#1252 - Add mesh.jl file (#1260)

* add mesh.jl file

* add deps and cleanup code

* review

* revise docstrings

Project.toml

@@ -28,6 +28,7 @@ GLPKMathProgInterface = "≥ 0.4.0"
 GR = "≥ 0.39.1"
 IntervalArithmetic = "≥ 0.14.0"
 JuMP = "≥ 0.19.2"
+Makie = "≥ 0.9.4"
 MathProgBase = "≥ 0.7.0"
 Optim = "≥ 0.14.1"
 Plots = "≥ 0.25.1"
@@ -44,12 +45,13 @@ Expokit = "a1e7a1ef-7a5d-5822-a38c-be74e1bb89f4"
 GLPK = "60bf3e95-4087-53dc-ae20-288a0d20c6a6"
 GR = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
 JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
+Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
 Optim = "429524aa-4258-5aef-a3af-852621145aeb"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 Polyhedra = "67491407-f73d-577b-9b50-8179a7c68029"
 TaylorModels = "314ce334-5f6e-57ae-acf6-00b6e903104a"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["CDDLib", "Distributions", "Documenter", "Expokit", "GLPK", "GR", "JuMP", "Optim", "Plots", "Polyhedra",
-        "TaylorModels", "Test"]
+test = ["CDDLib", "Distributions", "Documenter", "Expokit", "GLPK", "GR", "JuMP",
+        "Makie", "Optim", "Plots", "Polyhedra", "TaylorModels", "Test"]

src/LazySets.jl

@@ -26,6 +26,7 @@ include("helper_functions.jl")
 include("comparisons.jl")
 include("macros.jl")
 include("samples.jl")
+include("mesh.jl")
 
 # ==================
 # Abstract set types

src/init.jl

@@ -3,6 +3,7 @@ function __init__()
     @require Optim = "429524aa-4258-5aef-a3af-852621145aeb" load_optim()
     @require Polyhedra = "67491407-f73d-577b-9b50-8179a7c68029" load_polyhedra()
     @require Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" load_distributions()
+    @require Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a" load_makie()
 end
 
 function load_expokit()
@@ -20,12 +21,25 @@ function load_polyhedra()
     eval(load_polyhedra_hpolytope())
     eval(load_polyhedra_hpolyhedron())
     eval(load_polyhedra_vpolytope())
+    initialize_mesh()
 end
 
 function load_distributions()
     eval(load_distributions_samples())
 end
 
+function load_makie()
+    initialize_mesh()
+end
+
+function initialize_mesh()
+    if isdefined(@__MODULE__, :Polyhedra) &&
+       isdefined(@__MODULE__, :Makie)
+
+       eval(load_mesh())
+    end
+end
+
 """
     require(package::Symbol; fun_name::String="", explanation::String="")
 

