Bresenham3D.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cec00f5a",
   "metadata": {},
   "source": [
    "# Bresenhams Linien-Algorithmus in 3D\n",
    "\n",
    "Ein Lidar-Sensor steht am Punkt $(x_{0}, y_{0}, z_{0})$ und sendet seinen Laser in eine durch die Winkel $\\alpha$ und $\\beta$ festgelegte Richtung. Der Sensor misst eine Entfernung bis der Lichtstrahl auf einer Oberfläche auftrifft. Die Messung hat allerdings eine mit der Entfernung steigende Messungenauigkeit.\n",
    "\n",
    "Numpy beschleunigt berechnungen mit Vektoren und Listen von Vektoren. Matplotlib hilft die Ergebnisse zu visualisieren. Dafür zunächst einige Imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cdbf3d96",
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits import mplot3d\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "#%matplotlib notebook\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ab11303",
   "metadata": {},
   "source": [
    "Mit einigen tausend Lidar-Messungen lässt sich ein 3D-Modell des Raums erstellen, in denen der Sensor bewegt wird. Als Basis für das Modell dient ein Voxel-Gitter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b9d15da9",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.zeros((100, 100, 100), dtype=np.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78691241",
   "metadata": {},
   "source": [
    "Für jeden Voxel entlang des Laserstrahls jeder Messung lässt sich anhand des Messwerts und der erwarteten Messungenauigkeit eine Wahrscheinlichkeit angeben, dass an diesem Punkt durchsichtige Luft oder ein undurschsichtiges Objekt wie eine Wand ist. Nur welche Voxel befinden sich „entlang“ des Laserstrahls?\n",
    "\n",
    "Diese Frage lässt sich mit Bresehams Linien-Algorithmus berechnen. Der Algorithmus diente ursprünglich dazu 1 Pixel breite Linien auf einen 2D-Monitor zu zeichnen. Er funktioniert aber auch in 3D mit Voxeln statt pixeln.\n",
    "\n",
    "## Wo beginnt die Linie?\n",
    "\n",
    "Anders als in Bresehams Original-Algorithmus gibt es für die Lidar-Messungen nicht unbedingt ganzzahlige Koordinaten für den Startpunkt `start`$=(x_{0}, y_{0}, z_{0})$. Der Zielpunkt `target`$=(x_{1}, y_{1}, z_{1})$ muss ebenfalls nicht ganzzahlig sein. Beide Punkte müssen nicht innerhalb des Voxel-Rasters liegen.\n",
    "\n",
    "Eine Gerade ist definiert als: $\\begin{bmatrix} x \\\\ y \\\\ z \\end{bmatrix} = \\begin{bmatrix} x_{0} \\\\ y_{0} \\\\ z_{0} \\end{bmatrix} + p \\cdot \\begin{bmatrix} x_{1}-x_{0} \\\\ y_{1}-y_{0} \\\\ z_{1}-z_{0} \\end{bmatrix}$\n",
    "\n",
    "Um ihren Schnittpunkt mit der Y-Z-Ebene zu bestimmen, muss man nur das Gleichungssystem mit $x=0$ lösen:\n",
    "$\\begin{bmatrix} 0 \\\\ y \\\\ z \\end{bmatrix} = \\begin{bmatrix} x_{0} \\\\ y_{0} \\\\ z_{0} \\end{bmatrix} + p \\cdot \\begin{bmatrix} x_{1}-x_{0} \\\\ y_{1}-y_{0} \\\\ z_{1}-z_{0} \\end{bmatrix}$\n",
    "\n",
    "Dafür bestimmt man $p$ anhand der X-Koordinate und kann dann dieses $p$ in die Zeilen für Y und Z einsetzen. Glücklicherweise interessiert den Algorithmus nur, ob das berechnete $p$ positiv und kleiner als 1 ist, da nur dann die Gerade am Rand des Voxelgitters startet. Es reicht also zunächst $p$ zu bestimmen: \n",
    "$ 0 = x_{0} + p \\cdot (x_{1} - x_{0}) \\\\\n",
    "\\Leftrightarrow p = \\frac{-x_{0}}{x_{1}-x_{0}} $\n",
    "\n",
    "Analog ergibt sich ein $p_{y=0}$ mit $\\begin{bmatrix} x \\\\ 0 \\\\ z \\end{bmatrix}$: $p_{y=0} = \\frac{-y_{0}}{y_{1}-y_{0}}$\n",
    "\n",
    "Und zuletzt $p_{z=0}$ mit $\\begin{bmatrix} x \\\\ y \\\\ 0 \\end{bmatrix}$: $p_{z=0} = \\frac{-z_{0}}{z_{1}-z_{0}}$\n",
    "\n",
    "Die drei $p$ variablen lassen sich mit Numpy effizient in einem Schritt berechnen: $\\begin{bmatrix} p_{x=0} \\\\ p_{y=0} \\\\ p_{z=0} \\end{bmatrix} = \\begin{bmatrix} \\frac{-x_{0}}{x_{1}-x_{0}} \\\\ \\frac{-y_{0}}{y_{1}-y_{0}} \\\\ \\frac{-z_{0}}{z_{1}-z_{0}} \\end{bmatrix}$ `p_0 = -start / start_to_target_vector`\n",
    "\n",
    "Falls die X-, Y- oder Z-Konponente des Richtungsvektors jedoch negativ ist, muss der Algorithmus stattdessen prüfen, ob der Vektor von außerhalb des Maximums den durch die Voxel definierten Bereich durchquert. Mit dem Optimalen Parameter `step_size` ergibt sich das Maximum als `array_max = np.array(array.shape) * step_size`.\n",
    "\n",
    "Die $p_{max}$ mit den Ebenen, die die Maximalkanten des Voxel-Kubus berechnen sich folgendermaßen:\n",
    "$\\begin{bmatrix} p_{x=max} \\\\ p_{y=max} \\\\ p_{z=max} \\end{bmatrix} = \\begin{bmatrix} \\frac{x_{max}-x_{0}}{x_{1}-x_{0}} \\\\ \\frac{y_{max}-y_{0}}{y_{1}-y_{0}} \\\\ \\frac{z_{max}-z_{0}}{z_{1}-z_{0}} \\end{bmatrix}$ `p_max = (array_max - start) / start_to_target_vector`\n",
