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Asymptote.jl
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Asymptote.jl
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@doc raw"""
asymptote_export_S2_signals(filename; points, curves, tVectors, colors, options...)
Export given `points`, `curves`, and `tVectors` on the sphere $\mathbb S^2$
to Asymptote.
# Input
* `filename` – a file to store the Asymptote code in.
# Optional Arguments (Data)
* `colors` - dictionary of color arrays (indexed by symbols `:points`, `:curves`
and `:tvector`) where each entry has to provide as least as many colors as
the length of the corresponding sets.
* `curves` – an `Array` of `Arrays` of points on the sphere, where each inner array is
interpreted as a curve and is accompanied by an entry within `colors`
* `points` – an `Array` of `Arrays` of points on the sphere where each inner array is
itnerpreted as a set of points and is accompanied by an entry within `colors`
* `tVectors` – an `Array` of `Arrays` of tuples, where the first is a points, the second a
tangent vector and each set of vectors is accompanied by an entry
from within `colors`
# Optional Arguments (Asymptote)
* `arrowHeadSize` - (`6.0`) size of the arrowheads of the tangent vectors
* `arrowHeadSizes` – overrides the previous value to specify a value per tVector set.
* `cameraPosition` - (`(1., 1., 0.)`) position of the camera in the Asymptote
szene
* `lineWidth` – (`1.0`) size of the lines used to draw the curves.
* `lineWidths` – overrides the previous value to specify a value per curve and tVector set.
* `dotSize` – (`1.0`) size of the dots used to draw the points.
* `dotSizes` – overrides the previous value to specify a value per point set.
* `sphereColor` – (`RGBA{Float64}(0.85, 0.85, 0.85, 0.6)`) color of the sphere
the data is drawn on
* `sphereLineColor` – (`RGBA{Float64}(0.75, 0.75, 0.75, 0.6)`) color of the lines on the sphere
* `sphereLineWidth` – (`0.5`) line width of the lines on the sphere
* `target` – (`(0.,0.,0.)`) position the camera points at
"""
function asymptote_export_S2_signals(filename::String;
points::Array{Array{T,1},1} where T = Array{Array{Float64,1},1}(undef,0),
curves::Array{Array{T,1},1} where T = Array{Array{Float64,1},1}(undef,0),
tVectors::Array{Array{Tuple{T,T},1},1} where T = Array{Array{Tuple{Float64,Float64},1},1}(undef,0),
colors::Dict{Symbol, Array{RGBA{Float64},1} } = Dict{Symbol,Array{RGBA{Float64},1}}(),
arrowHeadSize::Float64 = 6.,
arrowHeadSizes::Array{Float64,1} = fill(arrowHeadSize,length(tVectors)),
cameraPosition::Tuple{Float64,Float64,Float64} = (1., 1., 0.),
lineWidth::Float64 = 1.0,
lineWidths::Array{Float64,1} = fill(lineWidth,length(curves)+length(tVectors)),
dotSize::Float64 = 1.0,
dotSizes::Array{Float64,1} = fill(dotSize,length(points)),
sphereColor::RGBA{Float64} = RGBA{Float64}(0.85, 0.85, 0.85, 0.6),
sphereLineColor::RGBA{Float64} = RGBA{Float64}(0.75, 0.75, 0.75, 0.6),
sphereLineWidth::Float64 = 0.5,
target::Tuple{Float64,Float64,Float64} = (0.,0.,0.),
)
io = open(filename,"w")
try
#
# Header
# ---
write(io,string("import settings;\nimport three;\nimport solids;",
"unitsize(4cm);\n\n",
"currentprojection=perspective( ",
"camera = $(cameraPosition), ",
"target = $(target) );\n",
"currentlight=nolight;\n\n",
"revolution S=sphere(O,0.995);\n",
"pen SpherePen = rgb($(red(sphereColor)),",
"$(green(sphereColor)),$(blue(sphereColor)))",
"+opacity($(alpha(sphereColor)));\n",
"pen SphereLinePen = rgb($(red(sphereLineColor)),",
"$(green(sphereLineColor)),$(blue(sphereLineColor)))",
"+opacity($(alpha(sphereLineColor)))+linewidth($(sphereLineWidth)pt);\n",
"draw(surface(S), surfacepen=SpherePen, meshpen=SphereLinePen);\n")
);
write(io,"\n/*\n Colors\n*/\n")
j=0
for (key,value) in colors # colors for all keys
penPrefix = "$(j)"
sets = 0
if key==:points
penPrefix="point"
sets = length(points)
elseif key==:curves
penPrefix="curve"
sets = length(curves)
elseif key==:tvectors
penPrefix="tVector"
sets = length(tVectors)
end
if length(value) < sets
throw( ErrorException(
"Not enough colors ($(length(value))) provided for $(sets) sets in $(key)."
