# Does delete! or Observable @view work with Axis3?

**URL:** <https://discourse.julialang.org/t/does-delete-or-observable-view-work-with-axis3/94061>\
**Category:** General Usage\
**Tags:** makie, geometric-algebra\
**Created:** [February 4, 2023, 6:18pm UTC](https://discourse.julialang.org/t/does-delete-or-observable-view-work-with-axis3/94061 "2023-02-04T18:18:09Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![g2g](https://avatars.discourse-cdn.com/v4/letter/g/41988e/32.png) [@g2g](https://discourse.julialang.org/u/g2g)\
**Post date:** [February 4, 2023, 6:18pm UTC](https://discourse.julialang.org/t/does-delete-or-observable-view-work-with-axis3/94061/1 "2023-02-04T18:18:09Z")

</div>

As part of an [essay](https://medium.com/@olarth/julia-and-projective-geometric-algebra-e2d5abb11519) (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](http://bivector.net)’s [3D slicer application](https://enkimute.github.io/ganja.js/examples/coffeeshop.html#pga3d_slicing) (e.g., for 3D printing) from JavaScript to Julia and Makie.

![tslice](https://global.discourse-cdn.com/julialang/original/3X/b/c/bc89cc1fe1ee58739a154f01caa83d4ee6378b57.gif)

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?

```julia
 # 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()

```

---

<div class="post-metadata">

**Author:** ![jules](https://avatars.discourse-cdn.com/v4/letter/j/41988e/32.png) [@jules](https://discourse.julialang.org/u/jules)\
**Post date:** [February 4, 2023, 6:55pm UTC](https://discourse.julialang.org/t/does-delete-or-observable-view-work-with-axis3/94061/2 "2023-02-04T18:55:15Z")

</div>

Do not execute `lines!` in every frame, instead do it once at the beginning with an `Observable` that holds the first set of points (or an empty vector). Then compute your new points in each frame and update the observable. The steps are roughly like this:

```julia
points = Observable(Point2f[])
lines!(ax, points)
for frame in frames
    points[] = calculate_new_points(frame)
end

```

It doesn’t have to be a vector of `Point2f` but there might be an edge case if you start with an empty matrix, not sure. Maybe it works if you make it a 0 by 2 matrix, but I think the conversion pipeline has to recognize what kind of point the matrix stores, 2d or 3d.

If you want to keep using your `LS` array, you can wrap it in an `Observable`, mutate it like you’re already doing it, and then call `notify` on the observable when you’re done mutating. The inputs of the two `lines` can then be derived from this basis using the logic you have written out already. An example:

```julia
LS_obs = Observable(LS)
slice_2d = @lift @view $LS_obs[1:3*nLS, 1:2]

# or you could write equivalently
slice_2d = lift(LS_obs) do array
    @view array[1:3*nLS, 1:2]
end

lines!(ax2d, slice_2d)
for frame in frames
    mutate_somehow!(LS)
    notify(LS_obs) # now slice_2d will update with the new data and the lines plot will, too
end
```

---

<div class="post-metadata">

**Author:** ![g2g](https://avatars.discourse-cdn.com/v4/letter/g/41988e/32.png) [@g2g](https://discourse.julialang.org/u/g2g)\
**Post date:** [February 5, 2023, 8:59pm UTC](https://discourse.julialang.org/t/does-delete-or-observable-view-work-with-axis3/94061/3 "2023-02-05T20:59:10Z")

</div>

> [@jules](#):
>
> An example:

Thanks for giving that example. (I would never have thought of adding a second layer of Observable.)