    "\n",
    "Die Wahl welcher der beiden möglichen $p$ hängt davon ab, ob der Richtungsvektor vom Ursprung weg oder zum Ursprung hin zeigt. Je nachdem kann Numpy den einen oder den anderen Wert wählen: `np.select([start_to_target_vector >= 0, start_to_target_vector < 0], [p_0, p_max])`. Vom Ergebnis interessiert nur der größte Wert und für den Fall, dass alle $p$ negativ wären, sollte der zuletzt gewählte Wert nie negativ werden. Das alles erledigt die folgende Zeile: `p = np.maximum(np.max(np.select([start_to_target_vector >= 0, start_to_target_vector < 0], [p_0, p_max])), 0)`\n",
    "\n",
    "Mit diesem $p$ lässt sich nun endlich die X-, Y- und Z-Komponente des Startpunkts berechnen: \n",
    "\n",
    "$\\begin{bmatrix} x_{start} \\\\ y_{start} \\\\ z_{start} \\end{bmatrix} = \\begin{bmatrix} x_{0} \\\\ y_{0} \\\\ z_{0} \\end{bmatrix} + p \\cdot \\begin{bmatrix} x_{1}-x_{0} \\\\ y_{1}-y_{0} \\\\ z_{1}-z_{0} \\end{bmatrix}$\n",
    "\n",
    "In Python-Code sieht das so aus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1730a0a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_start_point_in_voxel_grid(start, start_to_target_vector, array, step_size):\n",
    "    array_max = np.array(array.shape) * step_size\n",
    "    notzero_array = start_to_target_vector != 0\n",
    "    p_0 = np.zeros((3,), dtype=np.float32)\n",
    "    np.divide(0 - start, start_to_target_vector, out=p_0, where=notzero_array)\n",
    "    p_max = np.zeros((3,), dtype=np.float32)\n",
    "    np.divide(array_max - start, start_to_target_vector, out=p_max, where=notzero_array)\n",
    "    p = np.maximum(np.max(np.select([start_to_target_vector >= 0, start_to_target_vector < 0], [p_0, p_max])), 0)\n",
    "    return start + p * start_to_target_vector"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93a02318",
   "metadata": {},
   "source": [
    "## Linien-Vorbereitungen\n",
    "\n",
    "Bresehams Algorithmus folgt der Linie entlang ihrer steilsten Achse in 1-Pixel- bzw. 1-Voxel-Schritten. Für die verbleibenden zwei Dimensionen prüft er in jedem Schritt, ob das direkt benachbarte Voxel (in Richtung der steilsten Achse) der Linie noch gut genug folgt, oder ob stattdessen ein seitlich verschobenes Voxel besser passt. Die steilste Achse lässt sich mit dem Vektor $\\vec{target} - \\vec{start}$ berechnen: `start_to_target_vector = target - start`\n",
    "\n",
    "Ein Array mit den Nummern aller Dimensionen erzeugt `list(range(len(array.shape)))`. Mit der Numpy-Funktion `argmax()` lässt sich die steilste Dimension leicht bestimmen; da die Richtung auch negativ sein kann, bildet der Algorithmus vorher den Betrag. Die so berechnete Nummer der steilsten Dimension lässt sich nun aus der Liste aller Dimensionen löschen, wodurch die beiden weniger steilen Dimensionen übrig bleiben:\n",
    "\n",
    "```python\n",
    "error_dimensions = list(range(len(array.shape)))\n",
    "steepest_dimension = error_dimensions.pop(np.argmax(np.abs(start_to_target_vector)))\n",
    "```\n",
    "\n",
    "Da eine Gerade keine Krümmung hat, entfernt sie sich bei jedem Schritt um den gleichen konstanten Faktor von der steilsten Dimension. Wie weit lässt sich leicht mit dem Vektor vom Start zum Zielpunkt berechnen:\n",
    "\n",
    "```python\n",
    "error_per_step = (start_to_target_vector / start_to_target_vector[steepest_dimension]) * step_size\n",
    "```\n",
    "\n",
    "Anschließend geht es darum, den ersten Voxel zu bestimmen. Für diesen Punkt ergibt sich dann auch ein initialer Rundungsfehler:\n",
    "\n",
    "```python\n",
    "error = np.modf(start_point_in_voxel_grid / step_size)[0]\n",
    "start_voxel = np.around(start_point_in_voxel_grid / step_size, decimals=0)\n",
    "```\n",
    "\n",
    "Die Numpy-Funktion `modf()` gibt zwei Vektoren zurück: Zuerst den Rundungsfehler und danach den ganzzahligen Anteil. Der Bressehnham-Algorithmus braucht aber nur den Rundungsfehler.\n",
    "\n",
    "Als nächstes geht es darum die Richtung zu bestimmen, in die der Algorithmus der steilsten Achse folgt. Wenn der Vektor vom Start- zum Zielpunkt entlang der steilsten Dimension negativ ist, soll `line_direction` -1 sein, ansonsten 1. Mit einer Typkonvertierung des Booleans vom Vergleich zu einem Integer kommen die Werte 0 und 1 vor. Zu -1 und 1 kommt der Algorthmus durch verdoppeln und anschließend 1 anbziehen:\n",
    "\n",
    "```python\n",
