Use τₐ₀ and τᵣ₀

Project.toml

@@ -12,7 +12,7 @@ Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
-AbbreviatedTypes = "^0.1.4"
+AbbreviatedTypes = "^0.2.1"
 Makie = "^0.15.0"
 julia = "^1.7"
 

src/hyper/cuboid.jl

@@ -62,7 +62,7 @@ function surfpt_nearby(x::SReal{N}, s::Cuboid{N}) where {N}
     d = s.p * (x - s.c)
     n = n .* copysign.(1.0,d)  # operation returns SMatrix (reason for leaving n untransposed)
     absd = abs.(d)
-    onbnd = abs.(s.r.-absd) .≤ Base.rtoldefault(Float) .* s.r  # basically s.r .≈ absd but faster
+    onbnd = abs.(s.r.-absd) .≤ τᵣ₀ .* s.r  # basically s.r .≈ absd but faster
     isout = (s.r.<absd) .| onbnd
     ∆ = (s.r .- absd) .* cosθ  # entries can be negative
     if count(isout) == 0  # x strictly inside cuboid; ∆ all positive

src/planar/polygon.jl

@@ -80,7 +80,7 @@ function surfpt_nearby(x::SReal{2}, s::Polygon{K}) where {K}
 
     # Determine if x is outside of edges, inclusive.
     sz = abs.((-)(bounds(s)...))  # SVec{2}
-    onbnd = abs∆xe .≤ Base.rtoldefault(Float) * max(sz.data...)  # SVec{K}
+    onbnd = abs∆xe .≤ τᵣ₀ * max(sz.data...)  # SVec{K}
     isout = (∆xe.>0) .| onbnd  # SVec{K}
 
     # For x inside the polygon, it is easy to find the closest surface point: we can simply

src/planar/sector.jl

@@ -41,15 +41,15 @@ function surfpt_nearby(x::SReal{2}, s::Sector)
     # Calculate the closest point in the ρ dimension and outward normal direciton there.
     r2 = s.r / 2
     ρ = ld - r2  # positive if closer to arc; negative if closer to center
-    d̂ = ld ≤ Base.rtoldefault(Float) * r2  ? SVec(cos(s.ϕ₀),sin(s.ϕ₀)) : normalize(d)
+    d̂ = ld ≤ τᵣ₀ * r2  ? SVec(cos(s.ϕ₀),sin(s.ϕ₀)) : normalize(d)
 
     surfρ = ρ<0 ? 0.0 : s.r  # scalar: closest point to x between center and perimeter point
     noutρ = copysign(1.0,ρ) * d̂  # SVec{2}: outward direction normal at surfρ
 
     absρ = abs(ρ)
     abs∆ρ = abs(r2 - absρ)  # radial distance between x and either center or perimeter, whichever closer to x
 
-    onbndρ = abs∆ρ ≤ Base.rtoldefault(Float) * r2  # basically r2 ≈ ρ but faster
+    onbndρ = abs∆ρ ≤ τᵣ₀ * r2  # basically r2 ≈ ρ but faster
     isoutρ = (r2 < absρ) || onbndρ
 
     # Calculate the closest point in the ϕ dimension and outward normal direciton there.
@@ -67,7 +67,7 @@ function surfpt_nearby(x::SReal{2}, s::Sector)
     absϕ = abs(ϕ)
     abs∆ϕ = abs(s.∆ϕ2 - absϕ)  # angular distance between x and closer side of sector
 
-    onbndϕ = abs∆ϕ ≤ Base.rtoldefault(Float) * s.∆ϕ2  # basically ∆ϕ2 ≈ ϕ but faster
+    onbndϕ = abs∆ϕ ≤ τᵣ₀ * s.∆ϕ2  # basically ∆ϕ2 ≈ ϕ but faster
     isoutϕ = (s.∆ϕ2 < absϕ) || onbndϕ
 
     # Pick the surface point and outward direction normal depending on the location of x.

src/prism/prism.jl

@@ -73,15 +73,15 @@ function surfpt_nearby(x::SReal{3}, s::Prism)
     abs∆a = abs(s.h2 - la)  # scalar: distance between x and base point closest to x
     surfa = SVec(yb.data..., copysign(s.h2, ya))  # SVec{3}: coordinates of base point closest to x
     nouta = SVec(0.0, 0.0, copysign(1.0, ya))  # SVec{3}: outward direction normal at surfa
-    onbnda = abs∆a ≤ Base.rtoldefault(Float) * s.h2
+    onbnda = abs∆a ≤ τᵣ₀ * s.h2
     isouta = s.h2<la || onbnda
 
