[R] Visualization of a Convex Hull in R (Possibly with RGL)

[Duncan Murdoch]

On 26/07/2016 10:34 AM, Lorenzo Isella wrote:
> On Tue, Jul 26, 2016 at 10:48:22AM +0000, Michael Sumner wrote:
>> On Tue, 26 Jul 2016 at 20:29 Lorenzo Isella <lorenzo.isella at gmail.com>
>> wrote:
>>
>>> Dear All,
>>> I am not an expert about the calculation and visualization of convex
>>> hulls, but I am trying to do something relatively simple.
>>> Please consider the snippet at the end of the email.
>>> The array pts  represents the position of (the centres of) a set of
>>> spheres in 3D (whose radius is 0.5).
>>> I found the geometry package which provides bindings to the qhull
>>> (http://www.qhull.org/) library and allows me to calculate the convex
>>> hull of pts and some interesting properties, like the area and the
>>> volume of the convex hull.
>>> That is all fine, but I would like to represent the results in 3D.
>>> I would like to see a set of spheres with the given position in pts
>>> and the radius R=0.5 and the convex hull going based on the
>>> coordinates of pts.
>>> Does anybody know how to achieve that?
>>> Many thanks
>>>
>>> Lorenzo
>>>
>>>
>>>
>>> ####################################################################
>>>
>>>
>>> library(geometry)
>>>
>>>
>>>
>>> pts <- read.table("test-agg.dat")
>>>
>>> ## names(pts) <- c("x", "y", "z")
>>>
>>>
>>> pts <- structure(list(x = c(0.145138112090815, 0.880429452229448,
>>> -1.66682740805663,
>>> -0.955356943224252, 1.09396798448412, -2.63620653885452,
>>> 0.190270563436841,
>>> 2.77638842095489, -0.0914977922901252, -0.484087722062158,
>>> 0.674992784754569,
>>> 1.02571108118502, 2.78789154912298, -0.146882388586427,
>>> -1.71507089246001,
>>> -1.87886026272455, 6.61540228778138, 7.46818822627362,
>>> 4.80777628045963,
>>> 6.35487269602107, 4.70026626314108, 3.44366671298125,
>>> 2.92460648354883,
>>> 5.07053866161192, 7.2164343710271, 6.93292242981006, 7.84238243682145,
>>> 7.4321237311656, 9.59692827237335, 8.3454086671306, 6.574251622581,
>>> 6.93340304175759), y = c(-0.189309482569001, 1.67057595730283,
>>> -0.995542605143325, 2.31599069771684, 1.79876139786291,
>>> 0.165886909346058,
>>> 2.70740725397259, 1.70535678189514, -0.819087329147786,
>>> 0.967935667739331,
>>> -2.53860079551206, -1.60932884056828, -1.42050583991613,
>>> -2.36883245674979,
>>> 0.191848867151458, -1.58255618338079, 1.98324724741419,
>>> 3.0095048680572,
>>> 1.97159273200079, 2.26459561200295, 0.4461804374566, 1.87939977307282,
>>> 1.98510457359889, -0.103495422088799, -1.32050185858493,
>>> 0.584580736435273,
>>> -2.97562362406436, 0.106204178143333, -2.0843758994948,
>>> -1.1492729389287,
>>> -2.13797391772643, -4.45916649729404), z = c(-1.44428170702261,
>>> -1.45742688370091, -1.70267889327056, -1.93637881287001,
>>> -3.4452409532781,
>>> -3.02436538816822, 0.114790290814684, -2.10208878117278,
>>> 2.07425243689128,
>>> 1.26652602551291, 1.39914827137784, -0.345006925422662,
>>> 0.596828021941431,
>>> 3.351773622867, 2.68408561840144, 3.97006405709929, 0.82767367646934,
>>> -0.662142231346811, 1.68344957582882, 2.92819854377685,
>>> 0.386683699222387,
>>> -0.220305098209874, 2.37510769001993, -1.51041233970289,
>>> -0.707073219742548,
>>> -1.24585080403725, -1.63914669343685, 0.683153891726357,
>>> -1.26623658129696,
>>> 1.95073173465968, -2.94804638502708, -0.635785458903106)), .Names =
>>> c("x",
>>> "y", "z"), class = "data.frame", row.names = c(NA, -32L))
>>>
>>> res<-convhulln(pts, options = "FA")
>>>
>>>
>> In short
>>
>> library(rgl)
>> bg3d("grey")
>> spheres3d(pts, radius = 0.5, col = "white")
>> ## triangle functions generally expect triplets of points, one after another
>> ## and hull/triangulation functions generally return arrays of indexes
>> ## so transpose index of hull is the right order to draw triangles
>> triangles3d(pts[t(res$hull), ], col = "firebrick", alpha = 0.3)
>>
>> (But, I wonder if you mean to find the convex hull based on the outer shell
>> of those spheres? )
>>
>> Cheers, Mike.
>>
>
>
>
> Dear Mike,
> Thanks a lot, this is spot on.
> Yep, if possible I would even prefer to have the convex hull based on
> the outer shell of the spheres, but I wonder if that is easy to
> achieve with a few lines of code.
> Any ideas would be welcome.

The convex hull of a set of spheres isn't a polyhedron (parts of the 
spheres will appear in it, and it will have curved edges).  Shapes like 
that are hard to draw in rgl.

Duncan Murdoch