    "line_direction = int(start_to_target_vector[steepest_dimension] > 0) * 2 - 1\n",
    "```\n",
    "\n",
    "## Linien-Schritte\n",
    "\n",
    "Nachdem der Startpunkt und der Fehler pro Schritt festgelegt sind, kann der Algorthmus in einer Schleife an der Linie entlang laufen und die passenden Voxel in der Liste `voxels` einsammeln. Die Zählvariable für die Koordinate der steilsten Achse ist `i`. Jeder Schritt baut auf dem vorherigen auf, weshalb `current_voxel` die letzte Position protokolliert. Die beginnt mit einer Kopie von `start_voxel`. `np.copy()` ist notwendig, da die Variable `start_voxel` eine Referenz auf den Vektor enthält und diese in `voxels` archiviert werden soll. In der Kopie kann der Algorithmus Änderungen an den Zahlenwerten der Vektorkomponenten vornehmen, ohne nebenbei auch `start_voxel` zu verändern.\n",
    "\n",
    "Die Schleife wird mit `while True:` als Endlosschleife gestartet, weil die `if`-Anweisung im Schleifenkörper erst später überprüft, ob sie abgebrochen werden soll. Eine solche Konstruktion ähnelt einer `do {} while`-Schleife in anderen Sprachen, die es in Python so nicht gibt.\n",
    "\n",
    "Der erste Schritt bei jedem Durchlauf besteht darin `i` voranzuschreiten. Die Richtung ist durch `line_direction` festgelegt und kann daher 1 oder -1 sein. Die nächste Zeile addiert den zusätzlichen Fehler durch den neuen Schritt auf den bereits akkumulierten Fehler. Dank Numpy geht das in einem Befehl für alle Dimensionen:\n",
    "\n",
    "```python\n",
    "np.add(error, error_per_step / step_size, out=error)\n",
    "```\n",
    "\n",
    "Sollte der Betrag des Fehlers für eine Fehlerachse 0,5 überschreiten, muss der Algorithmus ein Voxel in diese Richtung gehen und 1 vom Fehler abziehen. Das ließe sich mit `if`-Anweisungen und einer Schleife über die Fehlerdimensionen formulieren, was aber Numpys fähigkeiten zum Parallelisieren mehrerer Berechnungen nicht nutzt. Stattdessen erstellt der Algorithmus eine Maske aus Boolean-Werten, wo die Linie einen Schritt zur Seite machen muss und bereitet die Richtung für diesen Schritt für alle Achsen vor:\n",
    "\n",
    "```python\n",
    "step_dims = np.abs(error) >= 0.5\n",
    "step_dir = (error > 0) * 2.0 - 1.0\n",
    "```\n",
    "\n",
    "Die Numpy-Funktionen `subtract()` und `add()` nehmen nun die Maske mit dem `where`-Parameter entgegen und führen ihe Berechnung nur dort aus, wo sie `True` ist:\n",
    "\n",
    "```python\n",
    "np.subtract(error, step_dir, out=error, where=step_dims)\n",
    "np.add(current_voxel, step_dir, out=current_voxel, where=step_dims)\n",
    "```\n",
    "\n",
    "Nachdem der Schritt nun gemacht und `current_voxel` aktualisiert ist, prüft der Algorithmus ob er schon fertig ist. Wenn eine der Koordinaten von `current_voxel` unter 0 sinkt oder die Größe des Voxelgitters überschreitet, ist der Algorithmus fertig und kann mit `break` aus der Schleife springen. \n",
    "\n",
    "Wenn er noch nicht fertig ist, hängt er eine Kopie von `current_voxel` an die `voxels` an und beginnt mit dem nächsten Schleifendurchlauf den nächsten Schritt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5118373c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bresenham(start, target, array, step_size=1.0):\n",
    "    start_to_target_vector = target - start\n",
    "    error_dimensions = list(range(len(array.shape)))\n",
    "    steepest_dimension = error_dimensions.pop(np.argmax(np.abs(start_to_target_vector)))\n",
    "    print(\"start_to_target_vector\", start_to_target_vector, \"  error_dimensions\", error_dimensions)\n",
    "    error_per_step = (start_to_target_vector / np.abs(start_to_target_vector[steepest_dimension])) * step_size\n",
    "    print(\"Error per step:\", error_per_step)\n",
    "    start_point_in_voxel_grid = find_start_point_in_voxel_grid(\n",
    "        start, start_to_target_vector, array, step_size)\n",
    "    error = np.modf(start_point_in_voxel_grid / step_size)[0]\n",
    "    start_voxel = np.around(start_point_in_voxel_grid / step_size, decimals=0)\n",
    "    line_direction = int(start_to_target_vector[steepest_dimension] > 0) * 2 - 1\n",
    "    voxels = [start_voxel]\n",
    "    print(\"Error at start:\", error)\n",
    "    current_voxel = np.copy(start_voxel)\n",
    "    print(current_voxel)\n",
    "    while True:\n",
    "        np.add(error, error_per_step / step_size, out=error)\n",
    "        print(\"i:\", current_voxel[steepest_dimension], \"Error:\", error)\n",
    "        step_dims = np.abs(error) >= 0.5\n",
    "        step_dir = ((error > 0) * 2.0 - 1.0)\n",
    "        print(\"step_dims & step_dir\", step_dims, step_dir)\n",
    "        np.subtract(error, step_dir, out=error, where=step_dims)\n",
    "        np.add(current_voxel, step_dir, out=current_voxel, where=step_dims)\n",
    "        print(current_voxel, \"Error:\", error)\n",
    "        if np.any(current_voxel < 0) or np.any(current_voxel > np.array(array.shape, dtype=np.float32)): \n",
    "            break\n",
    "        voxels.append(np.copy(current_voxel))\n",
    "    return voxels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "52a9aa11",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "start_to_target_vector [75.  12.5 13. ]   error_dimensions [1, 2]\n",
      "Error per step: [0.5        0.08333334 0.08666667]\n",
      "Error at start: [0. 0. 0.]\n",
      "[10.  4.  0.]\n",
      "i: 10.0 Error: [1.         0.16666667 0.17333333]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[11.  4.  0.] Error: [0.         0.16666667 0.17333333]\n",
      "i: 11.0 Error: [1.         0.33333334 0.34666666]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[12.  4.  0.] Error: [0.         0.33333334 0.34666666]\n",
      "i: 12.0 Error: [1.   0.5  0.52]\n",
      "step_dims & step_dir [ True  True  True] [1. 1. 1.]\n",
      "[13.  5.  1.] Error: [ 0.         -0.5        -0.48000002]\n",
      "i: 13.0 Error: [ 1.         -0.3333333  -0.30666667]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[14.  5.  1.] Error: [ 0.         -0.3333333  -0.30666667]\n",
      "i: 14.0 Error: [ 1.         -0.16666664 -0.13333334]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[15.  5.  1.] Error: [ 0.         -0.16666664 -0.13333334]\n",
      "i: 15.0 Error: [1.0000000e+00 2.9802322e-08 3.9999992e-02]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[16.  5.  1.] Error: [0.0000000e+00 2.9802322e-08 3.9999992e-02]\n",
      "i: 16.0 Error: [1.         0.1666667  0.21333332]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[17.  5.  1.] Error: [0.         0.1666667  0.21333332]\n",
      "i: 17.0 Error: [1.         0.33333337 0.38666666]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[18.  5.  1.] Error: [0.         0.33333337 0.38666666]\n",
      "i: 18.0 Error: [1.         0.50000006 0.56      ]\n",
      "step_dims & step_dir [ True  True  True] [1. 1. 1.]\n",
      "[19.  6.  2.] Error: [ 0.         -0.49999994 -0.44      ]\n",
      "i: 19.0 Error: [ 1.         -0.33333325 -0.26666665]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[20.  6.  2.] Error: [ 0.         -0.33333325 -0.26666665]\n",
      "i: 20.0 Error: [ 1.         -0.16666658 -0.09333332]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[21.  6.  2.] Error: [ 0.         -0.16666658 -0.09333332]\n",
      "i: 21.0 Error: [1.000000e+00 8.940697e-08 8.000001e-02]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[22.  6.  2.] Error: [0.000000e+00 8.940697e-08 8.000001e-02]\n",
      "i: 22.0 Error: [1.         0.16666676 0.25333333]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[23.  6.  2.] Error: [0.         0.16666676 0.25333333]\n",
      "i: 23.0 Error: [1.         0.33333343 0.42666668]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[24.  6.  2.] Error: [0.         0.33333343 0.42666668]\n",
      "i: 24.0 Error: [1.        0.5000001 0.6      ]\n",
      "step_dims & step_dir [ True  True  True] [1. 1. 1.]\n",
      "[25.  7.  3.] Error: [ 0.         -0.49999988 -0.39999998]\n",
      "i: 25.0 Error: [ 1.         -0.3333332  -0.22666664]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[26.  7.  3.] Error: [ 0.         -0.3333332  -0.22666664]\n",
      "i: 26.0 Error: [ 1.         -0.16666652 -0.05333331]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[27.  7.  3.] Error: [ 0.         -0.16666652 -0.05333331]\n",
      "i: 27.0 Error: [1.0000000e+00 1.4901161e-07 1.2000002e-01]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[28.  7.  3.] Error: [0.0000000e+00 1.4901161e-07 1.2000002e-01]\n",
      "i: 28.0 Error: [1.         0.16666682 0.29333335]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[29.  7.  3.] Error: [0.         0.16666682 0.29333335]\n",
      "i: 29.0 Error: [1.        0.3333335 0.4666667]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[30.  7.  3.] Error: [0.        0.3333335 0.4666667]\n",
      "i: 30.0 Error: [1.         0.5000002  0.64000005]\n",
      "step_dims & step_dir [ True  True  True] [1. 1. 1.]\n",
      "[31.  8.  4.] Error: [ 0.         -0.49999982 -0.35999995]\n",
