{ "cells": [ { "cell_type": "markdown", "id": "5acc6ce3-0e71-4451-97c6-eb4f2b61fcf3", "metadata": {}, "source": [ "# Retrieve Tate-Bryan angles form three orthogonal vectors (X, Y, Z) describing the attitude of a body relative to a fixed reference system described by the three unit vectors (x,y,z)\n", "O. Kaufmann, K Tsakirmpaloglou, 2022.\n", "see https://en.wikipedia.org/wiki/Euler_angles" ] }, { "cell_type": "code", "execution_count": 1, "id": "fd61943a-7d5a-4500-860d-f4959f89022d", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from geometron.geometries import vectors as ggv\n", "from geometron.geometries import transforms as ggt\n", "from geometron.plot import plot_3d_vectors, plot_2d_vectors" ] }, { "cell_type": "markdown", "id": "613ee09d-51de-41ae-b2eb-c08c73397937", "metadata": {}, "source": [ "## Define the unit vecors of the reference system" ] }, { "cell_type": "code", "execution_count": 2, "id": "ef23b3ae-0517-4361-9033-575284fd0207", "metadata": {}, "outputs": [], "source": [ "x = np.array([1.,0.,0.])\n", "y = np.array([0.,1.,0.])\n", "z = np.array([0.,0.,1.])" ] }, { "cell_type": "markdown", "id": "f0c09b4c-1f56-48bc-9c89-7ab6bb6c5e33", "metadata": {}, "source": [ "## Start with the reference system associated to the body aligned on the fixed reference system" ] }, { "cell_type": "code", "execution_count": 3, "id": "afce2930-f8d1-47dc-bf4c-689523a9dc55", "metadata": {}, "outputs": [], "source": [ "X = 2*x\n", "Y = 2*y\n", "Z = 2*z" ] }, { "cell_type": "markdown", "id": "0b376748-10b1-4c2c-ba49-1b1cee567dac", "metadata": {}, "source": [ "## Rotate the body along its axes" ] }, { "cell_type": "code", "execution_count": 4, "id": "ffc5b6c2-c62e-4aa9-a968-b29d33cf8100", "metadata": {}, "outputs": [], "source": [ "roll = 20.\n", "pitch = 90.\n", "yaw = -130." ] }, { "cell_type": "code", "execution_count": 5, "id": "3dcaae59-cb41-482a-b4b7-c7af94567787", "metadata": {}, "outputs": [], "source": [ "rx = ggt.rotate_around_vector(X, roll, degrees=True)\n", "X = rx@X\n", "Y = rx@Y\n", "Z = rx@Z\n", "ry = ggt.rotate_around_vector(Y, pitch, degrees=True)\n", "X = ry@X\n", "Y = ry@Y\n", "Z = ry@Z\n", "rz = ggt.rotate_around_vector(Z, yaw, degrees=True)\n", "X = rz@X\n", "Y = rz@Y\n", "Z = rz@Z" ] }, { "cell_type": "markdown", "id": "33f10d07-f71b-46eb-b849-e033265abddd", "metadata": {}, "source": [ "### Display resulting components of the three vectors" ] }, { "cell_type": "code", "execution_count": 6, "id": "8776d8c7-c9fc-4fbf-8760-1b6b61bd343c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([-1.09243052e-16, -1.87938524e+00, 6.84040287e-01]),\n", " array([ 5.64896473e-17, -6.84040287e-01, -1.87938524e+00]),\n", " array([ 2.00000000e+00, -8.98619447e-17, 1.68610676e-16]))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X, Y, Z" ] }, { "cell_type": "markdown", "id": "98df67e3-450a-4882-a969-4218b9ea86bb", "metadata": {}, "source": [ "## Display the body axes (X: red, Y: green, Z: blue) and the fixed reference system (x: cyan, y: yellow, z: magenta) " ] }, { "cell_type": "code", "execution_count": 7, "id": "2fc4e1cd-3a74-4917-8f6e-98682343931d", "metadata": { "nbsphinx-thumbnail": { "tooltip": "Body axes and reference system" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pl = plot_3d_vectors(np.vstack([X, Y, Z, x, y, z]), colors=['red', 'green', 'blue', 'cyan', 'yellow', 'magenta'], names=['X', 'Y', 'Z', 'x', 'y', 'z'],\n", " add_labels=True, show_grid=True)\n", "pl.show(jupyter_backend='ipyvtk')" ] }, { "cell_type": "markdown", "id": "a58ed425-d957-4034-9a21-a38d77abe6db", "metadata": {}, "source": [ "## Compute the Tate-Bryan angles (X1Y2Z3) of the body\n", "Special handeling would be needed in case of 90° rotation around Y\n", "see https://stackoverflow.com/questions/15022630/how-to-calculate-the-angle-from-rotation-matrix" ] }, { "cell_type": "code", "execution_count": 8, "id": "a93dbaa2-4f30-4d94-a1a3-ca9f7a1f3ca9", "metadata": {}, "outputs": [], "source": [ "phi = np.rad2deg(np.arctan2(-Z[1], Z[2]))" ] }, { "cell_type": "code", "execution_count": 9, "id": "d15072f0-90dc-4ade-a64a-97e61e2f1b32", "metadata": {}, "outputs": [], "source": [ "theta = np.rad2deg(np.arctan2(Z[0], np.sqrt(Z[1]**2+Z[2]**2)))" ] }, { "cell_type": "code", "execution_count": 10, "id": "2f123780-65ad-4ce9-9a4c-4972760886d2", "metadata": {}, "outputs": [], "source": [ "psi = np.rad2deg(np.arctan2(-Y[0], X[0]))" ] }, { "cell_type": "code", "execution_count": 11, "id": "26cc8205-1223-4f23-9fad-41bd1903db48", "metadata": {}, "outputs": [], "source": [ "theta = np.rad2deg(np.arctan2(Z[0], np.sqrt(Z[1]**2+Z[2]**2)))\n", "if np.allclose(theta, 90.):\n", " phi = 180.\n", " psi = np.rad2deg(np.arctan2(-X[1], Y[2]))\n", "else: \n", " phi = np.rad2deg(np.arctan2(-Z[1], Z[2]))\n", " psi = np.rad2deg(np.arctan2(-Y[0], X[0]))" ] }, { "cell_type": "markdown", "id": "b396d62a-db68-4dcf-9398-9273a71f432a", "metadata": {}, "source": [ "### Display the Euler angles" ] }, { "cell_type": "code", "execution_count": 12, "id": "cb15ac0c-18a5-41c2-82e8-d6241d6a80dc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(180.0, 90.0, 135.0)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "phi, theta, psi" ] }, { "cell_type": "code", "execution_count": 13, "id": "fcba6da7-682c-4fb9-991d-bc6a6bee9b3b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(False, True, False)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(phi, roll), np.allclose(theta, pitch), np.allclose(psi, yaw) " ] } ], "metadata": { "celltoolbar": "Edit 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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }