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chakravalachakravala
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disambiguated visual methods
1 parent 0d4e03c commit 8e7a997

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+79
-31
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2 files changed

+79
-31
lines changed

‎src/Cartan.jl

+55-27
Original file line numberDiff line numberDiff line change
@@ -73,6 +73,7 @@ TensorField(id::Int,dom,cod::Array,met::GlobalFiber) = TensorField(id,dom,cod,fi
7373
TensorField(dom::AbstractFrameBundle,cod::AbstractFrameBundle) = TensorField(dom,points(cod))
7474
TensorField(dom::AbstractArray{B,N} where B,cod::Array{F,N} where F,met::AbstractArray=Global{N}(InducedMetric())) where N = TensorField((global grid_id+=1),dom,cod,fiber(met))
7575
TensorField(dom::ChainBundle,cod::Vector,met::AbstractVector=Global{1}(InducedMetric())) = TensorField((global grid_id+=1),dom,cod,met)
76+
TensorField(a::TensorField,b::TensorField) = TensorField(fiber(a),fiber(b))
7677

7778
#const ParametricMesh{B,F,P<:AbstractVector{<:Chain}} = TensorField{B,F,1,P}
7879
const ScalarMap{B,F<:AbstractReal,P<:SimplexFrameBundle} = TensorField{B,F,1,P}
@@ -465,16 +466,16 @@ function __init__()
465466
#Makie.lines(t::TensorField{B,F,1};args...) where {B<:Coordinate{<:AbstractReal},F<:AbstractReal} = linegraph(t;args...)
466467
#Makie.lines!(t::TensorField{B,F,1};args...) where {B<:Coordinate{<:AbstractReal},F<:AbstractReal} = linegraph(t;args...)
467468
function linegraph(t::GradedField{G,B,F,1} where G;args...) where {B<:Coordinate{<:AbstractReal},F}
468-
x,y = Real.(domain(t)),value.(codomain(t))
469+
x,y = Real.(points(t)),value.(codomain(t))
469470
display(Makie.lines(x,Real.(getindex.(y,1));args...))
470-
for i ∈ 2:binomial(mdims(codomain(t)),G)
471+
for i ∈ 2:binomial(mdims(codomain(t)),grade(t))
471472
Makie.lines!(x,Real.(getindex.(y,i));args...)
472473
end
473474
end
474475
function linegraph!(t::GradedField{G,B,F,1} where G;args...) where {B<:Coordinate{<:AbstractReal},F}
475-
x,y = Real.(domain(t)),value.(codomain(t))
476+
x,y = Real.(points(t)),value.(codomain(t))
476477
display(Makie.lines!(x,Real.(getindex.(y,1));args...))
477-
for i ∈ 2:binomial(mdims(codomain(t)),G)
478+
for i ∈ 2:binomial(mdims(codomain(t)),grade(t))
478479
Makie.lines!(x,Real.(getindex.(y,i));args...)
479480
end
480481
end
@@ -490,6 +491,12 @@ function __init__()
490491
Makie.lines!(getindex.(t,i);args...)
491492
end
492493
end
494+
function Makie.arrows(M::VectorField,t::TensorField{B,<:Endomorphism,N,<:GridFrameBundle} where B;args...) where N
495+
Makie.arrows(TensorField(fiber(M),fiber(t));args...)
496+
end
497+
function Makie.arrows!(M::VectorField,t::TensorField{B,<:Endomorphism,N,<:GridFrameBundle} where B;args...) where N
498+
Makie.arrows!(TensorField(fiber(M),fiber(t)))
499+
end
493500
function Makie.arrows(t::TensorField{<:Coordinate{<:Chain},<:Endomorphism,N,<:GridFrameBundle};args...) where N
494501
display(Makie.arrows(getindex.(t,1);args...))
495502
for i ∈ 2:mdims(eltype(codomain(t)))
@@ -514,9 +521,9 @@ function __init__()
514521
Makie.arrows!(getindex.(t,i);args...)
515522
end
516523
end
517-
Makie.volume(t::VolumeGrid;args...) = Makie.volume(domain(t).v...,Real.(codomain(t));args...)
518-
Makie.volume!(t::VolumeGrid;args...) = Makie.volume!(domain(t).v...,Real.(codomain(t));args...)
519-
Makie.volumeslices(t::VolumeGrid;args...) = Makie.volumeslices(domain(t).v...,Real.(codomain(t));args...)
524+
Makie.volume(t::VolumeGrid;args...) = Makie.volume(points(t).v...,Real.(codomain(t));args...)
525+