      "i: 31.0 Error: [ 1.         -0.33333313 -0.18666662]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[32.  8.  4.] Error: [ 0.         -0.33333313 -0.18666662]\n",
      "i: 32.0 Error: [ 1.         -0.16666646 -0.01333329]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[33.  8.  4.] Error: [ 0.         -0.16666646 -0.01333329]\n",
      "i: 33.0 Error: [1.0000000e+00 2.0861626e-07 1.6000004e-01]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[34.  8.  4.] Error: [0.0000000e+00 2.0861626e-07 1.6000004e-01]\n",
      "i: 34.0 Error: [1.         0.16666688 0.33333337]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[35.  8.  4.] Error: [0.         0.16666688 0.33333337]\n",
      "i: 35.0 Error: [1.         0.33333355 0.5066667 ]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[36.  8.  5.] Error: [ 0.          0.33333355 -0.49333328]\n",
      "i: 36.0 Error: [ 1.          0.50000024 -0.31999993]\n",
      "step_dims & step_dir [ True  True False] [ 1.  1. -1.]\n",
      "[37.  9.  5.] Error: [ 0.         -0.49999976 -0.31999993]\n",
      "i: 37.0 Error: [ 1.         -0.33333308 -0.1466666 ]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[38.  9.  5.] Error: [ 0.         -0.33333308 -0.1466666 ]\n",
      "i: 38.0 Error: [ 1.         -0.1666664   0.02666673]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[39.  9.  5.] Error: [ 0.         -0.1666664   0.02666673]\n",
      "i: 39.0 Error: [1.0000000e+00 2.6822090e-07 2.0000006e-01]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[40.  9.  5.] Error: [0.0000000e+00 2.6822090e-07 2.0000006e-01]\n",
      "i: 40.0 Error: [1.         0.16666694 0.3733334 ]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[41.  9.  5.] Error: [0.         0.16666694 0.3733334 ]\n",
      "i: 41.0 Error: [1.         0.3333336  0.54666674]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[42.  9.  6.] Error: [ 0.          0.3333336  -0.45333326]\n",
      "i: 42.0 Error: [ 1.         0.5000003 -0.2799999]\n",
      "step_dims & step_dir [ True  True False] [ 1.  1. -1.]\n",
      "[43. 10.  6.] Error: [ 0.        -0.4999997 -0.2799999]\n",
      "i: 43.0 Error: [ 1.         -0.33333302 -0.10666658]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[44. 10.  6.] Error: [ 0.         -0.33333302 -0.10666658]\n",
      "i: 44.0 Error: [ 1.         -0.16666634  0.06666675]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[45. 10.  6.] Error: [ 0.         -0.16666634  0.06666675]\n",
      "i: 45.0 Error: [1.0000000e+00 3.2782555e-07 2.4000008e-01]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[46. 10.  6.] Error: [0.0000000e+00 3.2782555e-07 2.4000008e-01]\n",
      "i: 46.0 Error: [1.         0.166667   0.41333342]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[47. 10.  6.] Error: [0.         0.166667   0.41333342]\n",
      "i: 47.0 Error: [1.         0.33333367 0.58666676]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[48. 10.  7.] Error: [ 0.          0.33333367 -0.41333324]\n",
      "i: 48.0 Error: [ 1.          0.50000036 -0.2399999 ]\n",
      "step_dims & step_dir [ True  True False] [ 1.  1. -1.]\n",
      "[49. 11.  7.] Error: [ 0.         -0.49999964 -0.2399999 ]\n",
      "i: 49.0 Error: [ 1.         -0.33333296 -0.06666657]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[50. 11.  7.] Error: [ 0.         -0.33333296 -0.06666657]\n",
      "i: 50.0 Error: [ 1.         -0.16666628  0.10666676]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[51. 11.  7.] Error: [ 0.         -0.16666628  0.10666676]\n",
      "i: 51.0 Error: [1.000000e+00 3.874302e-07 2.800001e-01]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[52. 11.  7.] Error: [0.000000e+00 3.874302e-07 2.800001e-01]\n",
      "i: 52.0 Error: [1.         0.16666706 0.45333344]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[53. 11.  7.] Error: [0.         0.16666706 0.45333344]\n",
      "i: 53.0 Error: [1.         0.33333373 0.6266668 ]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[54. 11.  8.] Error: [ 0.          0.33333373 -0.37333322]\n",
      "i: 54.0 Error: [ 1.          0.5000004  -0.19999988]\n",
      "step_dims & step_dir [ True  True False] [ 1.  1. -1.]\n",
      "[55. 12.  8.] Error: [ 0.         -0.49999958 -0.19999988]\n",
      "i: 55.0 Error: [ 1.         -0.3333329  -0.02666655]\n",
      "step_dims & step_dir [ True False False] [ 1. -1. -1.]\n",
      "[56. 12.  8.] Error: [ 0.         -0.3333329  -0.02666655]\n",
      "i: 56.0 Error: [ 1.         -0.16666622  0.14666678]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[57. 12.  8.] Error: [ 0.         -0.16666622  0.14666678]\n",
