diff options
Diffstat (limited to 'operations/transformations/tinshift.html')
| -rw-r--r-- | operations/transformations/tinshift.html | 378 |
1 files changed, 378 insertions, 0 deletions
diff --git a/operations/transformations/tinshift.html b/operations/transformations/tinshift.html new file mode 100644 index 00000000..55024c1a --- /dev/null +++ b/operations/transformations/tinshift.html @@ -0,0 +1,378 @@ +<!DOCTYPE html> +<html class="writer-html5" lang="en" > +<head> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" /> + + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> + <title>Triangulated Irregular Network based transformation — PROJ 9.0.0 documentation</title> + <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" /> + <link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" /> + <link rel="shortcut icon" href="../../_static/favicon.png"/> + <link rel="canonical" href="https://proj.orgoperations/transformations/tinshift.html"/> + <!--[if lt IE 9]> + <script src="../../_static/js/html5shiv.min.js"></script> + <![endif]--> + + <script data-url_root="../../" id="documentation_options" src="../../_static/documentation_options.js"></script> + <script src="../../_static/jquery.js"></script> + <script src="../../_static/underscore.js"></script> + <script src="../../_static/doctools.js"></script> + <script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> + <script src="../../_static/js/theme.js"></script> + <link rel="author" title="About these documents" href="../../about.html" /> + <link rel="index" title="Index" href="../../genindex.html" /> + <link rel="search" title="Search" href="../../search.html" /> + <link rel="next" title="Vertical grid shift" href="vgridshift.html" /> + <link rel="prev" title="Horizontal grid shift" href="hgridshift.html" /> +</head> + +<body class="wy-body-for-nav"> + <div class="wy-grid-for-nav"> + <nav data-toggle="wy-nav-shift" class="wy-nav-side"> + <div class="wy-side-scroll"> + <div class="wy-side-nav-search" style="background: #353130" > + <a href="../../index.html"> + <img src="../../_static/logo.png" class="logo" alt="Logo"/> + </a> + <div class="version"> + 9.0.0 + </div> +<div role="search"> + <form id="rtd-search-form" class="wy-form" action="../../search.html" method="get"> + <input type="text" name="q" placeholder="Search docs" /> + <input type="hidden" name="check_keywords" value="yes" /> + <input type="hidden" name="area" value="default" /> + </form> +</div> + </div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu"> + <ul class="current"> +<li class="toctree-l1"><a class="reference internal" href="../../about.html">About</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../news.html">News</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../download.html">Download</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../install.html">Installation</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../usage/index.html">Using PROJ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../apps/index.html">Applications</a></li> +<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Coordinate operations</a><ul class="current"> +<li class="toctree-l2"><a class="reference internal" href="../projections/index.html">Projections</a></li> +<li class="toctree-l2"><a class="reference internal" href="../conversions/index.html">Conversions</a></li> +<li class="toctree-l2 current"><a class="reference internal" href="index.html">Transformations</a><ul class="current"> +<li class="toctree-l3"><a class="reference internal" href="affine.html">Affine transformation</a></li> +<li class="toctree-l3"><a class="reference internal" href="defmodel.html">Multi-component time-based deformation model</a></li> +<li class="toctree-l3"><a class="reference internal" href="deformation.html">Kinematic datum shifting utilizing a deformation model</a></li> +<li class="toctree-l3"><a class="reference internal" href="geogoffset.html">Geographic offsets</a></li> +<li class="toctree-l3"><a class="reference internal" href="helmert.html">Helmert transform</a></li> +<li class="toctree-l3"><a class="reference internal" href="horner.html">Horner polynomial evaluation</a></li> +<li class="toctree-l3"><a class="reference internal" href="molodensky.html">Molodensky transform</a></li> +<li class="toctree-l3"><a class="reference internal" href="molobadekas.html">Molodensky-Badekas transform</a></li> +<li class="toctree-l3"><a class="reference internal" href="hgridshift.html">Horizontal grid shift</a></li> +<li class="toctree-l3 current"><a class="current reference internal" href="#">Triangulated Irregular Network based transformation</a><ul> +<li class="toctree-l4"><a class="reference internal" href="#parameters">Parameters</a></li> +<li class="toctree-l4"><a class="reference internal" href="#example">Example</a></li> +</ul> +</li> +<li class="toctree-l3"><a class="reference internal" href="vgridshift.html">Vertical grid shift</a></li> +<li class="toctree-l3"><a class="reference internal" href="xyzgridshift.html">Geocentric grid shift</a></li> +</ul> +</li> +<li class="toctree-l2"><a class="reference internal" href="../pipeline.html">The pipeline operator</a></li> +<li class="toctree-l2"><a class="reference internal" href="../operations_computation.html">Computation