{ "cells": [ { "cell_type": "markdown", "id": "2fd39c41-0635-4cf3-b498-5b20ea92f9f1", "metadata": {}, "source": [ "# Vectors demonstration\n", "O. Kaufmann, 2021." ] }, { "cell_type": "code", "execution_count": 1, "id": "ab30a30b-7766-4de0-880a-9639799dc1da", "metadata": { "tags": [] }, "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\n", "from shapely.geometry import Point\n", "import matplotlib.pyplot as plt\n", "from matplotlib.ticker import MultipleLocator, FormatStrFormatter, AutoMinorLocator" ] }, { "cell_type": "markdown", "id": "1ee09d2f-ba6a-4974-9e0a-bfa44d662305", "metadata": {}, "source": [ "## Create some points and a vector" ] }, { "cell_type": "code", "execution_count": 2, "id": "eff62ea9-cc0b-46b4-a605-8227ed129717", "metadata": { "tags": [] }, "outputs": [], "source": [ "a = Point([0., 0., 0.])\n", "b = Point([1., 0., 0.])\n", "c = Point([0., 1., 0.])\n", "v = np.array([1., 2., 3.])" ] }, { "cell_type": "markdown", "id": "971923d4-f343-4cba-a079-c21a8813c527", "metadata": {}, "source": [ "## Perfom some operations and checks on vectors" ] }, { "cell_type": "code", "execution_count": 3, "id": "663e99f2-8056-4358-a805-43011891f4b9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.26726124, 0.53452248, 0.80178373])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.unit_vector(v)" ] }, { "cell_type": "code", "execution_count": 4, "id": "f19221df-9005-4c9a-b733-7d6380d079ac", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.almost_null(np.array([0.,0.,0.]))" ] }, { "cell_type": "code", "execution_count": 5, "id": "393a7151-650d-44d6-b869-12fef12794e3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.almost_colinear(ggv.ux, np.cross(ggv.uy, ggv.uz))" ] }, { "cell_type": "markdown", "id": "259010f0-a80e-42e9-a077-50bd9d0a60f2", "metadata": {}, "source": [ "## Compute the signed angle between two vectors" ] }, { "cell_type": "code", "execution_count": 6, "id": "123cb905-c783-4287-9750-5207d4b58f01", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-29.972103422676636" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.angle_between_vectors(ggv.ux, [0.867, -.5, 0.], degrees=True)" ] }, { "cell_type": "code", "execution_count": 7, "id": "25db1fd2-9638-4704-9e10-c189c2f896b7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "90.0" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.angle_between_vectors(ggv.ux, ggv.uy, degrees=True)" ] }, { "cell_type": "code", "execution_count": 8, "id": "05bda4d7-fa8d-43d7-b8b4-ed6b8c5f7583", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "90.0" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.angle_between_vectors(ggv.uy, ggv.uz, degrees=True)" ] }, { "cell_type": "code", "execution_count": 9, "id": "648586ba-aa46-4b96-9001-7fe97585f154", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-90.0" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.angle_between_vectors(ggv.uy, ggv.ux, degrees=True)" ] }, { "cell_type": "code", "execution_count": 10, "id": "b9cae00e-a69a-43d4-9eb0-65f04e44e500", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-90.0" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.angle_between_vectors(ggv.ux, ggv.uz, degrees=True)" ] }, { "cell_type": "markdown", "id": "65f3309a-2f5a-4274-a682-867504afcd29", "metadata": {}, "source": [ "## Compute the unit vector normal to a plane defined by two vectors or three points " ] }, { "cell_type": "code", "execution_count": 11, "id": "c8be9f3d-ea49-4115-8333-86466cd2efb6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0., 0., 1.])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.plane_normal([ggv.ux, ggv.uy])" ] }, { "cell_type": "code", "execution_count": 12, "id": "dae85b92-8973-42ef-af4b-b8088bd2fb18", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0., 0., 1.]])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.plane_normal([a, b, c])" ] }, { "cell_type": "markdown", "id": "4d520021-d1bd-4a03-8c07-505c2f3dbfa8", "metadata": {}, "source": [ "## Plot 2D vectors" ] }, { "cell_type": "code", "execution_count": 13, "id": "ac292b3f-8aa0-48fb-b645-da964608af03", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plot_2d_vectors(np.vstack([2*ggv.ux[:2], ggv.uy[:2]]), colors=['red', 'blue'], show_grid=True)\n", "ax.set_xlim([-2.,2])\n", "ax.set_ylim([-2.,2])\n", "ax.plot()" ] }, { "cell_type": "markdown", "id": "97cc503c-892e-4251-9d46-7a97f612e5e6", "metadata": {}, "source": [ "## Get vectors along dip and strike directions, get the normal to a plane defined by its dip and strike" ] }, { "cell_type": "code", "execution_count": 14, "id": "359dc941-f071-4b09-a188-11d64d90e073", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([-0.25 , -0.4330127, -0.8660254]),\n", " array([ 0.8660254, -0.5 , 0. ]))" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.dip_and_strike_vectors(60., 120., degrees=True)" ] }, { "cell_type": "code", "execution_count": 15, "id": "086e3f36-48a3-406a-99c4-54fe81e00dd9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-0.4330127, -0.75 , 0.5 ])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ggv.plane_normal_from_dip_and_strike(60., 120., degrees=True)" ] }, { "cell_type": "markdown", "id": "545976f8-686d-49f1-8859-cdd04c1d8006", "metadata": {}, "source": [ "## Plot 3D vectors" ] }, { "cell_type": "code", "execution_count": 17, "id": "96ba9275-78c7-4f43-8f53-0e50787a66f2", "metadata": { "nbsphinx-thumbnail": { "tooltip": "This tooltip message was defined in cell metadata" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v_dip, v_strike = ggv.dip_and_strike_vectors(60, 120, degrees=True)\n", "v_normal = ggv.plane_normal_from_dip_and_strike(60, 120, degrees=True)\n", "pl = plot_3d_vectors(np.vstack([v_dip, v_strike, v_normal]), colors=['red', 'green', 'blue'], names=['dip', 'strike', 'normal'],\n", " add_labels=True, show_grid=True)\n", "pl.show(jupyter_backend='static')" ] } ], "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": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 5 }