      "i: 57.0 Error: [1.0000000e+00 4.4703484e-07 3.2000011e-01]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[58. 12.  8.] Error: [0.0000000e+00 4.4703484e-07 3.2000011e-01]\n",
      "i: 58.0 Error: [1.         0.16666712 0.49333346]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[59. 12.  8.] Error: [0.         0.16666712 0.49333346]\n",
      "i: 59.0 Error: [1.        0.3333338 0.6666668]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[60. 12.  9.] Error: [ 0.         0.3333338 -0.3333332]\n",
      "i: 60.0 Error: [ 1.          0.5000005  -0.15999986]\n",
      "step_dims & step_dir [ True  True False] [ 1.  1. -1.]\n",
      "[61. 13.  9.] Error: [ 0.         -0.49999952 -0.15999986]\n",
      "i: 61.0 Error: [ 1.         -0.33333284  0.01333347]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[62. 13.  9.] Error: [ 0.         -0.33333284  0.01333347]\n",
      "i: 62.0 Error: [ 1.         -0.16666616  0.1866668 ]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[63. 13.  9.] Error: [ 0.         -0.16666616  0.1866668 ]\n",
      "i: 63.0 Error: [1.0000000e+00 5.0663948e-07 3.6000013e-01]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[64. 13.  9.] Error: [0.0000000e+00 5.0663948e-07 3.6000013e-01]\n",
      "i: 64.0 Error: [1.         0.16666718 0.5333335 ]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[65. 13. 10.] Error: [ 0.          0.16666718 -0.46666652]\n",
      "i: 65.0 Error: [ 1.          0.33333385 -0.29333317]\n",
      "step_dims & step_dir [ True False False] [ 1.  1. -1.]\n",
      "[66. 13. 10.] Error: [ 0.          0.33333385 -0.29333317]\n",
      "i: 66.0 Error: [ 1.          0.50000054 -0.11999984]\n",
      "step_dims & step_dir [ True  True False] [ 1.  1. -1.]\n",
      "[67. 14. 10.] Error: [ 0.         -0.49999946 -0.11999984]\n",
      "i: 67.0 Error: [ 1.         -0.33333278  0.05333349]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[68. 14. 10.] Error: [ 0.         -0.33333278  0.05333349]\n",
      "i: 68.0 Error: [ 1.         -0.1666661   0.22666682]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[69. 14. 10.] Error: [ 0.         -0.1666661   0.22666682]\n",
      "i: 69.0 Error: [1.0000000e+00 5.6624413e-07 4.0000015e-01]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[70. 14. 10.] Error: [0.0000000e+00 5.6624413e-07 4.0000015e-01]\n",
      "i: 70.0 Error: [1.         0.16666724 0.5733335 ]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[71. 14. 11.] Error: [ 0.          0.16666724 -0.4266665 ]\n",
      "i: 71.0 Error: [ 1.          0.3333339  -0.25333315]\n",
      "step_dims & step_dir [ True False False] [ 1.  1. -1.]\n",
      "[72. 14. 11.] Error: [ 0.          0.3333339  -0.25333315]\n",
      "i: 72.0 Error: [ 1.          0.5000006  -0.07999982]\n",
      "step_dims & step_dir [ True  True False] [ 1.  1. -1.]\n",
      "[73. 15. 11.] Error: [ 0.         -0.4999994  -0.07999982]\n",
      "i: 73.0 Error: [ 1.         -0.33333272  0.09333351]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[74. 15. 11.] Error: [ 0.         -0.33333272  0.09333351]\n",
      "i: 74.0 Error: [ 1.         -0.16666605  0.26666683]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[75. 15. 11.] Error: [ 0.         -0.16666605  0.26666683]\n",
      "i: 75.0 Error: [1.0000000e+00 6.2584877e-07 4.4000018e-01]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[76. 15. 11.] Error: [0.0000000e+00 6.2584877e-07 4.4000018e-01]\n",
      "i: 76.0 Error: [1.        0.1666673 0.6133335]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[77. 15. 12.] Error: [ 0.          0.1666673  -0.38666648]\n",
      "i: 77.0 Error: [ 1.          0.33333397 -0.21333314]\n",
      "step_dims & step_dir [ True False False] [ 1.  1. -1.]\n",
      "[78. 15. 12.] Error: [ 0.          0.33333397 -0.21333314]\n",
      "i: 78.0 Error: [ 1.          0.50000066 -0.03999981]\n",
      "step_dims & step_dir [ True  True False] [ 1.  1. -1.]\n",
      "[79. 16. 12.] Error: [ 0.         -0.49999934 -0.03999981]\n",
      "i: 79.0 Error: [ 1.         -0.33333266  0.13333352]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[80. 16. 12.] Error: [ 0.         -0.33333266  0.13333352]\n",
      "i: 80.0 Error: [ 1.         -0.16666599  0.30666685]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[81. 16. 12.] Error: [ 0.         -0.16666599  0.30666685]\n",
      "i: 81.0 Error: [1.000000e+00 6.854534e-07 4.800002e-01]\n",
      "step_dims & step_dir [ True False False] [1. 1. 1.]\n",