Makie.volume!(t::VolumeGrid;args...) = Makie.volume!(points(t).v...,Real.(codomain(t));args...)
526+
Makie.volumeslices(t::VolumeGrid;args...) = Makie.volumeslices(points(t).v...,Real.(codomain(t));args...)
520527
for fun ∈ (:surface,:surface!)
521528
@eval begin
522529
Makie.$fun(t::SurfaceGrid;args...) = Makie.$fun(points(t).v...,Real.(codomain(t));color=Real.(abs.(codomain(gradient_fast(Real(t))))),args...)
@@ -534,15 +541,15 @@ function __init__()
534541
end
535542
for fun ∈ (:contour,:contour!,:contourf,:contourf!,:contour3d,:contour3d!,:wireframe,:wireframe!)
536543
@eval begin
537-
Makie.$fun(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F};args...) = Makie.$fun(domain(t).v...,Real.(radius.(codomain(t)));args...)
544+
Makie.$fun(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F};args...) = Makie.$fun(points(t).v...,Real.(radius.(codomain(t)));args...)
538545
end
539546
end
540547
for fun ∈ (:heatmap,:heatmap!)
541548
@eval begin
542-
Makie.$fun(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F};args...) = Makie.$fun(domain(t).v...,Real.(angle.(codomain(t)));colormap=:twilight,args...)
549+
Makie.$fun(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F};args...) = Makie.$fun(points(t).v...,Real.(angle.(codomain(t)));colormap=:twilight,args...)
543550
end
544551
end
545-
for fun ∈ (:contour,:contour!,:contourf,:contourf!,:contour3d,:contour3d!,:heatmap,:heatmap!,:wireframe,:wireframe!)
552+
for fun ∈ (:contour,:contour!,:contourf,:contourf!,:contour3d,:contour3d!,:heatmap,:heatmap!)
546553
@eval begin
547554
Makie.$fun(t::SurfaceGrid;args...) = Makie.$fun(points(t).v...,Real.(codomain(t));args...)
548555
function Makie.$fun(t::GradedField{G,B,F,2,<:RealSpace{2}} where G;args...) where {B,F}
@@ -554,6 +561,8 @@ function __init__()
554561
end
555562
end
556563
end
564+
Makie.wireframe(t::SurfaceGrid;args...) = Makie.wireframe(graph(t);args...)
565+
Makie.wireframe!(t::SurfaceGrid;args...) = Makie.wireframe!(graph(t);args...)
557566
for fun ∈ (:streamplot,:streamplot!)
558567
@eval begin
559568
Makie.$fun(f::Function,t::Rectangle;args...) = Makie.$fun(f,t.v...;args...)
@@ -567,9 +576,10 @@ function __init__()
567576
for fun ∈ (:arrows,:arrows!)
568577
@eval begin
569578
Makie.$fun(t::ScalarField{<:Coordinate{<:Chain},F,2,<:RealSpace{2}} where F;args...) = Makie.$fun(Makie.Point.(fiber(graph(Real(t))))[:],Makie.Point.(fiber(normal(Real(t))))[:];args...)
570-
Makie.$fun(t::VectorField{<:Coordinate{<:Chain},<:Chain{V,G,T,2} where {V,G,T},2,<:AlignedRegion{2}};args...) = Makie.$fun(domain(t).v...,getindex.(codomain(t),1),getindex.(codomain(t),2);args...)
579+
Makie.$fun(t::VectorField{<:Coordinate{<:Chain{W,L,F,2} where {W,L,F}},<:Chain{V,G,T,2} where {V,G,T},2,<:AlignedRegion{2}};args...) = Makie.$fun(domain(t).v...,getindex.(codomain(t),1),getindex.(codomain(t),2);args...)
571580
Makie.$fun(t::VectorField{<:Coordinate{<:Chain},F,2,<:RealSpace{2}} where F;args...) = Makie.$fun(Makie.Point.(points(t))[:],Makie.Point.(codomain(t))[:];args...)
572581
Makie.$fun(t::VectorField{<:Coordinate{<:Chain},F,N,<:GridFrameBundle} where {F,N};args...) = Makie.$fun(Makie.Point.(points(t))[:],Makie.Point.(codomain(t))[:];args...)
582+
Makie.$fun(t::VectorField,f::VectorField;args...) = Makie.$fun(Makie.Point.(fiber(t))[:],Makie.Point.(fiber(t))[:];args...)
573583
Makie.$fun(t::Rectangle,f::Function;args...) = Makie.$fun(t.v...,f;args...)
574584
Makie.$fun(t::Hyperrectangle,f::Function;args...) = Makie.$fun(t.v...,f;args...)
575585
Makie.$fun(t::ScalarMap;args...) = Makie.$fun(points(points(t)),Real.(codomain(t));args...)
@@ -602,16 +612,34 @@ function __init__()
602612
