{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to sample from a mesh?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from geomfum.dataset import NotebooksDataset\n",
    "from geomfum.metric.mesh import (\n",
    "    GraphShortestPathMetric,\n",
    "    HeatDistanceMetric,\n",
    "    VertexEuclideanMetric,\n",
    ")\n",
    "from geomfum.plot import MeshPlotter\n",
    "from geomfum.sample import FarthestPointSampler, PoissonSampler, VertexProjectionSampler\n",
    "from geomfum.shape import TriangleMesh\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = NotebooksDataset()\n",
    "mesh = TriangleMesh.from_file(dataset.get_filename(\"cat-00\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## \"Coordinate\" samplers\n",
    "\n",
    "If we're interested in sampling coordinates of points on the mesh, we can use `PoissonSampler`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "poisson_sampler = PoissonSampler.from_registry(min_n_samples=3, which=\"pymeshlab\")\n",
    "sampled_vertices = poisson_sampler.sample(mesh)\n",
    "sampled_vertices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vertex indices samplers\n",
    "\n",
    "If we're interested in sampling vertex indices instead, we can leverage \"coordinate\" samplers like `PoissonSampler` by projecting the coordinates to the closest vertices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vertex_sampler = VertexProjectionSampler(sampler=poisson_sampler)\n",
    "sampled_indices = vertex_sampler.sample(mesh)\n",
    "sampled_indices.astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get vertex coordinates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampled_vertices = mesh.vertices[sampled_indices]\n",
    "sampled_vertices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the sampled points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plotter = MeshPlotter.from_registry(colormap=\"RdBu\", which=\"plotly\")\n",
    "plotter.add_mesh(mesh)\n",
    "plotter.highlight_vertices(sampled_vertices)\n",
    "plotter.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Farthest point sampler\n",
    "\n",
    "Alternatively, we can sample vertex indices directly with `FarthestPointSampler`. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Select the metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "metrics = {\n",
    "    \"euclidean\": VertexEuclideanMetric,\n",
    "    \"heat-distance\": HeatDistanceMetric,\n",
    "    \"graph\": GraphShortestPathMetric,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The vertex **7181** corresponds to the extreme of the cat’s tail. We start to sample from this point.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fps = {}\n",
    "samp = FarthestPointSampler(6,)\n",
    "\n",
    "for name, metric in metrics.items():\n",
    "    mesh.equip_with_metric(metric)\n",
    "    samples = samp.sample(mesh, first_point= 7181)\n",
    "    fps[name] = samples\n",
    "    print(f\"FPS {name}: {samples}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the sampled points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plotter = MeshPlotter.from_registry(colormap=\"RdBu\", which=\"plotly\")\n",
    "plotter.add_mesh(mesh)\n",
    "plotter.highlight_vertices(mesh.vertices[fps['euclidean']])\n",
    "plotter.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plotter = MeshPlotter.from_registry(colormap=\"RdBu\", which=\"pyvista\")\n",
    "plotter.add_mesh(mesh)\n",
    "plotter.highlight_vertices(mesh.vertices[fps['heat-distance']])\n",
    "plotter.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "metric = list(fps.keys())[0]\n",
    "plotter = MeshPlotter.from_registry(colormap=\"RdBu\", which=\"polyscope\")\n",
    "plotter.add_mesh(mesh)\n",
    "plotter.highlight_vertices(mesh.vertices[fps['graph']],)\n",
    "#plotter.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling from a subset\n",
    "\n",
    "The vertex **4265** corresponds to the extreme of the cat’s muzzle, i want to select the FPs on the tail."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "points_on_the_tail = list(range(len(mesh.vertices) - 100, len(mesh.vertices)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fps = {}\n",
    "dataset = NotebooksDataset()\n",
    "samp = FarthestPointSampler(6,)\n",
    "for name, metric in metrics.items():\n",
    "    mesh.equip_with_metric(metric)\n",
    "    samples = samp.sample(mesh, points_pool = points_on_the_tail, first_point= 4265)\n",
    "    fps[name] = samples\n",
    "    print(f\"FPS {name}: {samples}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plotter = MeshPlotter.from_registry(colormap=\"RdBu\", which=\"plotly\")\n",
    "plotter.add_mesh(mesh)\n",
    "plotter.highlight_vertices(mesh.vertices[fps['euclidean']])\n",
    "plotter.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further reading\n",
    "\n",
    "* [How to compute descriptors?](./03_descriptors.ipynb)\n",
    "\n",
    "* [How to set landmarks?](./06_landmarks.ipynb)"
   ]
  }
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