      "[82. 16. 12.] Error: [0.000000e+00 6.854534e-07 4.800002e-01]\n",
      "i: 82.0 Error: [1.         0.16666736 0.65333354]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[83. 16. 13.] Error: [ 0.          0.16666736 -0.34666646]\n",
      "i: 83.0 Error: [ 1.          0.33333403 -0.17333312]\n",
      "step_dims & step_dir [ True False False] [ 1.  1. -1.]\n",
      "[84. 16. 13.] Error: [ 0.          0.33333403 -0.17333312]\n",
      "i: 84.0 Error: [1.0000000e+00 5.0000072e-01 2.0861626e-07]\n",
      "step_dims & step_dir [ True  True False] [1. 1. 1.]\n",
      "[85. 17. 13.] Error: [ 0.0000000e+00 -4.9999928e-01  2.0861626e-07]\n",
      "i: 85.0 Error: [ 1.         -0.3333326   0.17333354]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[86. 17. 13.] Error: [ 0.         -0.3333326   0.17333354]\n",
      "i: 86.0 Error: [ 1.         -0.16666593  0.34666687]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[87. 17. 13.] Error: [ 0.         -0.16666593  0.34666687]\n",
      "i: 87.0 Error: [1.0000000e+00 7.4505806e-07 5.2000022e-01]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[88. 17. 14.] Error: [ 0.0000000e+00  7.4505806e-07 -4.7999978e-01]\n",
      "i: 88.0 Error: [ 1.          0.16666742 -0.30666643]\n",
      "step_dims & step_dir [ True False False] [ 1.  1. -1.]\n",
      "[89. 17. 14.] Error: [ 0.          0.16666742 -0.30666643]\n",
      "i: 89.0 Error: [ 1.         0.3333341 -0.1333331]\n",
      "step_dims & step_dir [ True False False] [ 1.  1. -1.]\n",
      "[90. 17. 14.] Error: [ 0.         0.3333341 -0.1333331]\n",
      "i: 90.0 Error: [1.         0.5000008  0.04000023]\n",
      "step_dims & step_dir [ True  True False] [1. 1. 1.]\n",
      "[91. 18. 14.] Error: [ 0.         -0.49999923  0.04000023]\n",
      "i: 91.0 Error: [ 1.         -0.33333254  0.21333356]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[92. 18. 14.] Error: [ 0.         -0.33333254  0.21333356]\n",
      "i: 92.0 Error: [ 1.         -0.16666587  0.3866669 ]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[93. 18. 14.] Error: [ 0.         -0.16666587  0.3866669 ]\n",
      "i: 93.0 Error: [1.0000000e+00 8.0466270e-07 5.6000024e-01]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[94. 18. 15.] Error: [ 0.0000000e+00  8.0466270e-07 -4.3999976e-01]\n",
      "i: 94.0 Error: [ 1.          0.16666748 -0.2666664 ]\n",
      "step_dims & step_dir [ True False False] [ 1.  1. -1.]\n",
      "[95. 18. 15.] Error: [ 0.          0.16666748 -0.2666664 ]\n",
      "i: 95.0 Error: [ 1.          0.33333415 -0.09333308]\n",
      "step_dims & step_dir [ True False False] [ 1.  1. -1.]\n",
      "[96. 18. 15.] Error: [ 0.          0.33333415 -0.09333308]\n",
      "i: 96.0 Error: [1.         0.50000083 0.08000025]\n",
      "step_dims & step_dir [ True  True False] [1. 1. 1.]\n",
      "[97. 19. 15.] Error: [ 0.         -0.49999917  0.08000025]\n",
      "i: 97.0 Error: [ 1.         -0.33333248  0.25333357]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[98. 19. 15.] Error: [ 0.         -0.33333248  0.25333357]\n",
      "i: 98.0 Error: [ 1.         -0.1666658   0.42666692]\n",
      "step_dims & step_dir [ True False False] [ 1. -1.  1.]\n",
      "[99. 19. 15.] Error: [ 0.         -0.1666658   0.42666692]\n",
      "i: 99.0 Error: [1.0000000e+00 8.6426735e-07 6.0000026e-01]\n",
      "step_dims & step_dir [ True False  True] [1. 1. 1.]\n",
      "[100.  19.  16.] Error: [ 0.0000000e+00  8.6426735e-07 -3.9999974e-01]\n",
      "i: 100.0 Error: [ 1.          0.16666754 -0.2266664 ]\n",
      "step_dims & step_dir [ True False False] [ 1.  1. -1.]\n",
      "[101.  19.  16.] Error: [ 0.          0.16666754 -0.2266664 ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[array([10.,  4.,  0.], dtype=float32),\n",
       " array([11.,  4.,  0.], dtype=float32),\n",
       " array([12.,  4.,  0.], dtype=float32),\n",
       " array([13.,  5.,  1.], dtype=float32),\n",
       " array([14.,  5.,  1.], dtype=float32),\n",
       " array([15.,  5.,  1.], dtype=float32),\n",
       " array([16.,  5.,  1.], dtype=float32),\n",
       " array([17.,  5.,  1.], dtype=float32),\n",
       " array([18.,  5.,  1.], dtype=float32),\n",
       " array([19.,  6.,  2.], dtype=float32),\n",
       " array([20.,  6.,  2.], dtype=float32),\n",
       " array([21.,  6.,  2.], dtype=float32),\n",
       " array([22.,  6.,  2.], dtype=float32),\n",
       " array([23.,  6.,  2.], dtype=float32),\n",
       " array([24.,  6.,  2.], dtype=float32),\n",
       " array([25.,  7.,  3.], dtype=float32),\n",