Removing the complexity of projective geometric algebra, here is an MWE.  
 ![tmslice](https://global.discourse-cdn.com/julialang/original/3X/a/d/ad94c07cd793eff0e37698acfed70b30e120252d.gif)

```julia
# tmslice.jl : test tetrahedron slice
# to test Makie 2d and 3d plotting
#
# 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

function tmslice()
	# load mesh of 3D object
	F = load("tetrahedron.obj")
	nFace = length(F)
	
	# 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 = "horizontal cross section",
		aspect = 1)
	m = mesh!(ax3d, F)
	
	# plot first slice
	nFrame = 360
	zMax = 1.632993162
	ZLR = LinRange(-zMax, zMax, nFrame+1)
	Z = zMax .- abs.(ZLR)
	rMax = 1.15470053838
	R = abs.(LinRange(-rMax, rMax, nFrame+1))
	THETA = LinRange(pi/2, 5*pi/2, 4)
	LS = fill(NaN32, 15, 3) # Line Segment buffer 
	LS[1:4,1] = R[1] .* cos.(THETA)
	LS[1:4,2] = R[1] .* sin.(THETA)
	LS[1:4,3] .= Z[1]
	LS_obs = Observable(LS)
	slice2d = @lift @view $LS_obs[1:5, 1:2]
	slice3d = @lift @view $LS_obs[1:5, :]
	lines!(ax2d, slice2d, color=:black)
	lines!(ax3d, slice3d, color=:black, linewidth=5)
	fig
	
	# record video of slicing
	record(fig, "tmslice.mp4", 1:nFrame) do iFrame
		ax3d.azimuth[] = -3pi/4 - 2pi*(iFrame-1)/nFrame
		LS[1:4,1] = R[iFrame] .* cos.(THETA)
		LS[1:4,2] = R[iFrame] .* sin.(THETA)
		LS[1:4,3] .= Z[iFrame]
		notify(LS_obs)
	end
end # tmslice()

```

I was concerned about plotting a variable number of line segments in the slices, but that works too!  
 ![tm2slice](https://global.discourse-cdn.com/julialang/original/3X/d/b/db7c510adc6adc6a4b63133f19c309e9b2045635.gif)

```julia
# tm2slice.jl : test tetrahedron slice
# to test Makie 2d and 3d plotting when the
#	number of line segments per slice varies
#
# 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

function tm2slice()
	# load mesh of 3D object
	F = load("tetrahedron.obj")
	nFace = length(F)
	
	# 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 = "horizontal cross section",
		aspect = 1)
	m = mesh!(ax3d, F)
	
	# plot first slice
	nFrame = 360
	zMax = 1.632993162
	ZLR = LinRange(-zMax, zMax, nFrame+1)
	Z = zMax .- abs.(ZLR)
	rMax = 1.15470053838
	R = abs.(LinRange(-rMax, rMax, nFrame+1))
	THETA = LinRange(pi/2, 5*pi/2, 4)
	LS = fill(NaN32, 15, 3) # Line Segment buffer 
	LS[1:4,1] = R[1] .* cos.(THETA)
	LS[1:4,2] = R[1] .* sin.(THETA)
	LS[1:4,3] .= Z[1]
	nTri = 1
	LS_obs = Observable(LS)
	slice2d = @lift @view $LS_obs[1:5*nTri, 1:2]
	slice3d = @lift @view $LS_obs[1:5*nTri, :]
	lines!(ax2d, slice2d, color=:black)
	lines!(ax3d, slice3d, color=:black, linewidth=5)
	fig
	
	# record video of slicing
	record(fig, "tm2slice.mp4", 1:nFrame) do iFrame
		ax3d.azimuth[] = -3pi/4 - 2pi*(iFrame-1)/nFrame
		
		iSet = div(iFrame, 8, RoundDown)
		nTri = mod(iSet, 3) + 1
		for iTri = 1:nTri
			i = 5*(iTri-1) + 1 # starting index of triangle
			s = 1 + (iTri-1)*0.10 # scale of triangle
			LS[i:i+3,1] = (R[iFrame]*s) .* cos.(THETA)
			LS[i:i+3,2] = (R[iFrame]*s) .* sin.(THETA)
			LS[i:i+3,3] .= Z[iFrame]
		end
		notify(LS_obs)
	end
end # tm2slice()

```