{
"cells": [
{
"cell_type": "markdown",
"source": [
"Weaving a simple curved surface with positive curvature."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
""
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Load packages"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using IntervalSets\n",
"using BasicBSpline\n",
"using StaticArrays\n",
"using ElasticSurfaceEmbedding"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"## Define the shape of the surface"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "D (generic function with 1 method)"
},
"metadata": {},
"execution_count": 2
}
],
"cell_type": "code",
"source": [
"ElasticSurfaceEmbedding.𝒑₍₀₎(u¹,u²) = SVector(u¹, u², u¹^2+u²^2)\n",
"n = 10\n",
"D(i,n) = (-1.0..1.0, (i-1)/n..i/n)"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"## Compute the shape of the embeddings"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"steptree = ElasticSurfaceEmbedding.StepTree()\n",
"for i in 1:10\n",
" initial_state!(steptree, D(i,n))\n",
" newton_onestep!(steptree, fixingmethod=:fix3points)\n",
" newton_onestep!(steptree)\n",
" newton_onestep!(steptree)\n",
" newton_onestep!(steptree)\n",
" newton_onestep!(steptree)\n",
" refinement!(steptree, p₊=(0,1), k₊=suggest_knotvector(steptree))\n",
" newton_onestep!(steptree)\n",
" newton_onestep!(steptree)\n",
" pin!(steptree)\n",
"end"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"## Export the shapes in SVG format"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "10-element Vector{String}:\n \"paraboloid/pinned/pinned-9.svg\"\n \"paraboloid/pinned/pinned-18.svg\"\n \"paraboloid/pinned/pinned-27.svg\"\n \"paraboloid/pinned/pinned-36.svg\"\n \"paraboloid/pinned/pinned-45.svg\"\n \"paraboloid/pinned/pinned-54.svg\"\n \"paraboloid/pinned/pinned-63.svg\"\n \"paraboloid/pinned/pinned-72.svg\"\n \"paraboloid/pinned/pinned-81.svg\"\n \"paraboloid/pinned/pinned-90.svg\""
},
"metadata": {},
"execution_count": 4
}
],
"cell_type": "code",
"source": [
"export_pinned_steps(\"paraboloid\", steptree, xlims=(-2,2), ylims=(-2,2), unitlength=(100,\"mm\"), mesh=(20,1))"
],
"metadata": {},
"execution_count": 4
},
{
"cell_type": "markdown",
"source": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
""
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"---\n",
"\n",
"*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
],
"metadata": {}
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.10.4"
},
"kernelspec": {
"name": "julia-1.10",
"display_name": "Julia 1.10.4",
"language": "julia"
}
},
"nbformat": 4
}