     surfb2, noutb2 = surfpt_nearby(yb, s.b)  # (SVec{2}, SVec{2}): side point closest to x and outward direction normal to side there
     abs∆b = norm(surfb2 - yb)  # scalar: distance between x and side point closest to x
     surfb = SVec(surfb2.data..., ya)  # SVec{3}: coordinates of side point closest to x
     noutb = SVec(noutb2.data..., 0.0)  # SVec{3}: outward direction normal to side surface at surfb
     basesize = abs.((-)(bounds(s.b)...))  # SVec{2}: size of bounding rectancle of base
-    onbndb = abs∆b ≤ Base.rtoldefault(Float) * max(basesize.data...)
+    onbndb = abs∆b ≤ τᵣ₀ * max(basesize.data...)
     isoutb = yb∉s.b || onbndb
 
     if isouta && isoutb  # x outside in both axis and base dimensions

src/util/plotting.jl

@@ -1,4 +1,4 @@
-const EPS_REL = Base.rtoldefault(Float)  # machine epsilon
+const EPS_REL = τᵣ₀  # machine epsilon
 
 # Define drawshape() and drawshape!() functions.
 # hres and vres are the number of sampling points in the corresponding Cartesion derctions.

test/cross_section.jl

@@ -13,7 +13,7 @@
 
     ∆ = rand(2)
     s2 = translate(s, ∆)
-    @test all(([r,0], [-r,0], [0,r], [0,-r], [0,0]) .+ Ref(∆) .∈ Ref(s2))
+    @test all(([r*one⁻,0], [-r*one⁻,0], [0,r*one⁻], [0,-r*one⁻], [0,0]) .+ Ref(∆) .∈ Ref(s2))
     @test !any(([r*one⁺,0], [-r*one⁺,0], [0,r*one⁺], [0,-r*one⁺]) .+ Ref(∆) .∈ Ref(s2))
 
 end  # @testset "CrossSection, ball"

