CODEWITHSUNDEEP
rrgl
Rafa
Rafa

Reputation: 169

Calculating projection of 3D mesh onto arbitrary directions

I have 3D meshes representing closed surfaces not necessarily convex for which I would like to get orthographic projections onto arbitrary directions (to put in context, the 3D meshes represent satellites and the end goal is to use the projections to calculate atmospheric drag).

As a first step, I am just aiming to compute the surface area of the resulting projection. Is there any way to perform such operation with rgl? Since the meshes represent closed surfaces, the projections will not contain multiple disconnected polygons.

I believe I can get the set of triangles/quads visible from a given direction by using the facing3d() function, specifying the direction in the up argument. But I am unsure on how to proceed from there.

Upvotes: 0

Views: 253

Answers (1)

user2554330
user2554330

Reputation: 44867

You can do the projections using the rgl::shadow3d() function, and calculate area using geometry::polyarea(). For example,

library(rgl)
library(geometry)

satellite <- translate3d(icosahedron3d(), x = 0, y = 0, z = 5) 

vertices <- asEuclidean2(satellite$vb)

xrange <- range(vertices[1,])
yrange <- range(vertices[2,])

floor <- mesh3d(x = c(2*xrange, 2*rev(xrange)),
                y = rep(2*yrange, each = 2),
                z = 0, quads = 1:4)

open3d()
#> glX 
#>   1
shadow <- shadow3d(floor, satellite, plot = FALSE, 
                   minVertices=1000 # Need this to get a good shadow
                   )
shade3d(satellite, col= "red")
shade3d(floor, col = "white", polygon_offset = 1, alpha = 0.1)
shade3d(shadow, col = "gray")



vertices <- unique(t(asEuclidean2(shadow$vb)))[,1:2]
hull <- chull(vertices)
hullx <- vertices[hull,1]
hully <- vertices[hull,2]
plot(c(hullx, hullx[1]), c(hully, hully[1]), type = "l")


polyarea(hullx, hully)
#> [1] 3.266855

Created on 2022-12-13 with reprex v2.0.2

Upvotes: 1

Related Questions