warp wip

examples/2d.jl

@@ -1,5 +1,5 @@
 using Revise
-using Descartes: Circle, Square, LinearExtrude, translate
+using Descartes: Circle, Square, LinearExtrude, translate, Grid
 using GeometryBasics: Mesh
 
 function beam(;beam_size = [50,10,10],
@@ -15,6 +15,7 @@ function beam(;beam_size = [50,10,10],
         h = translate([hole_interval*i, beam_size[2]/2])Circle(hole_d/2)
         c = diff(c, h)
     end
+    c = intersect(c, Grid(1))
     LinearExtrude(c, beam_size[3])
 end
 
@@ -26,5 +27,6 @@ beam(;hole_ct=5)
 m = Mesh(beam())
 
 using WGLMakie
+WGLMakie.activate!(resize_to=:body)
 mesh(m)
 #save("2d_beam.ply",m)

examples/Manifest.toml

@@ -1,8 +1,8 @@
 # This file is machine-generated - editing it directly is not advised
 
-julia_version = "1.10.3"
+julia_version = "1.10.4"
 manifest_format = "2.0"
-project_hash = "307f054144a276e094fb1ddb88ac6864dbbb8dee"
+project_hash = "79f437763e6a1eb62c3106094973df8666180632"
 
 [[deps.AbstractFFTs]]
 deps = ["LinearAlgebra"]

examples/Project.toml

@@ -1,9 +1,11 @@
 [deps]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+CoordinateTransformations = "150eb455-5306-5404-9cee-2592286d6298"
 Descartes = "ea4ead7c-22ac-5e77-afc5-cd927cdc0b20"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
 HCubature = "19dc6840-f33b-545b-b366-655c7e3ffd49"
+Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
 QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
 Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

examples/csg.jl

@@ -20,7 +20,7 @@ translate([24,0,0]) {
 """
 
 
-using Descartes: Cuboid, Sphere
+using Descartes: Cuboid, Sphere, translate
 using GeometryBasics
 
 a = translate([-24,0,0])union(

examples/example001.jl

@@ -28,7 +28,7 @@ example001();
 
 """
 
-using Descartes: Cylinder, Sphere
+using Descartes: Cylinder, Sphere, rotate
 using GeometryBasics: Mesh
 
 function example001()

examples/triangle_wave.jl

@@ -1,7 +1,10 @@
 using Revise
-using Descartes: Descartes, TriangleWave, FRep, Grid
-using WGLMakie
-
+using Descartes: Descartes, TriangleWave, FRep, Grid, PolarWarp
+using WGLMakie, Makie
+using CoordinateTransformations
+using StaticArrays
+using ForwardDiff
+using LinearAlgebra
 t = TriangleWave(2.)
 
 x = 1:0.1:10
@@ -11,9 +14,36 @@ lines(x,y)
 
 g = Grid(1.0)
 
-x_vals = 1:0.1:10
-y_vals = 1:0.1:10
+x_vals = -10:0.1:10
+y_vals = -10:0.1:10
 
+# basic Grid
 z = [FRep(g, (x, y)) for x in x_vals, y in y_vals]
+extrema(z)
+heatmap(x_vals, y_vals, z, alpha=0.6)
+
+
+# Apply warp
+g_polar = PolarWarp(g, 8)
+
+z = [min(FRep(g_polar, (x, y))...) for x in x_vals, y in y_vals]
+extrema(z)
+heatmap(x_vals, y_vals, z, alpha=0.6)
+
+
+
+polar_f(v) = FRep(g_polar, v)
+polar_f([1,2])
+polar_f_min(v) = min(polar_f(v)...)
+polar_f_min([1,2])
+
+polar_f_jac(v) = ForwardDiff.jacobian(polar_f, v)
+z = [polar_f_jac([x, y]) for x in x_vals, y in y_vals]
+
+# TODO : Correction factor
+exper1(v) = norm(inv(polar_f_jac(v))*ForwardDiff.gradient(polar_f_min, v))
+
+z = [exper1([x, y]) for x in x_vals, y in y_vals]
+extrema(z)
 heatmap(x_vals, y_vals, z, alpha=0.6)
 

