{
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  {
   "cell_type": "markdown",
   "id": "a1",
   "metadata": {},
   "source": [
    "# Vector Fields\n",
    "\n",
    "Vector-valued CoefficientFunctions can be visualized as arrow glyphs on surfaces, clipping planes, or as field lines."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2",
   "metadata": {},
   "source": [
    "## Surface Vectors\n",
    "\n",
    "Arrows on the boundary surface of a 3D mesh:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ngsolve import *\n",
    "from ngsolve_webgpu import *\n",
    "from webgpu.jupyter import Draw\n",
    "\n",
    "mesh = Mesh(unit_cube.GenerateMesh(maxh=0.2))\n",
    "cf = CF((x, y, 1))\n",
    "md = MeshData(mesh)\n",
    "fd = FunctionData(md, cf, order=1)\n",
    "vecs = SurfaceVectors(fd)\n",
    "Draw(vecs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4",
   "metadata": {},
   "source": [
    "`SurfaceVectors` samples the vector field on surface elements and renders 3D arrows. `grid_size` controls the density of arrows (default 20)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5",
   "metadata": {},
   "source": [
    "## Clipping Vectors\n",
    "\n",
    "Arrows on a clipping plane through the volume:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ngsolve import *\n",
    "from ngsolve_webgpu import *\n",
    "from webgpu.clipping import Clipping\n",
    "from webgpu.jupyter import Draw\n",
    "\n",
    "mesh = Mesh(unit_cube.GenerateMesh(maxh=0.2))\n",
    "cf = CF((x, y, 1))\n",
    "md = MeshData(mesh)\n",
    "fd = FunctionData(md, cf, order=1)\n",
    "clipping = Clipping()\n",
    "clipping.center = [0.5, 0.5, 0.5]\n",
    "vecs = ClippingVectors(fd, clipping=clipping)\n",
    "Draw(vecs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7",
   "metadata": {},
   "source": [
    "`ClippingVectors` works like `SurfaceVectors` but on the clipping cross-section. The clipping plane is controlled by the `Clipping` object."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8",
   "metadata": {},
   "source": [
    "## Field Lines\n",
    "\n",
    "Streamlines traced through a 3D vector field:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ngsolve import *\n",
    "from ngsolve_webgpu.cf import FieldLines\n",
    "from webgpu.jupyter import Draw\n",
    "\n",
    "mesh = Mesh(unit_cube.GenerateMesh(maxh=0.3))\n",
    "cf = CF((-y, x, 0.1))\n",
    "fieldlines = FieldLines(cf, mesh, num_lines=100, length=0.5, thickness=0.0015)\n",
    "Draw(fieldlines)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a10",
   "metadata": {},
   "source": [
    "`FieldLines` integrates streamlines from random start points. Key parameters:\n",
    "- `num_lines` — number of streamlines (default 100)\n",
    "- `length` — integration length (default 0.5)\n",
    "- `thickness` — line thickness relative to bounding box (default 0.0015)\n",
    "- `direction` — 0=both, 1=forward, -1=backward"
   ]
  }
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