what is the intersection of these five tetrahedra. But I didn?t have any tool to compute it. Now I have. Let?s see.
# compute the intersection #### inter <- MeshesIntersection( tetrahedraCompound[["meshes"]], numbersType = "lazyExact", clean = TRUE ) # plot #### open3d(windowRect = c(50, 50, 562, 562), zoom = 0.75) bg3d("#363940") # first the five tetrahedra with transparency #### invisible(lapply( rglmeshes, shade3d, color = "yellow", alpha = 0.1 )) # now the intersection #### rglinter <- tmesh3d( "vertices" = t(inter[["vertices"]]), "indices" = t(inter[["faces"]]), "homogeneous" = FALSE ) shade3d(rglinter, color = "gainsboro") # and finally the edges #### plotEdges( inter[["vertices"]], inter[["exteriorEdges"]], only = inter[["exteriorVertices"]], color = "darkmagenta" )
Here is the result:
This is an icosahedron, I think.
Unfortunately, R CMD CHECK still throws some warnings which prevent me to publish this package on CRAN. I hope this issue will be solved.