of coordinate operations between two CRS</a></li> +</ul> +</li> +<li class="toctree-l1"><a class="reference internal" href="../../resource_files.html">Resource files</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../geodesic.html">Geodesic calculations</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../development/index.html">Development</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../specifications/index.html">Specifications</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../community/index.html">Community</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../faq.html">FAQ</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li> +<li class="toctree-l1"><a class="reference internal" href="../../zreferences.html">References</a></li> +</ul> + + </div> + </div> + </nav> + + <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" style="background: #353130" > + <i data-toggle="wy-nav-top" class="fa fa-bars"></i> + <a href="../../index.html">PROJ</a> + </nav> + + <div class="wy-nav-content"> + <div class="rst-content"> + <div role="navigation" aria-label="Page navigation"> + <ul class="wy-breadcrumbs"> + <li><a href="../../index.html" class="icon icon-home"></a> »</li> + <li><a href="../index.html">Coordinate operations</a> »</li> + <li><a href="index.html">Transformations</a> »</li> + <li>Triangulated Irregular Network based transformation</li> + <li class="wy-breadcrumbs-aside"> + <a href="https://github.com/OSGeo/PROJ/edit/8.2/docs/source/operations/transformations/tinshift.rst" class="fa fa-github"> Edit on GitHub</a> + </li> + </ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation"> + <a href="hgridshift.html" class="btn btn-neutral float-left" title="Horizontal grid shift" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vgridshift.html" class="btn btn-neutral float-right" title="Vertical grid shift" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + <hr/> +</div> + <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> + <div itemprop="articleBody"> + + <section id="triangulated-irregular-network-based-transformation"> +<span id="tinshift"></span><h1>Triangulated Irregular Network based transformation<a class="headerlink" href="#triangulated-irregular-network-based-transformation" title="Permalink to this headline">¶</a></h1> +<div class="versionadded"> +<p><span class="versionmodified added">New in version 7.2.0.</span></p> +</div> +<table class="docutils align-default"> +<colgroup> +<col style="width: 24%" /> +<col style="width: 76%" /> +</colgroup> +<tbody> +<tr class="row-odd"><td><p><strong>Alias</strong></p></td> +<td><p>tinshift</p></td> +</tr> +<tr class="row-even"><td><p><strong>Input type</strong></p></td> +<td><p>Projected or geographic coordinates (horizontal), meters (vertical)</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Output type</strong></p></td> +<td><p>Projected or geographic coordinates (horizontal), meters (vertical)</p></td> +</tr> +<tr class="row-even"><td><p><strong>Domain</strong></p></td> +<td><p>2D or 3D</p></td> +</tr> +<tr class="row-odd"><td><p><strong>Available forms</strong></p></td> +<td><p>Forward and inverse</p></td> +</tr> +</tbody> +</table> +<p>The <code class="docutils literal notranslate"><span class="pre">tinshift</span></code> transformation takes one mandatory +argument, <code class="docutils literal notranslate"><span class="pre">file</span></code>, that points to a JSON file, which contains the +triangulation and associated metadata. Input and output coordinates must be +geographic or projected coordinates. +Depending on the content of the JSON file, horizontal, vertical or both +components of the coordinates may be transformed.</p> +<p>The transformation is invertible, with the same computational complexity than +the forward transformation.</p> +<section id="parameters"> +<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2> +<section id="required"> +<h3>Required<a class="headerlink" href="#required" title="Permalink to this headline">¶</a></h3> +<dl class="std option"> +<dt class="sig sig-object std" id="cmdoption-arg-file"> +<span class="sig-name descname"><span class="pre">+file</span></span><span class="sig-prename descclassname"><span class="pre">=<filename></span></span><a class="headerlink" href="#cmdoption-arg-file" title="Permalink to this definition">¶</a></dt> +<dd><p>Filename to the JSON file for the TIN.</p> +</dd></dl> + +</section> +</section> +<section id="example"> +<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2> +<p>Transforming a point with the Finland EPSG:2393 (“KKJ / Finland Uniform +Coordinate System”) projected CRS to EPSG:3067 (“ETRS89 / TM35FIN(E,N)”)</p> +<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ echo 3210000.0000 6700000.0000 0 2020 | cct +proj=tinshift +file=./triangulation_kkj.json + +209948.3217 6697187.0009 0.0000 2020 +</pre></div> +</div> +<section id="algorithm"> +<h3>Algorithm<a class="headerlink" href="#algorithm" title="Permalink to this headline">¶</a></h3> +<p>Internally, <code class="docutils literal notranslate"><span class="pre">tinshift</span></code> ingest the whole file into memory. It is considered that +triangulation should be small enough for that.