))
end
i=0
# export all colors
for c in value
i=i+1;
if i>sets
# avoid access errors in lineWidth or dotSizes if more colors then sets are given
break
end
write(io,string("pen $(penPrefix)Style$(i) = ",
"rgb($(red(c)),$(green(c)),$(blue(c)))",
(key==:curves) ? "+linewidth($(lineWidths[i])pt)" : "",
(key==:tvectors) ? "+linewidth($(lineWidths[length(curves)+i])pt)" : "",
(key==:points) ? "+linewidth($(dotSizes[i])pt)" : "",
"+opacity($(alpha(c)));\n"));
end
end
if length(points)>0
write(io,"\n/*\n Exported Points\n*/\n")
end
i=0
for pSet in points
i=i+1
for point in pSet
write(io,string("dot( (",string([string(v,",") for v in point]...)[1:end-1],"), pointStyle$(i));\n"));
end
end
i=0
if length(curves)>0
write(io,"\n/*\n Exported Curves\n*/\n")
end
for curve in curves
i=i+1
write(io,"path3 p$(i) = ");
j=0
for point in curve
j=j+1
pString = "("*string([ "$v," for v in point]...)[1:end-1]*")"
write(io, j>1 ? " .. $(pString)" : pString)
end
write( io,string(";\n draw(p$(i), curveStyle$(i));\n") );
end
i=0
if length(tVectors)>0
write(io,"\n/*\n Exported tangent vectors\n*/\n")
end
for tVecs in tVectors
i=i+1
j=0
for vector in tVecs
j=j+1
base = vector[1]
endPoints = base + vector[2]
write(io,string("draw( (",
string( [string(v,",") for v in base]...)[1:end-1],")--(",
string( [string(v,",") for v in endPoints]...)[1:end-1],
"), tVectorStyle$(i),Arrow3($(arrowHeadSizes[i])));\n"));
end
end
finally
close(io)
end
end
@doc raw"""
asymptote_export_S2_data(filename)
Export given `data` as an array of points on the sphere, i.e. one-, two-
or three-dimensional data with points on the [Sphere](https://juliamanifolds.github.io/Manifolds.jl/stable/manifolds/sphere.html) $\mathbb S^2$.
# Input
* `filename` – a file to store the Asymptote code in.
# Optional Arguments (Data)
* `data` – a point representing the 1-,2-, or 3-D array of points
* `elevationColorScheme` - A `ColorScheme` for elevation
* `scaleAxes` - (`(1/3,1/3,1/3)`) move spheres closer to each other by a factor
per direction
# Optional Arguments (Asymptote)
* `arrowHeadSize` - (`1.8`) size of the arrowheads of the vectors (in mm)
* `cameraPosition` - position of the camrea (default: centered above xy-plane)
szene
* `target` - position the camera points at (default: center of xy-plane within
data).
"""
function asymptote_export_S2_data(filename::String;
data = fill([0.,0.,1.],0,0),
arrowHeadSize::Float64 = 1.8,
scaleAxes = (1/3.,1/3.,1/3.),
cameraPosition::Tuple{Float64,Float64,Float64} = scaleAxes.*( (size(data,1)-1)/2 ,(size(data,2)-1)/2, max(size(data,3),0)+10),
target::Tuple{Float64,Float64,Float64} = scaleAxes.*( (size(data,1)-1)/2 ,(size(data,2)-1)/2, 0.),
elevationColorScheme = ColorSchemes.viridis,
)
io = open(filename,"w")
try
write(io,string("import settings;\nimport three;\n",
"size(7cm);\n",
"DefaultHead.size=new real(pen p=currentpen) {return $(arrowHeadSize)mm;};\n",
"currentprojection=perspective( ",
"camera = $(cameraPosition), up=Y,",
"target = $(target) );\n\n"));
dims = [size(data,i) for i=[1,2,3]]
for x=1:dims[1]
for y=1:dims[2]
for z=1:dims[3]
v = Tuple(data[x,y,z]) #extract value
el = asin( min(1,max(-1,v[3])) ); # since 3 is between -1 and 1 this yields a value between 0 and pi
# map elevation to colormap
c = get(elevationColorScheme,el+π/2, (0.,Float64(π)) );
# write arrow in this colormap
# transpose image to comply with image adresses (first index column downwards, second rows)
write(io,string("draw( $(scaleAxes.*(x-1,y-1,z-1))",
"--$(scaleAxes.*(x-1,y-1,z-1).+v),",
" rgb($(red(c)),$(green(c)),$(blue(c))), Arrow3);\n"));
end
end
end
finally
close(io)
end
end
@doc raw"""
asymptote_export_SPD(filename)
export given `data` as a point on a `Power{SPDPoint}` manifold, i.e. one-, two-
or three-dimensional data with points on the manifold of symmetric positive
definite matrices.
# Input
* `filename` – a file to store the Asymptote code in.