examples/warp.jl

@@ -0,0 +1,65 @@
+# https://www.desmos.com/calculator/mcjscmo6fq
+
+using WGLMakie
+#Plots.plotly()
+# Parameters (TODO: make const or propogate through functions for better performance)
+p = 1
+t = 0.5
+w0 = 8
+
+w = 2π / (p * w0)
+
+x_vals = range(-10, 10, length=1200)
+y_vals = range(-10, 10, length=1200)
+
+"""
+TriangleWave function
+"""
+function f_x(x)
+    abs(mod(-2 * p * x, p))
+end
+
+"""
+Grid function
+"""
+function f(v)
+    minimum(f_x.(v))
+end
+
+z = [f((x, y)) - t/2 < 0 for x in x_vals, y in y_vals]
+heatmap(x_vals, y_vals, z, alpha=0.6)
+
+function h(v)
+    mr = hypot(v...)
+    mt = atan(v[2], v[1])*w
+    min(f_x(mr), f_x(mt))
+end
+
+z = [h((x, y)) - t/2 <= 0 for x in x_vals, y in y_vals]
+heatmap(x_vals, y_vals, z, alpha=0.6)
+
+function j(v)
+    w / hypot(v...)
+end
+
+z = [h((x, y))/j((x,y)) - t/2 <= 0 for x in x_vals, y in y_vals]
+heatmap(x_vals, y_vals, z, alpha=0.6, title="Grid Function", xlabel="x", ylabel="y", legend=false, aspect_ratio=:equal)
+
+using ForwardDiff
+
+function h_g(v)
+    g = ForwardDiff.gradient(h, [v...]) # TODO: make this faster
+    hypot(g...)
+end
+
+z = [h((x, y))/h_g((x,y)) - t/2 <= 0 for x in x_vals, y in y_vals]
+heatmap(x_vals, y_vals, z, alpha=0.6, title="Grid Function", xlabel="x", ylabel="y", legend=false, aspect_ratio=:equal)
+
+function h_norm(v)
+    mr = hypot(v...)
+    mt = atan(v[2], v[1])*w
+    min(f_x(mr), f_x(mt)/j(v))
+end
+
+z = [h_norm((x, y)) - t/2 <= 0 for x in x_vals, y in y_vals]
+heatmap(x_vals, y_vals, z, alpha=0.6)

src/frep.jl

@@ -121,3 +121,9 @@ end
 function FRep(g::Grid, v)
     minimum(FRep(TriangleWave(g.period), e) for e in v)
 end
+
+function FRep(p::PolarWarp, v)
+    mr = hypot(v...)
+    mt = atan(v[2], v[1])*p.w/2π
+    [FRep(p.primitive, mr), FRep(p.primitive, mt)]
+end

src/hyperrectangles.jl

@@ -59,6 +59,10 @@ function HyperRectangle(csg::CSGIntersect)
     h
 end
 
+function HyperRectangle(g::Grid{T}) where T
+    HyperRectangle(Vec(-100,100), Vec(200,200))
+end
+
 function HyperRectangle(csg::CSGDiff)
     HyperRectangle(csg.left)
 end
@@ -96,3 +100,7 @@ function intersect(h1::HyperRectangle, h2::HyperRectangle)
     mm = min.(maximum(h1), maximum(h2))
     HyperRectangle(m, mm - m)
 end
+
+function Base.intersect(h1::HyperRectangle, ::Nothing)
+    h1
+end

src/types.jl

@@ -95,6 +95,11 @@ end
 
 A simple grid structure with a `period` field of type `T`.
 """
-struct Grid{T}
+struct Grid{T} <: AbstractPrimitive{2, T}
     period::T
 end
+
+struct PolarWarp{T} <: AbstractPrimitive{2, T}
+    primitive
+    w::T
+end