</p> +<p>When a point is transformed, one must find the triangle into which it falls into. +Instead of iterating over all triangles, we build a in-memory quadtree to speed-up +the identification of candidates triangles.</p> +<p>To determine if a point falls into a triangle, one computes its 3 +<a class="reference external" href="https://en.wikipedia.org/wiki/Barycentric_coordinate_system#Conversion_between_barycentric_and_Cartesian_coordinates">barycentric coordinates</a> +from its projected coordinates, <span class="math notranslate nohighlight">\(\lambda_i\)</span> for <span class="math notranslate nohighlight">\(i=1,2,3\)</span>. +They are real values (in the [0,1] range for a point inside the triangle), +giving the weight of each of the 3 vertices of the triangles.</p> +<p>Once those weights are known, interpolating the target horizontal +coordinate is a matter of doing the linear combination of those weights with +the target horizontal coordinates at the 3 vertices of the triangle (<span class="math notranslate nohighlight">\(Xt_i\)</span> and <span class="math notranslate nohighlight">\(Yt_i\)</span>):</p> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}X_{target} = Xt_1 * \lambda_1 + Xt_2 * \lambda_2 + Xt_3 * \lambda_3\\Y_{target} = Yt_1 * \lambda_1 + Yt_2 * \lambda_2 + Yt_3 * \lambda_3\end{aligned}\end{align} \]</div> +<p>This interpolation is exact at the vertices of the triangulation, and has linear properties +inside each triangle. It is completely equivalent to other formulations of +triangular interpolation, such as</p> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}X_{target} = A + X_{source} * B + Y_{source} * C\\Y_{target} = D + X_{source} * E + Y_{source} * F\end{aligned}\end{align} \]</div> +<p>where the A, B, C, D, E, F constants (for a given triangle) are found by solving +the 2 systems of 3 linear equations, constraint by the source and target coordinate pairs +of the 3 vertices of the triangle:</p> +<div class="math notranslate nohighlight"> +\[ \begin{align}\begin{aligned}Xt_i = A + Xs_i * B + Ys_i * C\\Yt_i = D + Xs_i * E + Ys_i * F\end{aligned}\end{align} \]</div> +<p>Similarly for a vertical coordinate transformation, where <span class="math notranslate nohighlight">\(Zoff_i\)</span> is the vertical +offset at each vertex of the triangle:</p> +<div class="math notranslate nohighlight"> +\[Z_{target} = Z_{source} + Zoff_1 * \lambda_1 + Zoff_2 * \lambda_2 + Zoff_3 * \lambda_3\]</div> +</section> +<section id="constraints-on-the-triangulation"> +<h3>Constraints on the triangulation<a class="headerlink" href="#constraints-on-the-triangulation" title="Permalink to this headline">¶</a></h3> +<p>No check is done on the consistence of the triangulation. It is highly +recommended that triangles do not overlap each other (when considering the +source coordinates or the forward transformation, or the target coordinates for +the inverse transformation), otherwise which triangle will be selected is +unspecified. Besides that, the triangulation does not need to have particular +properties (like being a Delaunay triangulation)</p> +</section> +<section id="file-format"> +<h3>File format<a class="headerlink" href="#file-format" title="Permalink to this headline">¶</a></h3> +<p>The triangulation is stored in a text-based format, using JSON as a serialization.</p> +<p>Below a minimal example, from the KKJ to ETRS89 transformation, with just a +single triangle:</p> +<div class="highlight-json notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"file_type"</span><span class="p">:</span><span class="w"> </span><span class="s2">"triangulation_file"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"format_version"</span><span class="p">:</span><span class="w"> </span><span class="s2">"1.0"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"name"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Name"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"version"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Version"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"publication_date"</span><span class="p">:</span><span class="w"> </span><span class="s2">"2018-07-01T00:00:00Z"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"license"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Creative Commons Attribution 4.0 International"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"description"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Test triangulation"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"authority"</span><span class="p">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"name"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Authority name"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"url"</span><span class="p">:</span><span class="w"> </span><span class="s2">"http://example.com"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"address"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Adress"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"email"</span><span class="p">:</span><span class="w"> </span><span class="s2">"test@example.com"</span><span class="w"></span> +<span class="w"> </span><span class="p">},</span><span class="w"></span> +<span class="w"> </span><span