src/mesh.jl

@@ -0,0 +1,140 @@
+function load_mesh()
+return quote
+
+using .Polyhedra: Mesh
+using .Makie: mesh, mesh!
+import .Makie.AbstractPlotting: Automatic
+
+export plot3d, plot3d!
+
+# helper function for 3D plotting; converts S to a polytope in H-representation
+function plot3d_helper(S::LazySet{N}, backend) where {N}
+    @assert dim(S) <= 3 "plot3d can only be used to plot sets of dimension three (or lower); " *
+        "but the given set is $(dim(S))-dimensional"
+
+    @assert applicable(constraints_list, S) "plot3d requires that the list of constraints of `S`, " *
+        "`constraints_list(S)` is applicable; try overapproximating with an `HPolytope` first"
+
+    P = HPolytope(constraints_list(S))
+    remove_redundant_constraints!(P)
+    P_poly = polyhedron(P, backend=backend)
+    P_poly_mesh = Mesh(P_poly)
+    return P_poly_mesh
+end
+
+"""
+    plot3d(S::LazySet{N}; backend=default_polyhedra_backend(S, N),
+           alpha=1.0, color=:blue, colormap=:viridis, colorrange=Automatic(),
+           interpolate=false, linewidth=1, overdraw=false, shading=true,
+           transparency=true, visible=true) where {N}
+
+Plot a three-dimensional convex set using Makie.
+
+### Input
+
+- `S`            -- convex set
+- `backend`      -- (optional, default: `default_polyhedra_backend(S, N)`) polyhedral
+                    computations backend 
+- `alpha`        -- (optional, default: `1.0`) float in `[0,1]`; the alpha or
+                    transparency value
+- `color`        -- (optional, default: `:blue`) `Symbol` or `Colorant`; the color
+                    of the main plot element (markers, lines, etc.) and it can be
+                    a color symbol/string like `:red`
+- `colormap`     -- (optional, default: `:viridis`) the color map of the main plot;
+                    call `available_gradients()` to see what gradients are available,
+                    and it can also be used as `[:red, :black]`
+- `colorrange`   -- (optional, default: `Automatic()`) a tuple `(min, max)` where
+                    `min` and `max` specify the data range to be used for indexing
+                    the colormap
+- `interpolate`  -- (optional, default: `false`) a bool for heatmap and images,
+                    it toggles color interpolation between nearby pixels
+- `linewidth`    -- (optional, default: `1`) a number that specifies the width of
+                    the line in `line` and `linesegments` plots
+- `overdraw`     -- (optional, default: `false`)
+- `shading`      -- (optional, default: `true`) a boolean that specifies if shading
+                    should be on or not (for meshes)
+- `transparency` -- (optional, default: `true`) if `true`, the set is transparent
+                    otherwise it is displayed as a solid object
+- `visible`      -- (optional, default: `true`) a bool that toggles visibility
+                    of the plot
+
+For a complete list of attributes and usage see
+[Makie's documentation](http://makie.juliaplots.org/stable/plot-attributes.html).
+
+### Notes
+
+This plot recipe works by computing the list of constraints of `S` and converting
+to a polytope in H-representation. Then, this polytope is transformed with
+`Polyhedra.Mesh` and it is plotted using the `mesh` function.
+
+If the function `constraints_list` is not applicable to your set `S`, try
+overapproximation first; e.g. via
+
+```julia
+julia> using LazySets.Approximations
+
+julia> Sapprox = overapproximate(S, SphericalDirections(10))
+
+julia> plot3d(Sapprox)
+```
+The number `10` above corresponds to the number of directions considered; for 
+better resolution use higher values (but it will take longer).
+
+For efficiency consider using the `CDDLib` backend, as in
+
+```julia
+julia> using CDDLib
+
+julia> plot3d(Sapprox, backend=CDDLib.Library())
+```
+
+### Examples
+
+The functionality requires *both* `Polyhedra` and `Makie`; so after
+loading `LazySets`, do `using Makie, Polyhedra` (or `using Polyhedra, Makie`, the
+order doesn't matter).
+
+```julia
+julia> using LazySets, Makie, Polyhedra
+
+julia> plot3d(10. * rand(Hyperrectangle, dim=3))
+
+julia> plot3d!(10. * rand(Hyperrectangle, dim=3), color=:red)
+```
+"""
+function plot3d(S::LazySet{N}; backend=default_polyhedra_backend(S, N),
+                alpha=1.0, color=:blue, colormap=:viridis, colorrange=Automatic(), interpolate=false,
+                linewidth=1, overdraw=false, shading=true, transparency=true, visible=true) where {N}
+
+    P_poly_mesh = plot3d_helper(S, backend)
+    return mesh(P_poly_mesh, alpha=alpha, color=color, colormap=colormap, colorrange=colorrange,
+                interpolate=interpolate, linewidth=linewidth, transparency=transparency, visible=visible)
+end
+
+"""
+    plot3d!(S::LazySet{N}; backend=default_polyhedra_backend(S, N),
+            alpha=1.0, color=:blue, colormap=:viridis, colorrange=Automatic(), interpolate=false,
+            linewidth=1, overdraw=false, shading=true, transparency=true, visible=true) where {N}
+
+Plot a three-dimensional convex set using Makie.
+
+### Input
+
+See `plot3d` for the description of the inputs. For a complete list of attributes
+and usage see [Makie's documentation](http://makie.juliaplots.org/stable/plot-attributes.html).
+
+### Notes
+
+See the documentation of `plot3d` for examples.
+"""
+function plot3d!(S::LazySet{N}; backend=default_polyhedra_backend(S, N),
+                alpha=1.0, color=:blue, colormap=:viridis, colorrange=Automatic(), interpolate=false,
+                linewidth=1, overdraw=false, shading=true, transparency=true, visible=true) where {N}
+
+    P_poly_mesh = plot3d_helper(S, backend)
+    return mesh!(P_poly_mesh, alpha=alpha, color=color, colormap=colormap, colorrange=colorrange,
+                 interpolate=interpolate, linewidth=linewidth, transparency=transparency, visible=visible)
+end
+
+end # quote
+end # function load_mesh()