# Optional Arguments (Data)
* `data` – a point representing the 1-,2-, or 3-D array of `SPDPoints`
* `colorScheme` - A `ColorScheme` for Geometric Anisotropy Index
* `scaleAxes` - (`(1/3,1/3,1/3)`) move symmetric positive definite matrices
closer to each other by a factor per direction compared to the distance
esimated by the maximal eigenvalue of all involved SPD points
# Optional Arguments (Asymptote)
* `cameraPosition` - position of the camrea (default: centered above xy-plane)
szene.
* `target` - position the camera points at (default: center of xy-plane within data).
Both values `cameraPosition` and `target` are scaled by `scaledAxes*EW`, where
`EW` is the maximal eigenvalue in the `data`.
"""
function asymptote_export_SPD(filename::String;
data = fill(Matrix{Float64}(I,3,3),0,0),
scaleAxes = (1/3.,1/3.,1/3.) #multiplied with the maximal eigenvalue if data is present
.* ( length(data) > 0 ? maximum(maximum(eigvals.( data ))) : 1 ),
cameraPosition::Tuple{Float64,Float64,Float64} = ( (size(data,1)-1)/2 ,(size(data,2)-1)/2, max(size(data,3),0.)+10.),
target::Tuple{Float64,Float64,Float64} = ( (size(data,1)-1)/2 ,(size(data,2)-1)/2, 0.),
colorScheme = ColorSchemes.viridis,
)
io = open(filename,"w")
try
write(io,string("import settings;\nimport three;\n",
"surface ellipsoid(triple v1,triple v2,triple v3,real l1,real l2, real l3, triple pos=O) {\n",
" transform3 T = identity(4);\n",
" T[0][0] = l1*v1.x;\n T[1][0] = l1*v1.y;\n T[2][0] = l1*v1.z;\n",
" T[0][1] = l2*v2.x;\n T[1][1] = l2*v2.y;\n T[2][1] = l2*v2.z;\n",
" T[0][2] = l3*v3.x;\n T[1][2] = l3*v3.y;\n T[2][2] = l3*v3.z;\n",
" T[0][3] = pos.x;\n T[1][3] = pos.y;\n T[2][3] = pos.z;\n",
" return T*unitsphere;\n}\n\n",
"size(200);\n\n",
"real gDx=$(scaleAxes[1]);\n",
"real gDy=$(scaleAxes[2]);\n",
"real gDz=$(scaleAxes[3]);\n\n",
"currentprojection=perspective(up=Y, ",
"camera = (gDx*$(cameraPosition[1]),gDy*$(cameraPosition[2]),gDz*$(cameraPosition[3])), ",
"target = (gDx*$(target[1]),gDy*$(target[2]),gDz*$(target[3])) );\n",
"currentlight=Viewport;\n\n",
));
dims = [size(data,1) size(data,2) size(data,3) ];
for x=1:dims[1]
for y=1:dims[2]
for z=1:dims[3]
A = data[x,y,z] #extract matrix
F = eigen(A)
if maximum(abs.(A)) > 0. # a nonzero matrix (exclude several pixel
# Following Moakher & Batchelor: Geometric Anisotropic Index:
λ = F.values
V = F.vectors
Lλ = log.(λ)
GAI = sqrt( 2/3*sum( Lλ.^2 ) - 2/3 * sum(sum( tril( Lλ * Lλ',-1), dims=1), dims=2)[1])
c = get(colorScheme, GAI/(1+GAI), (0,1) )
write(io,string(" draw( ellipsoid( ($(V[1,1]),$(V[2,1]),$(V[3,1])),",
" ($(V[1,2]),$(V[2,2]),$(V[3,2])), ($(V[1,3]),$(V[2,3]),$(V[3,3])),",
" $(λ[1]), $(λ[2]), $(λ[3]), ",
" (gDx*$(x-1), gDy*$(y-1), gDz*$(z-1))),",
" rgb($(red(c)),$(green(c)),$(blue(c))) );\n"));
end
end
end
end
finally
close(io)
end
end
export renderAsymptote, asyExportS2Signals, asyExportS2Data, asyExportSPDData
"""
render_asymptote(filename; render=4, format="png", ...)
render an exported asymptote file specified in the `filename`, which can also
be given as a relative or full path
# Input
* `filename` – filename of the exported `asy` and rendered image
# Keyword Arguments
the default values are given in brackets
* `render` – (`4`) render level of asymptote, i.e. its `-render` option
* `format` – (`"png"`) final rendered format, i.e. asymptote's `-f` option
* `export_file` - (the filename with format as ending) specify the export filename
"""
function render_asymptote(
filename;
render::Int=4,
format="png",
exportFolder = string( filename[1:( [findlast(".",filename)...][1])], format),
)
renderCmd = `asy -render $(render) -f $(format) -globalwrite -o "$(relpath(exportFolder))" $(filename)`
run(renderCmd)
end