As part of an essay (including a listing of the 3D PGA reference implementation ripga3d.jl in the appendix) proposing that Julia + Makie + projective geometric algebra (PGA) are an excellent combination for implementing intense geometry applications, I’m trying to port bivector.net’s 3D slicer application (e.g., for 3D printing) from JavaScript to Julia and Makie.

The moving horizontal slice looks good in the 2D animation but not in the 3D animation (because the previous horizontal slice in the 3D animation is not erased). I wasn’t able to get the Observable @view or the delete!() to erase the previous horizontal slice in Axis3. Any suggestions?

```
# tslice.jl : test tetrahedron slice
# to test Julia port of ganja.js 3D slicing example
#
# The test tetrahedron has three faces (the base face
# is empty), all edges of length 2.0, and a peak that
# is directly above (i.e., z offset) the origin. All the
# test tetrahedron's vertices and faces are defined,
# according to the wavefront 3D object file format,
# by seven lines of text (within the following
# multiline comment):
#=
v 1.0 -0.5773502692 0.0
v 0.0 1.15470053838 0.0
v -1.0 -0.5773502692 0.0
v 0.0 0.0 1.632993162
f 1 2 4
f 2 3 4
f 3 1 4
=#
using GLMakie, GLMakie.FileIO
using GeometryBasics
include("ripga3d.jl")
function tslice()
# load and scale (by 13) faces of bunny object
F = load("tetrahedron.obj")
nFace = length(F)
# define cut line segment buffer & references to it
LS = fill(NaN32, 3*nFace, 3)
nLS = 0
nPrevLS = 0
s2d::Any = 0
s3d::Any = 0
# precalculate face vector and triangle side bivectors
FS3 = Array{Float32,2}(undef,64,nFace)
for iF = 1:nFace # for each triangle face in bunny object
P1 = point(F[iF][1][1],F[iF][1][2],F[iF][1][3])
P2 = point(F[iF][2][1],F[iF][2][2],F[iF][2][3])
P3 = point(F[iF][3][1],F[iF][3][2],F[iF][3][3])
# P12 = ga"P1∨P2"
# P23 = ga"P2∨P3"
# P31 = ga"P3∨P1"
# FS3[ 1:16,iF] = ga"P1∨P2∨P3" # face
# FS3[17:32,iF] = ga"FS3[1:16,iF]·P12" # side 1
# FS3[33:48,iF] = ga"FS3[1:16,iF]·P23" # side 2
# FS3[49:64,iF] = ga"FS3[1:16,iF]·P31" # side 3
P12 = P1 & P2
P23 = P2 & P3
P31 = P3 & P1
FS3[ 1:16,iF] = P1 & P2 & P3 # face
FS3[17:32,iF] = FS3[1:16,iF] | P12 # side 1
FS3[33:48,iF] = FS3[1:16,iF] | P23 # side 2
FS3[49:64,iF] = FS3[1:16,iF] | P31 # side 3
end
# initialize figures
fig = Figure(resolution = (1000, 500))
ax3d = Axis3(fig[1,1],
elevation = pi/16,
azimuth = -3*pi/4,
viewmode = :fit,
aspect = (1,1,1))
ax2d = Axis(fig[1,2],
limits = (-1,1, -0.75,1.25),
yticks = (-0.75:0.5:1.25),
title = "cross section at horizontal slice plane",
aspect = 1)
m = mesh!(ax3d, F)
# perform slicing
zMax = 1.632993162
nFrame = 360
record(fig, "tslice.mp4", 1:nFrame) do frame
ax3d.azimuth[] = -3pi/4 - 2pi*(frame-1)/nFrame
zCut = zMax - abs(zMax - 2*zMax*(frame-1)/nFrame)
cut = zCut*e0 - e3
# erase old slice
if nPrevLS > 0
delete!(ax2d, s2d)
# NOTE: currently, delete! on ax3d causes the following error:
# ERROR: MethodError: no method matching delete!(::Axis3, ::Lines{Tuple{Vector{Point{3, Float32}}}})
# delete!(ax3d, s3d)
nPrevLS = 0
end
for iF = 1:nFace
N = FS3[1:16,iF]
side1 = FS3[17:32,iF]
side2 = FS3[33:48,iF]
side3 = FS3[49:64,iF]
# lc = ga"N∧cut"
# P1 = ga"lc∧side1" # line^plane->point
lc = N ^ cut
P1 = lc ^ side1 # line^plane->point
nPoint = 0
if P1[15] != 0
nPoint += 1
iLS = 3*nLS + nPoint
LS[iLS,:] = [P1[14] P1[13] P1[12]] ./ P1[15]
end
# P2 = ga"lc∧side2" # line^plane->point
P2 = lc ^ side2 # line^plane->point
if P2[15] != 0
nPoint += 1
iLS = 3*nLS + nPoint
LS[iLS,:] = [P2[14] P2[13] P2[12]] ./ P2[15]
end
# P3 = ga"lc∧side3" # line^plane->point
P3 = lc ^ side3 # line^plane->point
if P3[15] != 0
nPoint += 1
iLS = 3*nLS + nPoint
LS[iLS,:] = [P3[14] P3[13] P3[12]] ./ P3[15]
end
if nPoint == 2
nLS += 1
elseif nPoint == 3
iLS = 3*nLS + 3
LS[iLS,:] .= NaN32
end
end # for each face
# plot new slice
if nLS > 0
slice2d = @view LS[1:3*nLS,1:2]
s2d = lines!(ax2d, slice2d, color=:black)
slice3d = @view LS[1:3*nLS,:]
s3d = lines!(ax3d, slice3d, color=:white)
nPrevLS = nLS
nLS = 0 # reset line segment buffer
end
end # for each video frame
end # tslice()
```