29736f4fa046c111d44ada71a0b1922e

notebook.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "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": "3.7.3"
    },
    "colab": {
      "name": "29736f4fa046c111d44ada71a0b1922e",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/WesleyYue/b268038fe5c61a3833950f4c482d1596/notebook.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Kxj5v5rjCMc_",
        "colab_type": "code",
        "outputId": "ec12d5bf-5b1b-462e-9d34-b9faa5b51bb0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 377
        }
      },
      "source": [
        "!pip install numpy pytransform3d"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (1.17.4)\n",
            "Collecting pytransform3d\n",
            "  Downloading https://files.pythonhosted.org/packages/db/50/3b28c11f214eb4003c02d97ab2bc1aaa9123895c2c0058107fa29449f979/pytransform3d-1.1.1.tar.gz\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from pytransform3d) (1.3.3)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.6/dist-packages (from pytransform3d) (3.1.2)\n",
            "Requirement already satisfied: lxml in /usr/local/lib/python3.6/dist-packages (from pytransform3d) (4.2.6)\n",
            "Requirement already satisfied: beautifulsoup4 in /usr/local/lib/python3.6/dist-packages (from pytransform3d) (4.6.3)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->pytransform3d) (1.1.0)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->pytransform3d) (2.6.1)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->pytransform3d) (2.4.5)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib->pytransform3d) (0.10.0)\n",
            "Requirement already satisfied: setuptools in /usr/local/lib/python3.6/dist-packages (from kiwisolver>=1.0.1->matplotlib->pytransform3d) (42.0.2)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.6/dist-packages (from python-dateutil>=2.1->matplotlib->pytransform3d) (1.12.0)\n",
            "Building wheels for collected packages: pytransform3d\n",
            "  Building wheel for pytransform3d (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for pytransform3d: filename=pytransform3d-1.1.1-cp36-none-any.whl size=28793 sha256=1435accc0c01c6dffa07be7e4430254417e12b4c7b34270489298c24665430ef\n",
            "  Stored in directory: /root/.cache/pip/wheels/1a/07/33/6e38e02d04412cc7b01dbe200bf79afa55bb5481028a10d923\n",
            "Successfully built pytransform3d\n",
            "Installing collected packages: pytransform3d\n",
            "Successfully installed pytransform3d-1.1.1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "73hHZMJ6BhbP",
        "colab_type": "code",
        "outputId": "862636bd-7c6b-4b52-cfda-e2364e9d9854",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "%pylab inline\n",
        "import pytransform3d.rotations as pr"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Populating the interactive namespace from numpy and matplotlib\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1Xz3gCl1BhbU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "theta_A2B = 0.5 * np.pi\n",
        "theta_B2A = -theta_A2B\n",
        "\n",
        "R = pr.matrix_from_angle(2, 0.5 * np.pi)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1T6bdNPfBlP2",
        "colab_type": "code",
        "outputId": "cae9e19b-9633-47da-f9ad-626342c554cd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "import cv2\n",
        "cv_R, _ = cv2.Rodrigues(np.array([0,0, theta_B2A]))\n",
        "\n",
        "print(R)\n",
        "print(cv_R)\n",
        "print(np.allclose(R, cv_R))"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 6.123234e-17  1.000000e+00  0.000000e+00]\n",
            " [-1.000000e+00  6.123234e-17  0.000000e+00]\n",
            " [ 0.000000e+00  0.000000e+00  1.000000e+00]]\n",
            "[[ 6.123234e-17  1.000000e+00  0.000000e+00]\n",
            " [-1.000000e+00  6.123234e-17  0.000000e+00]\n",
            " [ 0.000000e+00  0.000000e+00  1.000000e+00]]\n",
            "True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oW0ezVcaBhba",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "random_state = random.RandomState(0)\n",
        "points = random_state.randn(10, 2) * 0.1 + np.array([[1, 1]])\n",
        "points = np.hstack((points, np.zeros((len(points), 1))))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vw5JvG9mBhbd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot_coordinate_frame(ls=\"-\"):\n",
        "    subplot(111, aspect=\"equal\")\n",
        "    plot([0, 2], [0, 0], c=\"r\", ls=ls)\n",
        "    plot([0, 0], [0, 2], c=\"g\", ls=ls)\n",
        "    xlim((-2, 2))\n",
        "    ylim((-2, 2))\n",
        "    grid()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9PbIh6kDBhbg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def rotate_points(R, points):\n",
        "    return points.dot(R.T)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zVir1DGMBhbi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot_points(points):\n",
        "    scatter(points[:, 0], points[:, 1])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oNI_2lR2Bhbl",
        "colab_type": "code",
        "outputId": "d9f85880-9b7e-49b7-ec22-0b8740a0eb96",
        "colab": {}
      },
      "source": [
        "plot_coordinate_frame()\n",
        "plot_points(points)\n",
        "# new coordinate frame\n",
        "plot([-0.05, -0.05], [0, 2], c=\"r\", ls=\"--\")\n",
        "plot([-2, 0], [0.05, 0.05], c=\"g\", ls=\"--\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f7145a07ac8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 65
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NaCHm0W6Bhbp",
        "colab_type": "code",
        "outputId": "e96130bb-1a6f-4133-bf40-8d628aa47114",
        "colab": {}
      },
      "source": [
        "rotated_points = rotate_points(R, points)\n",
        "plot_coordinate_frame(ls=\"--\")\n",
        "plot_points(rotated_points)\n",
        "# old coordinate frame\n",
        "plot([0, 0], [-0.05, -2], c=\"r\")\n",
        "plot([0, 2], [-0.05, -0.05], c=\"g\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f7146316f60>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 75
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}