       " array([26.,  7.,  3.], dtype=float32),\n",
       " array([27.,  7.,  3.], dtype=float32),\n",
       " array([28.,  7.,  3.], dtype=float32),\n",
       " array([29.,  7.,  3.], dtype=float32),\n",
       " array([30.,  7.,  3.], dtype=float32),\n",
       " array([31.,  8.,  4.], dtype=float32),\n",
       " array([32.,  8.,  4.], dtype=float32),\n",
       " array([33.,  8.,  4.], dtype=float32),\n",
       " array([34.,  8.,  4.], dtype=float32),\n",
       " array([35.,  8.,  4.], dtype=float32),\n",
       " array([36.,  8.,  5.], dtype=float32),\n",
       " array([37.,  9.,  5.], dtype=float32),\n",
       " array([38.,  9.,  5.], dtype=float32),\n",
       " array([39.,  9.,  5.], dtype=float32),\n",
       " array([40.,  9.,  5.], dtype=float32),\n",
       " array([41.,  9.,  5.], dtype=float32),\n",
       " array([42.,  9.,  6.], dtype=float32),\n",
       " array([43., 10.,  6.], dtype=float32),\n",
       " array([44., 10.,  6.], dtype=float32),\n",
       " array([45., 10.,  6.], dtype=float32),\n",
       " array([46., 10.,  6.], dtype=float32),\n",
       " array([47., 10.,  6.], dtype=float32),\n",
       " array([48., 10.,  7.], dtype=float32),\n",
       " array([49., 11.,  7.], dtype=float32),\n",
       " array([50., 11.,  7.], dtype=float32),\n",
       " array([51., 11.,  7.], dtype=float32),\n",
       " array([52., 11.,  7.], dtype=float32),\n",
       " array([53., 11.,  7.], dtype=float32),\n",
       " array([54., 11.,  8.], dtype=float32),\n",
       " array([55., 12.,  8.], dtype=float32),\n",
       " array([56., 12.,  8.], dtype=float32),\n",
       " array([57., 12.,  8.], dtype=float32),\n",
       " array([58., 12.,  8.], dtype=float32),\n",
       " array([59., 12.,  8.], dtype=float32),\n",
       " array([60., 12.,  9.], dtype=float32),\n",
       " array([61., 13.,  9.], dtype=float32),\n",
       " array([62., 13.,  9.], dtype=float32),\n",
       " array([63., 13.,  9.], dtype=float32),\n",
       " array([64., 13.,  9.], dtype=float32),\n",
       " array([65., 13., 10.], dtype=float32),\n",
       " array([66., 13., 10.], dtype=float32),\n",
       " array([67., 14., 10.], dtype=float32),\n",
       " array([68., 14., 10.], dtype=float32),\n",
       " array([69., 14., 10.], dtype=float32),\n",
       " array([70., 14., 10.], dtype=float32),\n",
       " array([71., 14., 11.], dtype=float32),\n",
       " array([72., 14., 11.], dtype=float32),\n",
       " array([73., 15., 11.], dtype=float32),\n",
       " array([74., 15., 11.], dtype=float32),\n",
       " array([75., 15., 11.], dtype=float32),\n",
       " array([76., 15., 11.], dtype=float32),\n",
       " array([77., 15., 12.], dtype=float32),\n",
       " array([78., 15., 12.], dtype=float32),\n",
       " array([79., 16., 12.], dtype=float32),\n",
       " array([80., 16., 12.], dtype=float32),\n",
       " array([81., 16., 12.], dtype=float32),\n",
       " array([82., 16., 12.], dtype=float32),\n",
       " array([83., 16., 13.], dtype=float32),\n",
       " array([84., 16., 13.], dtype=float32),\n",
       " array([85., 17., 13.], dtype=float32),\n",
       " array([86., 17., 13.], dtype=float32),\n",
       " array([87., 17., 13.], dtype=float32),\n",
       " array([88., 17., 14.], dtype=float32),\n",
       " array([89., 17., 14.], dtype=float32),\n",
       " array([90., 17., 14.], dtype=float32),\n",
       " array([91., 18., 14.], dtype=float32),\n",
       " array([92., 18., 14.], dtype=float32),\n",
       " array([93., 18., 14.], dtype=float32),\n",
       " array([94., 18., 15.], dtype=float32),\n",
       " array([95., 18., 15.], dtype=float32),\n",
       " array([96., 18., 15.], dtype=float32),\n",
       " array([97., 19., 15.], dtype=float32),\n",
       " array([98., 19., 15.], dtype=float32),\n",
       " array([99., 19., 15.], dtype=float32),\n",
       " array([100.,  19.,  16.], dtype=float32)]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "start = np.array([5, 2, 0], dtype=np.float32)\n",
    "target = np.array([80, 14.5, 13], dtype=np.float32)\n",
    "step_size = 0.5\n",
    "voxels = bresenham(start, target, a, step_size=step_size)\n",
    "voxels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "656a91cc",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 684x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from plot_helpers import plot_voxel_line\n",
    "fig = plot_voxel_line(voxels, step_size, a, start, target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a4e77bf7",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}