test/cylinder.jl

@@ -11,9 +11,9 @@
     @test all([(p = [0.3sx/√2,0.3sy/√2,1.1sz]; surfpt_nearby(1.1p,c) ≈ (p, normalize(1.1p-p))) for sx = (-1,1), sy = (-1,1), sz = (-1,1)])  # outside corners
     @test all([(p = [0.3sx,0,1.1sz]; surfpt_nearby(1.1p,c) ≈ (p, normalize(1.1p-p))) for sx = (-1,1), sz = (-1,1)])  # outside corners
     @test all([(p = [0,0.3sy,1.1sz]; surfpt_nearby(1.1p,c) ≈ (p, normalize(1.1p-p))) for sy = (-1,1), sz = (-1,1)])  # outside corners
-    @test all([(p = [0.3sx/√2,0.3sy/√2,1.1sz]; (x,nout) = surfpt_nearby(p,c); (x≈p && all([sx 0 0; 0 sy 0; 0 0 sz]*nout.≥-10eps()))) for sx = (-1,1), sy = (-1,1), sz = (-1,1)])  # on rims
-    @test all([(p = [0.3sx,0,1.1sz]; (x,nout) = surfpt_nearby(p,c); (x≈p && all([sx 0 0; 0 0 sz]*nout.≥-10eps()))) for sx = (-1,1), sz = (-1,1)])  # on rims
-    @test all([(p = [0,0.3sy,1.1sz]; (x,nout) = surfpt_nearby(p,c); (x≈p && all([0 sy 0; 0 0 sz]*nout.≥-10eps()))) for sy = (-1,1), sz = (-1,1)])  # on rims
+    @test all([(p = [0.3sx/√2,0.3sy/√2,1.1sz]; (x,nout) = surfpt_nearby(p,c); (x≈p && all([sx 0 0; 0 sy 0; 0 0 sz]*nout.≥-10τₐ₀))) for sx = (-1,1), sy = (-1,1), sz = (-1,1)])  # on rims
+    @test all([(p = [0.3sx,0,1.1sz]; (x,nout) = surfpt_nearby(p,c); (x≈p && all([sx 0 0; 0 0 sz]*nout.≥-10τₐ₀))) for sx = (-1,1), sz = (-1,1)])  # on rims
+    @test all([(p = [0,0.3sy,1.1sz]; (x,nout) = surfpt_nearby(p,c); (x≈p && all([0 sy 0; 0 0 sz]*nout.≥-10τₐ₀))) for sy = (-1,1), sz = (-1,1)])  # on rims
     @test all([(p = [0.3sx/√2/2,0.3sy/√2/2,1.1sz]; surfpt_nearby([p[1],p[2],ρ*p[3]],c) ≈ (p,[0,0,sz])) for ρ = (one⁻⁻,1,one⁺⁺), sx = (-1,0,1), sy = (-1,0,1), sz = (-1,1)])  # around bases
     @test all([(p = [0.3sx,0,1.1sz/2]; surfpt_nearby([ρ*p[1],p[2],p[3]],c) ≈ (p,[sx,0,0])) for ρ = (one⁻⁻,1,one⁺⁺), sx = (-1,1), sz = (-1,0,1)])  # around side
     @test all([(p = [0,0.3sy,1.1sz/2]; surfpt_nearby([p[1],ρ*p[2],p[3]],c) ≈ (p,[0,sy,0])) for ρ = (one⁻⁻,1,one⁺⁺), sy = (-1,1), sz = (-1,0,1)])  # around side
@@ -42,9 +42,9 @@ end  # @testset "Cylinder"
     @test all([(p = 0.3(s1*ax1+s2*ax2)/√2+1.1s3*ax3; surfpt_nearby(1.1p,cr) ≈ (p, normalize(1.1p-p))) for s1 = (-1,1), s2 = (-1,1), s3 = (-1,1)])  # outside corners
     @test all([(p = 0.3s1*ax1+1.1s3*ax3; surfpt_nearby(1.1p,cr) ≈ (p, normalize(1.1p-p))) for s1 = (-1,1), s3 = (-1,1)])  # outside corners
     @test all([(p = 0.3s2*ax2+1.1s3*ax3; surfpt_nearby(1.1p,cr) ≈ (p, normalize(1.1p-p))) for s2 = (-1,1), s3 = (-1,1)])  # outside corners
-    @test all([(p = 0.3(s1*ax1+s2*ax2)/√2+1.1s3*ax3; (x,nout) = surfpt_nearby(p,cr); (x≈p && all([s1*ax1 s2*ax2 s3*ax3]'*nout.≥-10eps()) && norm(nout)≈1)) for s1 = (-1,1), s2 = (-1,1), s3 = (-1,1)])  # on rims
-    @test all([(p = 0.3s1*ax1+1.1s3*ax3; (x,nout) = surfpt_nearby(p,cr); (x≈p && all([s1*ax1 s3*ax3]'*nout.≥-10eps()) && norm(nout)≈1)) for s1 = (-1,1), s3 = (-1,1)])  # on rims
-    @test all([(p = 0.3s2*ax2+1.1s3*ax3; (x,nout) = surfpt_nearby(p,cr); (x≈p && all([s2*ax2 s3*ax3]'*nout.≥-10eps()) && norm(nout)≈1)) for s2 = (-1,1), s3 = (-1,1)])  # on rims
+    @test all([(p = 0.3(s1*ax1+s2*ax2)/√2+1.1s3*ax3; (x,nout) = surfpt_nearby(p,cr); (x≈p && all([s1*ax1 s2*ax2 s3*ax3]'*nout.≥-10τₐ₀) && norm(nout)≈1)) for s1 = (-1,1), s2 = (-1,1), s3 = (-1,1)])  # on rims
+    @test all([(p = 0.3s1*ax1+1.1s3*ax3; (x,nout) = surfpt_nearby(p,cr); (x≈p && all([s1*ax1 s3*ax3]'*nout.≥-10τₐ₀) && norm(nout)≈1)) for s1 = (-1,1), s3 = (-1,1)])  # on rims
+    @test all([(p = 0.3s2*ax2+1.1s3*ax3; (x,nout) = surfpt_nearby(p,cr); (x≈p && all([s2*ax2 s3*ax3]'*nout.≥-10τₐ₀) && norm(nout)≈1)) for s2 = (-1,1), s3 = (-1,1)])  # on rims
     @test all([surfpt_nearby(0.3(s1*ax1+s2*ax2)/√2/2+ρ*1.1s3*ax3,cr) ≈ (0.3(s1*ax1+s2*ax2)/√2/2+1.1s3*ax3,s3*ax3) for ρ = (one⁻⁻,1,one⁺⁺), s1 = (-1,0,1), s2 = (-1,0,1), s3 = (-1,1)])  # around bases
     @test all([surfpt_nearby(ρ*0.3s1*ax1+1.1s3*ax3/2,cr) ≈ (0.3s1*ax1+1.1s3*ax3/2, s1*ax1) for ρ = (one⁻⁻,1,one⁺⁺), s1 = (-1,1), s3 = (-1,0,1)])  # around side
     @test all([surfpt_nearby(ρ*0.3s2*ax2+1.1s3*ax3/2,cr) ≈ (0.3s2*ax2+1.1s3*ax3/2, s2*ax2) for ρ = (one⁻⁻,1,one⁺⁺), s2 = (-1,1), s3 = (-1,0,1)])  # around side

test/runtests.jl

@@ -5,9 +5,8 @@ using Random: MersenneTwister
 using Statistics: mean
 using Test
 
-const rtol = Base.rtoldefault(Float)
-const one⁻ = 1 - rtol  # scale factor slightly less than 1
-const one⁺ = 1 + rtol  # scare factor slightly greater than 1
+const one⁻ = 1 - τᵣ₀  # scale factor slightly less than 1
+const one⁺ = 1 + τᵣ₀  # scare factor slightly greater than 1
 const one⁻⁻, one⁺⁺ = 0.9, 1.1  # (scale factor less than 1, scale factor greater than 1)
 
 Base.isapprox(a::Tuple, b::Tuple; kws...) = all(p -> isapprox(p...; kws...), zip(a,b))