{ "cells": [ { "cell_type": "markdown", "id": "1154c8b1", "metadata": {}, "source": [ "# Computing the Reeb graph of a filtered simplicial complex\n", "\n", "This notebook gives a tutorial to computing the Reeb graph from a filtered simplicial complex. We assume that this complex is given as the `LowerStar` class (see [LowerStar documentation](../modules/reeb/lowerstar.rst) for details). " ] }, { "cell_type": "code", "execution_count": 2, "id": "6c24918c", "metadata": {}, "outputs": [], "source": [ "from cereeberus import LowerStar, ReebGraph, computeReeb" ] }, { "cell_type": "markdown", "id": "2f86d2ed", "metadata": {}, "source": [ "Consider the following simplicial complex with height function. \n", "\n", "\"Small\n", "\n", "First, we construct this simplicial complex with a lower star filtration, were we need only specify the top dimensional simplices. Note that the `LowerStar` class is built on gudhi's `SimplexTree`, so it retains all of that class' functionality. " ] }, { "cell_type": "code", "execution_count": 3, "id": "4f7a5c9e", "metadata": {}, "outputs": [], "source": [ "K = LowerStar()\n", "K.insert([0, 1, 2])\n", "K.insert([1, 3])\n", "K.insert([2,3])\n", "K.insert([0,4])\n", "K.assign_filtration([0], 0.0)\n", "K.assign_filtration([1], 3.0)\n", "K.assign_filtration([2], 5.0)\n", "K.assign_filtration([3], 7)\n", "K.assign_filtration([4], 9.0)\n" ] }, { "cell_type": "markdown", "id": "ca71be24", "metadata": {}, "source": [ "Then computing the Reeb graph of this complex is as easy as the following. " ] }, { "cell_type": "code", "execution_count": 4, "id": "4c3e5cf0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R = computeReeb(K)\n", "R.draw()" ] }, { "cell_type": "markdown", "id": "ef111214", "metadata": {}, "source": [ "For a slightly more complex example, we have the following Torus example generator. " ] }, { "cell_type": "code", "execution_count": 5, "id": "73b9c65e", "metadata": {}, "outputs": [], "source": [ "from cereeberus.data import Torus" ] }, { "cell_type": "code", "execution_count": 6, "id": "86d760fa", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T = Torus()\n", "T.generate_grid(grid_size = 4)\n", "T.assign_random_values(0,100, seed=1986)\n", "T.draw()" ] }, { "cell_type": "code", "execution_count": 7, "id": "d1e98698", "metadata": {}, "outputs": [], "source": [ "R = computeReeb(T)\n", "R.remove_all_regular_vertices() # Simplify for visualization" ] }, { "cell_type": "code", "execution_count": 8, "id": "b1da0cef", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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