for fun ∈ (:mesh,:mesh!,:wireframe,:wireframe!)
603613
@eval Makie.$fun(M::GridFrameBundle;args...) = Makie.$fun(GeometryBasics.Mesh(M);args...)
604614
end
605-
function Makie.mesh(M::TensorField{B,F,2,<:GridFrameBundle} where {B,F};args...)
615+
function linegraph(M::TensorField{B,<:Chain,2,<:GridFrameBundle} where B;args...)
606616
variation(M,Makie.lines,Makie.lines!)
607617
alteration(M,Makie.lines!,Makie.lines!)
608-
#Makie.mesh(GeometryBasics.Mesh(base(M));color=fiber(M)[:],args...)
609618
end
610-
function Makie.mesh!(M::TensorField{B,F,2,<:GridFrameBundle} where {B,F};args...)
619+
function linegraph!(M::TensorField{B,<:Chain,2,<:GridFrameBundle} where B;args...)
611620
variation(M,Makie.lines!,Makie.lines!)
612621
alteration(M,Makie.lines!,Makie.lines!)
613-
#Makie.mesh!(GeometryBasics.Mesh(base(M));color=fiber(M)[:],args...)
614622
end
623+
function Makie.mesh(M::TensorField{B,<:Chain,2,<:GridFrameBundle} where B;args...)
624+
Makie.mesh(GridFrameBundle(fiber(M));args...)
625+
end
626+
function Makie.mesh!(M::TensorField{B,<:Chain,2,<:GridFrameBundle} where B;args...)
627+
Makie.mesh!(GridFrameBundle(fiber(M));args...)
628+
end
629+
function Makie.mesh(M::TensorField{B,<:AbstractReal,2,<:GridFrameBundle} where B;args...)
630+
Makie.mesh(GeometryBasics.Mesh(base(M));color=fiber(M)[:],args...)
631+
end
632+
function Makie.mesh!(M::TensorField{B,<:AbstractReal,2,<:GridFrameBundle} where B;args...)
633+
Makie.mesh!(GeometryBasics.Mesh(base(M));color=fiber(M)[:],args...)
634+
end
635+
function Makie.mesh(M::TensorField{B,<:Chain,2,<:GridFrameBundle} where B,f::TensorField;args...)
636+
Makie.mesh(GridFrameBundle(fiber(M));color=fiber(f)[:],args...)
637+
end
638+
function Makie.mesh!(M::TensorField{B,<:Chain,2,<:GridFrameBundle} where B,f::TensorField;args...)
639+
Makie.mesh!(GridFrameBundle(fiber(M));color=fiber(f)[:],args...)
640+
end
641+
Makie.wireframe(M::TensorField{B,<:Chain,2,<:GridFrameBundle} where B;args...) = Makie.wireframe(GridFrameBundle(fiber(M));args...)
642+
Makie.wireframe!(M::TensorField{B,<:Chain,2,<:GridFrameBundle} where B;args...) = Makie.wireframe!(GridFrameBundle(fiber(M));args...)
615643
function Makie.mesh(M::SimplexFrameBundle;args...)
616644
if mdims(points(M)) == 2
617645
sm = submesh(M)[:,1]
@@ -634,21 +662,21 @@ function __init__()
634662
@require UnicodePlots="b8865327-cd53-5732-bb35-84acbb429228" begin
635663
UnicodePlots.lineplot(t::ScalarMap;args...) = UnicodePlots.lineplot(getindex.(domain(t),2),codomain(t);args...)
636664
UnicodePlots.lineplot(t::PlaneCurve;args...) = UnicodePlots.lineplot(getindex.(codomain(t),1),getindex.(codomain(t),2);args...)
637-
UnicodePlots.lineplot(t::RealFunction;args...) = UnicodePlots.lineplot(Real.(domain(t)),Real.(codomain(t));args...)
638-
UnicodePlots.lineplot(t::ComplexMap{B,F,1};args...) where {B<:AbstractReal,F} = UnicodePlots.lineplot(real.(Complex.(codomain(t))),imag.(Complex.(codomain(t)));args...)
639-
UnicodePlots.lineplot(t::GradedField{G,B,F,1};args...) where {G,B<:Coordinate{<:AbstractReal},F} = UnicodePlots.lineplot(Real.(domain(t)),Grassmann.array(codomain(t));args...)
640-
UnicodePlots.contourplot(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F};args...) = UnicodePlots.contourplot(t.dom.v[1][2:end-1],t.dom.v[2][2:end-1],(x,y)->radius(t(Chain(x,y)));args...)
641-
UnicodePlots.contourplot(t::SurfaceGrid;args...) = UnicodePlots.contourplot(t.dom.v[1][2:end-1],t.dom.v[2][2:end-1],(x,y)->t(Chain(x,y));args...)
642-
UnicodePlots.surfaceplot(t::SurfaceGrid;args...) = UnicodePlots.surfaceplot(t.dom.v[1][2:end-1],t.dom.v[2][2:end-1],(x,y)->t(Chain(x,y));args...)
643-
