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cyschneck committed Sep 25, 2024
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17 changes: 13 additions & 4 deletions _preview/1/README.html
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<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="notebooks/how-to-cite.html">How to Cite This Cookbook</a></li>
</ul>
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Introduction</span></p>
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Foundations</span></p>
<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="notebooks/notebook-template.html">Project Pythia Notebook Template</a></li>
<li class="toctree-l1"><a class="reference internal" href="notebooks/foundations/coordinates.html">Coordinate Types</a></li>
<li class="toctree-l1"><a class="reference internal" href="notebooks/foundations/terminology.html">Great Circle Terminology</a></li>
</ul>
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Tutorials</span></p>
<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="notebooks/tutorials/arc_path.html">Great Circle Arcs and Path</a></li>
<li class="toctree-l1"><a class="reference internal" href="notebooks/tutorials/arc_to_point.html">Great Circles and a Point</a></li>
<li class="toctree-l1"><a class="reference internal" href="notebooks/tutorials/parallels_max_min.html">Great Circles and Parallels</a></li>
</ul>

</div>
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<li><p>Foundations and Terminology</p></li>
<li><p>Working with Great Circles</p></li>
</ul>
<p>Where avaiable, this cookbook will demonstrate how to determine the features of a great circle with both existing open-source Python packages and through spherical trigonometry and mathematics</p>
<p>Where available, this cookbook will demonstrate how to determine the features of a great circle with both existing open-source Python packages and through spherical trigonometry and mathematics</p>
<section id="foundations-and-terminology">
<h3>Foundations and Terminology<a class="headerlink" href="#foundations-and-terminology" title="Link to this heading"><i class="fas fa-link"></i></a></h3>
<ul class="simple">
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<li><p>Find the intersection of two great circle paths (always exists)</p></li>
</ul>
<ol class="arabic simple" start="5">
<li><p><strong>Angles and Great Cirlces</strong></p></li>
<li><p><strong>Angles and Great Circles</strong></p></li>
</ol>
<ul class="simple">
<li><p>Calculate the acute and obtuse angle of two great circle paths</p></li>
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</div>
<div class="toctree-wrapper compound">
</div>
<div class="toctree-wrapper compound">
</div>
</section>

<script type="text/x-thebe-config">
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4 changes: 2 additions & 2 deletions _preview/1/_sources/README.md
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- Foundations and Terminology
- Working with Great Circles

Where avaiable, this cookbook will demonstrate how to determine the features of a great circle with both existing open-source Python packages and through spherical trigonometry and mathematics
Where available, this cookbook will demonstrate how to determine the features of a great circle with both existing open-source Python packages and through spherical trigonometry and mathematics

### Foundations and Terminology

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- Find the intersection of two great circle arcs (if it exists)
- Find the intersection of two great circle paths (always exists)

5. **Angles and Great Cirlces**
5. **Angles and Great Circles**
- Calculate the acute and obtuse angle of two great circle paths
- Calculate the directed angle of two great circle paths based on an intersection point
- Working with Spherical Triangles formed by great circle arcs
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4 changes: 2 additions & 2 deletions _preview/1/_sources/notebooks/foundations/coordinates.ipynb
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"source": [
"### Cartesian Coordinates\n",
"\n",
"Cartesian coordinates describe points in space based on perpendicular axis lines that meet at a singlle point of orign, where any point's position is described based on the distance to the orgin along xyz axis\n",
"Cartesian coordinates describe points in space based on perpendicular axis lines that meet at a singlle point of origin, where any point's position is described based on the distance to the origin along xyz axis\n",
"\n",
"**Geodesic to Cartesian Coordinates**\n",
"\n",
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"source": [
"### Spherical Coordinates\n",
"\n",
"Spherical coordinates describe points in space based on three values: radial distance (rho, r) along the radial line between point and the origin, polar angle (theta, θ) between the radial line and the polar axis, and azimuth angle (phi, φ) which is the angle of rotation of the radial line around the polar axis. With a fixed radius, the 3-point coordinates (r, θ, φ) provide a coordiante along a sphere\n",
"Spherical coordinates describe points in space based on three values: radial distance (rho, r) along the radial line between point and the origin, polar angle (theta, θ) between the radial line and the polar axis, and azimuth angle (phi, φ) which is the angle of rotation of the radial line around the polar axis. With a fixed radius, the 3-point coordinates (r, θ, φ) provide a coordinate along a sphere\n",
"\n",
"- Radial distance: distance from center to surface of sphere\n",
"- Polar angle: angle between radial line and polar axis\n",
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8 changes: 4 additions & 4 deletions _preview/1/_sources/notebooks/foundations/terminology.ipynb
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"## Overview\n",
"Great Circles are powerful tools used in navigation like ships and planes as well as in geoscience for working with and understnading remote sensing via satellites. Great Circle mathematics make use of spherical geometry, where, rather than lines, shapes on a sphere are formed by the intersection of arcs along the curved surface.\n",
"\n",
"While spherical geoemtry played an important role historically in the fields of astronomy and navigation, its teaching has largely fallen out of favor since the 1950's making finding comphrenshive resources difficult.\n",
"While spherical geometry played an important role historically in the fields of astronomy and navigation, its teaching has largely fallen out of favor since the 1950's making finding comphrenshive resources difficult.\n",
"\n",
"This notebook will cover some of the important and unqiue terminology used when working with Great Circles and spherical geometry\n",
"This notebook will cover some of the important and unique terminology used when working with Great Circles and spherical geometry\n",
"\n",
"1. Spherical Geometry\n",
"1. Great Circles\n",
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"\n",
"<img src=\"https://upload.wikimedia.org/wikipedia/commons/6/6a/Insect_on_a_torus_tracing_out_a_non-trivial_geodesic.gif\" alt=\"Straight Line on a curved surface\" width=400></img>\n",
"\n",
"This is espeically apparent when working with satellite data where the apparent \"straight path\" that a satellite will trace across the the surface of a planet \n",
"This is especially apparent when working with satellite data where the apparent \"straight path\" that a satellite will trace across the the surface of a planet \n",
"\n",
"<img src=\"https://www.earthdata.nasa.gov/s3fs-public/styles/small_third_320px_/public/2021-12/Aqua%20orbit%20resize.jpg?VersionId=jEIj8OggQelV01yl3SaAffu1hOWFbKvt&itok=8JY0VP7Y\" alt=\"Straight Line on a curved surface\" width=400></img>\n",
"\n",
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"- [Ed Williams \"Avitation Formulary\"](https://edwilliams.org/avform147.htm)\n",
"- [Movable Type Scripts](https://www.movable-type.co.uk/scripts/latlong.html)\n",
"- \"Heavenly Mathematics: The Forgotten Art of SPherical Trigonometry\" by Glen Van Brummelen\n",
"- \"SPherical Trigonometry: A Comphrehensive Approach\" by Ira Arevalo Fajardo"
"- \"SPherical Trigonometry: A Comprehensive Approach\" by Ira Arevalo Fajardo"
]
},
{
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