Merge pull request #15 from JuliaGeometry/mixed-types

relax typing in marchingTetrahedra so that isovalue can be a different type

Author: SimonDanisch

src/marching_tetrahedra.jl

@@ -124,7 +124,7 @@ end
 Checks if a voxel has faces. Should be false for most voxels.
 This function should be made as fast as possible.
 """
-function hasFaces(vals::Vector{T}, iso::T) where T<:Real
+function hasFaces(vals::Vector{<:Real}, iso::Real)
     @inbounds v = vals[1]
     if v < iso
         @inbounds for i=2:8
@@ -141,7 +141,7 @@ end
 """
 Determines which case in the triangle table we are dealing with
 """
-function tetIx(tIx::IType, vals::Vector{T}, iso::T, vxidx::VoxelIndices{IType}) where {T<:Real, IType <: Integer}
+function tetIx(tIx::IType, vals::Vector{<:Real}, iso::Real, vxidx::VoxelIndices{IType}) where {IType <: Integer}
     @inbounds v1 = vals[vxidx.subTets[tIx][1]]
     @inbounds v2 = vals[vxidx.subTets[tIx][2]]
     @inbounds v3 = vals[vxidx.subTets[tIx][3]]
@@ -160,7 +160,7 @@ regardless of which of its neighboring voxels is asking for it) in order
 for vertex sharing to be implemented properly.
 """
 function vertId(e::IType, x::IType, y::IType, z::IType,
-nx::IType, ny::IType, vxidx::VoxelIndices{IType}) where IType <: Integer
+nx::IType, ny::IType, vxidx::VoxelIndices{IType}) where {IType <: Integer}
     @inbounds dx, dy, dz = vxidx.voxCrnrPos[vxidx.voxEdgeCrnrs[e][1]]
     vxidx.voxEdgeDir[e]+7*(x-1+dx+nx*(y-1+dy+ny*(z-1+dz)))
 end
@@ -172,18 +172,17 @@ eps represents the "bump" factor to keep vertices away from voxel
 corners (thereby preventing degeneracies).
 """
 function vertPos(e::IType, x::IType, y::IType, z::IType,
-vals::Vector{T}, iso::T, eps::T, vxidx::VoxelIndices{IType}) where {T<:Real, IType <: Integer}
+vals::Vector{T}, iso::Real, eps::Real, vxidx::VoxelIndices{IType}) where {T<:Real, IType <: Integer}
 
     @inbounds ixs     = vxidx.voxEdgeCrnrs[e]
     @inbounds srcVal  = vals[ixs[1]]
     @inbounds tgtVal  = vals[ixs[2]]
-    a       = (iso-srcVal)/(tgtVal-srcVal)
-    a       = min(max(a, eps), one(T)-eps)
+    a       = min(max((iso-srcVal)/(tgtVal-srcVal), eps), one(T)-eps)
     b       = one(T)-a
     @inbounds c1x,c1y,c1z = vxidx.voxCrnrPos[ixs[1]]
     @inbounds c2x,c2y,c2z = vxidx.voxCrnrPos[ixs[2]]
 
-    Point{3,T}(
+    Point(
           x+b*c1x+a*c2x,
           y+b*c1y+a*c2y,
           z+b*c1z+a*c2z
@@ -196,9 +195,9 @@ present.
 """
 function getVertId(e::IType, x::IType, y::IType, z::IType,
  nx::IType, ny::IType,
- vals::Vector{T}, iso::T,
- vts::Dict{IType, Point{3,T}},
- eps::T, vxidx::VoxelIndices{IType}) where {T<:Real, IType <: Integer}
+ vals::Vector{T}, iso::Real,
+ vts::Dict{IType, Point{3,S}},
+ eps::Real, vxidx::VoxelIndices{IType}) where {T <: Real, S <: Real, IType <: Integer}
 
     vId = vertId(e, x, y, z, nx, ny, vxidx)
     if !haskey(vts, vId)
@@ -222,11 +221,11 @@ end
 Processes a voxel, adding any new vertices and faces to the given
 containers as necessary.
 """
-function procVox(vals::Vector{T}, iso::T,
+function procVox(vals::Vector{T}, iso::Real,
 x::IType, y::IType, z::IType,
 nx::IType, ny::IType,
-vts::Dict{IType, Point{3,T}}, fcs::Vector{Face{3,IType}},
-eps::T, vxidx::VoxelIndices{IType}) where {T<:Real, IType <: Integer}
+vts::Dict{IType, Point{3,S}}, fcs::Vector{Face{3,IType}},
+eps::Real, vxidx::VoxelIndices{IType}) where {T <: Real, S <: Real, IType <: Integer}
 
     # check each sub-tetrahedron in the voxel
     for i::IType = 1:6
@@ -252,8 +251,9 @@ end
 Given a 3D array and an isovalue, extracts a mesh represention of the
 an approximate isosurface by the method of marching tetrahedra.
 """
-function marchingTetrahedra(lsf::AbstractArray{T,3}, iso::T, eps::T, indextype::Type{IT}) where {T<:Real, IT <: Integer}
-    vts        = Dict{indextype, Point{3,T}}()
+function marchingTetrahedra(lsf::AbstractArray{T,3}, iso::Real, eps::Real, indextype::Type{IT}) where {T<:Real, IT <: Integer}
+    vertex_eltype = promote_type(T, typeof(iso), typeof(eps))
+    vts        = Dict{indextype, Point{3,vertex_eltype}}()
     fcs        = Array{Face{3,indextype}}(0)
     sizehint!(vts, div(length(lsf),8))
     sizehint!(fcs, div(length(lsf),4))

test/REQUIRE

@@ -0,0 +1 @@
+ForwardDiff 0.7

test/runtests.jl

@@ -1,6 +1,7 @@
 using Meshing
 using Base.Test
 using GeometryTypes
+using ForwardDiff
 
 
 @testset "meshing" begin
@@ -26,6 +27,13 @@ using GeometryTypes
             sqrt(sum(dot(v,v))) - 1 # sphere
         end
 
+        if "--profile" in ARGS
+            HomogenousMesh(s2, MarchingTetrahedra())
+            Profile.clear()
+            @profile HomogenousMesh(s2, MarchingTetrahedra())
+            #ProfileView.view()
+        end
+
         msh = HomogenousMesh(s2, MarchingTetrahedra())
         @test length(vertices(msh)) == 973
         @test length(faces(msh)) == 1830
@@ -94,12 +102,54 @@ using GeometryTypes
             @test faces(m4) == faces(m5)
         end
     end
-end
 
+    @testset "mixed types" begin
+        # https://github.com/JuliaGeometry/Meshing.jl/issues/9
+        samples = randn(10, 10, 10)
+        m1 = HomogenousMesh(SignedDistanceField(
+            HyperRectangle(Vec(0,0,0), Vec(1, 1, 1)),
+            samples), MarchingTetrahedra())
+        m2 = HomogenousMesh(SignedDistanceField(
+            HyperRectangle(Vec(0,0,0), Vec(1, 1, 1)),
+            Float32.(samples)), MarchingTetrahedra())
+        @test all(isapprox.(vertices(m1), vertices(m2), rtol=1e-6))
+        @test all(faces(m1) == faces(m2))
+
+        @testset "forward diff" begin
+            # Demonstrate that we can even take derivatives through the meshing algorithm
+            f = x -> norm(x)
+            bounds = HyperRectangle(Vec(-1, -1, -1), Vec(2, 2, 2))
+            resolution = 0.1
+            sdf = SignedDistanceField(f, bounds, resolution)
+
+            function surface_distance_from_origin(isovalue)
+                # Compute the mean distance of each vertex in the isosurface
+                # mesh from the origin. This should return a value equal to the
+                # isovalue and should have a derivative of 1.0 w.r.t. the
+                # isovalue. This function is just meant to serve as an example
+                # of some quantity you might want to differentiate in a mesh,
+                # and has the benefit for testing of having a trivial expected
+                # solution.
+                mesh = HomogenousMesh(sdf, MarchingTetrahedra(isovalue))
+                mean(norm.(vertices(mesh)))
+            end
+
+            isoval = 0.85
+            @test surface_distance_from_origin(isoval) ≈ isoval atol=1e-2
+            @test ForwardDiff.derivative(surface_distance_from_origin, isoval) ≈ 1 atol=1e-2
+        end
 
-if "--profile" in ARGS
-    HomogenousMesh(s2)
-    Profile.clear()
-    @profile HomogenousMesh(s2)
-    #ProfileView.view()
+        @testset "type stability" begin
+            # verify that we don't lose type stability just by mixing arguments
+            # of different types
+            data = randn(5, 5, 5)
+            iso = 0.2
+            eps = 1e-4
+            @inferred(Meshing.marchingTetrahedra(data, iso, eps, Int))
+            @inferred(Meshing.marchingTetrahedra(Float32.(data), Float64(iso), Float16(eps), Int32))
+            @inferred(Meshing.marchingTetrahedra(Float64.(data), Float32(iso), Float64(eps), Int64))
+        end
+    end
 end
+
+