UnicodePlots.surfaceplot(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F};args...) = UnicodePlots.surfaceplot(t.dom.v[1][2:end-1],t.dom.v[2][2:end-1],(x,y)->radius(t(Chain(x,y)));colormap=:twilight,args...)
665+
UnicodePlots.lineplot(t::RealFunction;args...) = UnicodePlots.lineplot(Real.(points(t)),Real.(codomain(t));args...)
666+
UnicodePlots.lineplot(t::ComplexMap{B,F,1};args...) where {B<:Coordinate{<:AbstractReal},F} = UnicodePlots.lineplot(real.(Complex.(codomain(t))),imag.(Complex.(codomain(t)));args...)
667+
UnicodePlots.lineplot(t::GradedField{G,B,F,1} where {G,F};args...) where B<:Coordinate{<:AbstractReal} = UnicodePlots.lineplot(Real.(points(t)),Grassmann.array(codomain(t));args...)
668+
UnicodePlots.contourplot(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F};args...) = UnicodePlots.contourplot(points(t).v[1][2:end-1],points(t).v[2][2:end-1],(x,y)->radius(t(Chain(x,y)));args...)
669+
UnicodePlots.contourplot(t::SurfaceGrid;args...) = UnicodePlots.contourplot(points(t).v[1][2:end-1],points(t).v[2][2:end-1],(x,y)->t(Chain(x,y));args...)
670+
UnicodePlots.surfaceplot(t::SurfaceGrid;args...) = UnicodePlots.surfaceplot(points(t).v[1][2:end-1],points(t).v[2][2:end-1],(x,y)->t(Chain(x,y));args...)
671+
UnicodePlots.surfaceplot(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F};args...) = UnicodePlots.surfaceplot(points(t).v[1][2:end-1],points(t).v[2][2:end-1],(x,y)->radius(t(Chain(x,y)));colormap=:twilight,args...)
644672
UnicodePlots.spy(t::SurfaceGrid;args...) = UnicodePlots.spy(Real.(codomain(t));args...)
645-
UnicodePlots.heatmap(t::SurfaceGrid;args...) = UnicodePlots.heatmap(Real.(codomain(t));xfact=step(t.dom.v[1]),yfact=step(t.dom.v[2]),xoffset=t.dom.v[1][1],yoffset=t.dom.v[2][1],args...)
646-
UnicodePlots.heatmap(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F};args...) = UnicodePlots.heatmap(Real.(angle.(codomain(t)));xfact=step(t.dom.v[1]),yfact=step(t.dom.v[2]),xoffset=t.dom.v[1][1],yoffset=t.dom.v[2][1],colormap=:twilight,args...)
673+
UnicodePlots.heatmap(t::SurfaceGrid;args...) = UnicodePlots.heatmap(Real.(codomain(t));xfact=step(points(t).v[1]),yfact=step(points(t).v[2]),xoffset=points(t).v[1][1],yoffset=points(t).v[2][1],args...)
674+
UnicodePlots.heatmap(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F};args...) = UnicodePlots.heatmap(Real.(angle.(codomain(t)));xfact=step(points(t).v[1]),yfact=step(points(t).v[2]),xoffset=points(t).v[1][1],yoffset=points(t).v[2][1],colormap=:twilight,args...)
647675
Base.display(t::PlaneCurve) = (display(typeof(t)); display(UnicodePlots.lineplot(t)))
648676
Base.display(t::RealFunction) = (display(typeof(t)); display(UnicodePlots.lineplot(t)))
649-
Base.display(t::ComplexMap{B,F,1,<:Interval}) where {B,F} = (display(typeof(t)); display(UnicodePlots.lineplot(t)))
650-
Base.display(t::ComplexMap{B,F,2,<:RealSpace{2}} where {B,F}) = (display(typeof(t)); display(UnicodePlots.heatmap(t)))
651-
Base.display(t::GradedField{G,B,F,1,<:Interval}) where {G,B,F} = (display(typeof(t)); display(UnicodePlots.lineplot(t)))
677+
Base.display(t::ComplexMap{B,<:AbstractComplex,1,<:Interval}) where B = (display(typeof(t)); display(UnicodePlots.lineplot(t)))
678+
Base.display(t::ComplexMap{B,<:AbstractComplex,2,<:RealSpace{2}} where B) = (display(typeof(t)); display(UnicodePlots.heatmap(t)))
679+
Base.display(t::GradedField{G,B,<:TensorGraded,1,<:Interval} where {G,B}) = (display(typeof(t)); display(UnicodePlots.lineplot(t)))
652680
Base.display(t::SurfaceGrid) = (display(typeof(t)); display(UnicodePlots.heatmap(t)))
653681
end
654682
@require GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" begin

