add helicatenoid

docs/gallery/weaving_examples/config.json

@@ -2,6 +2,7 @@
     "order": [
         "paraboloid.jl",
         "hyperbolic_paraboloid.jl",
+        "helicatenoid.jl",
         "stereographicprojection.jl"
     ]
 }

docs/gallery/weaving_examples/helicatenoid.jl

@@ -0,0 +1,60 @@
+# ---
+# title: Helicatenoid
+# cover: ../assets/helicatenoid.jpg
+# description: Weaving a transformable curved surface from catenoid to helicoid.
+# ---
+
+# ![](../assets/helicatenoid.jpg)
+
+# ## Load packages
+using IntervalSets
+using BasicBSpline
+using StaticArrays
+using ElasticSurfaceEmbedding
+
+# ## Define the shape of the surface (non-periodic direction)
+ElasticSurfaceEmbedding.𝒑₍₀₎(u¹,u²) = SVector(cos(u²)*cosh(u¹),sin(u²)*cosh(u¹),u¹)
+n=9
+Dx(n) = (-π/2..π/2,-π/(4n)..π/(4n))
+
+# ## Compute the shape of the embeddings
+show_strain(Dx(n))
+
+steptree = initial_state(Dx(n), n₁=33)
+newton_onestep!(steptree, fixingmethod=:fix3points)
+newton_onestep!(steptree)
+newton_onestep!(steptree)
+newton_onestep!(steptree)
+newton_onestep!(steptree)
+refinement!(steptree, p₊=(0,1), k₊=(EmptyKnotVector(), KnotVector([0])))
+newton_onestep!(steptree)
+newton_onestep!(steptree)
+pin!(steptree)
+
+# ## Export the shape in SVG format
+export_pinned_steps("helicatenoid-a", steptree, unitlength=(40,"mm"), mesh=(18,1))
+
+# ## Define the shape of the surface (periodic direction)
+ElasticSurfaceEmbedding.𝒑₍₀₎(u¹,u²) = SVector(cos(u¹)*cosh(u²),sin(u¹)*cosh(u²),u²)
+Dy(i,n) = (-π..π,(i-1)*π/(2n)..(i)*π/(2n))
+
+## Check the maximum strain
+for i in 1:9
+    show_strain(Dy(i,n))
+end
+
+## Numerical computing
+steptree = StepTree()
+for i in 1:9
+    initial_state!(steptree, Dy(i,n), n₁=33)
+    newton_onestep!(steptree, fixingmethod=:fix3points)
+    newton_onestep!(steptree, )
+    newton_onestep!(steptree, )
+    refinement!(steptree, p₊=(0,1), k₊=(EmptyKnotVector(),KnotVector([(i-1/2)*π/(2n)])))
+    newton_onestep!(steptree)
+    newton_onestep!(steptree)
+    pin!(steptree)
+end
+
+# ## Export the shapes in SVG format
+export_pinned_steps("helicatenoid-b", steptree, unitlength=(40,"mm"), mesh=(36,1))