‎src/diffgeo.jl

+24-4
Original file line numberDiff line numberDiff line change
@@ -310,8 +310,8 @@ for fun ∈ (:_slow,:_fast)
310310
:(Chain($([:($$cd(f,l[$n],Val($n),i...)) for n ∈ list(1,N)]...)))
311311
end
312312
$cd(f::RealRegion) = ProductSpace($cd.(f.v))
313-
$cd(f::GridFrameBundle{Coordinate{P,G},N,<:PointArray{P,G,N,<:RealRegion,<:Global{N,<:InducedMetric}}}) where {P,G,N} = ProductSpace($cd.(base(f).v))
314-
$cd(f::GridFrameBundle{Coordinate{P,G},N,<:PointArray{P,G,N,<:RealRegion}}) where {P,G,N} = applymetric.($cd(base(f)),fiber(f))
313+
$cd(f::GridFrameBundle{Coordinate{P,G},N,<:PointArray{P,G,N,<:RealRegion,<:Global{N,<:InducedMetric}}}) where {P,G,N} = ProductSpace($cd.(base(base(f)).v))
314+
$cd(f::GridFrameBundle{Coordinate{P,G},N,<:PointArray{P,G,N,<:RealRegion}}) where {P,G,N} = applymetric.($cd(base(base(f))),fiber(f))
315315
function $cd(f::AbstractRange,l::Tuple=size(f))
316316
d = Vector{eltype(f)}(undef,l[1])
317317
@threads for i ∈ 1:l[1]
@@ -530,15 +530,30 @@ end
530530

531531
export arclength, arctime, trapz, cumtrapz, linecumtrapz, psum, pcumsum
532532
export centraldiff, tangent, tangent_fast, unittangent, speed, normal, unitnormal
533-
export curvenormal, unitcurvenormal
533+
export curvenormal, unitcurvenormal, ribbon, tangentsurface, planecurve
534+
export normalnorm, area, surfacearea, weingarten, gauss
534535

535536
# use graph for IntervalMap? or RealFunction!
536537
tangent(f::IntervalMap) = gradient(f)
537-
tangent(f::ScalarField) = det(gradient(graph(f)))
538+
tangent(f::ScalarField) = tangent(graph(f))
539+
tangent(f::VectorField) = det(gradient(f))
538540
normal(f::ScalarField) = ⋆tangent(f)
541+
normal(f::VectorField) = ⋆tangent(f)
539542
unittangent(f::ScalarField,n=tangent(f)) = TensorField(domain(f), codomain(n)./abs.(.⋆codomain(n)))
543+
unittangent(f::VectorField,n=tangent(f)) = TensorField(domain(f), codomain(n)./abs.(.⋆codomain(n)))
540544
unittangent(f::IntervalMap) = unitgradient(f)
541545
unitnormal(f) = ⋆unittangent(f)
546+
normalnorm(f) = Real(abs(normal(f)))
547+
548+
ribbon(f::AbstractCurve,g::Vector{<:AbstractCurve}) = TensorField(points(f)⊕LinRange(0,1,length(g)+1),hcat(fiber(f),fiber.(g)...))
549+
ribbon(f::AbstractCurve,g::AbstractCurve,n::Int=100) = tangentsurface(f,g-f,n)
550+
tangentsurface(f::AbstractCurve,g::AbstractCurve,n::Int=100) = ribbon(f,Ref(f).+(LinRange(inv(n),1,n).*Ref(g)))
551+
tangentsurface(f::AbstractCurve,v::Real=1,n::Int=100) = tangentsurface(f,v*tangent(f),n)
552+
553+
area(f::VectorField) = integral(normalnorm(f))
554+
surfacearea(f::VectorField) = integrate(normalnorm(f))
555+
weingarten(f::VectorField) = gradient(unitnormal(f))
556+
gauss(f::VectorField) = Real(abs(det(weingarten(f))))
542557

543558
function speed(f::IntervalMap,d=centraldiff(points(f)),t=centraldiff(codomain(f),d))
544559
TensorField(domain(f), abs.(t))
@@ -656,6 +671,11 @@ end
656671
#bishoppolar(f::TensorField) = TensorField(domain(f), Chain.(value.(codomain(curvature(f))),getindex.(codomain(cumtrapz(torsion(f))),1)))
657672
#bishop(f::TensorField,κ=value.(codomain(curvature(f))),θ=getindex.(codomain(cumtrapz(torsion(f))),1)) = TensorField(domain(f), Chain.(κ.*cos.(θ),κ.*sin.(θ)))
658673

674+
function planecurve(κ::RealFunction,φ::Real=0.0)
675+
int = iszero(φ) ? integral(κ) : integral(κ)+φ
676+
integral(Chain.(cos(int),sin(int)))
677+
end
678+
659679
export surfacemetric, surfaceframe
660680

661681
surfacemetric(dom::ScalarField,f::Function) = surfacemetric(TensorField(dom,f))

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