class="nt">"links"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"></span> +<span class="w"> </span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"href"</span><span class="p">:</span><span class="w"> </span><span class="s2">"https://example.com/about.html"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"rel"</span><span class="p">:</span><span class="w"> </span><span class="s2">"about"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"type"</span><span class="p">:</span><span class="w"> </span><span class="s2">"text/html"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"title"</span><span class="p">:</span><span class="w"> </span><span class="s2">"About"</span><span class="w"></span> +<span class="w"> </span><span class="p">},</span><span class="w"></span> +<span class="w"> </span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"href"</span><span class="p">:</span><span class="w"> </span><span class="s2">"https://example.com/download"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"rel"</span><span class="p">:</span><span class="w"> </span><span class="s2">"source"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"type"</span><span class="p">:</span><span class="w"> </span><span class="s2">"application/zip"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"title"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Authoritative source"</span><span class="w"></span> +<span class="w"> </span><span class="p">},</span><span class="w"></span> +<span class="w"> </span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"href"</span><span class="p">:</span><span class="w"> </span><span class="s2">"https://creativecommons.org/licenses/by/4.0/"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"rel"</span><span class="p">:</span><span class="w"> </span><span class="s2">"license"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"type"</span><span class="p">:</span><span class="w"> </span><span class="s2">"text/html"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"title"</span><span class="p">:</span><span class="w"> </span><span class="s2">"Creative Commons Attribution 4.0 International license"</span><span class="w"></span> +<span class="w"> </span><span class="p">},</span><span class="w"></span> +<span class="w"> </span><span class="p">{</span><span class="w"></span> +<span class="w"> </span><span class="nt">"href"</span><span class="p">:</span><span class="w"> </span><span class="s2">"https://example.com/metadata.xml"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"rel"</span><span class="p">:</span><span class="w"> </span><span class="s2">"metadata"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"type"</span><span class="p">:</span><span class="w"> </span><span class="s2">"application/xml"</span><span class="p">,</span><span class="w"></span> +<span class="w"> </span><span class="nt">"title"</span><span class="p">:</span><span class="w"> </span><span class="s2">" ISO 19115 XML encoded metadata regarding the deformation model"</span><span class="w"></span> +<span class="w"> </span><span class="p">}</span><span class="w"></span> +<span class="w"> </span><span class="p">],</span><span class="w"></span> +<span class="w"> </span><span class="nt">"transformed_components"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"> </span><span class="s2">"horizontal"</span><span class="w"> </span><span class="p">],</span><span class="w"></span> +<span class="w"> </span><span class="nt">"vertices_columns"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"> </span><span class="s2">"source_x"</span><span class="p">,</span><span class="w"> </span><span class="s2">"source_y"</span><span class="p">,</span><span class="w"> </span><span class="s2">"target_x"</span><span class="p">,</span><span class="w"> </span><span class="s2">"target_y"</span><span class="w"> </span><span class="p">],</span><span class="w"></span> +<span class="w"> </span><span class="nt">"triangles_columns"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"> </span><span class="s2">"idx_vertex1"</span><span class="p">,</span><span class="w"> </span><span class="s2">"idx_vertex2"</span><span class="p">,</span><span class="w"> </span><span class="s2">"idx_vertex3"</span><span class="w"> </span><span class="p">],</span><span class="w"></span> +<span class="w"> </span><span class="nt">"vertices"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"> </span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">49</span><span class="p">,</span><span class="mf">2.1</span><span class="p">,</span><span class="mf">49.1</span><span class="p">],</span><span class="w"> </span><span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">50</span><span class="p">,</span><span class="mf">3.1</span><span class="p">,</span><span class="mf">50.1</span><span class="p">],</span><span class="w"> </span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">50</span><span class="p">,</span><span class="w"> </span><span class="mf">2.1</span><span class="p">,</span><span class="mf">50.1</span><span class="p">]</span><span class="w"> </span><span class="p">],</span><span class="w"></span> +<span class="w"> </span><span class="nt">"triangles"</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">]</span><span class="w"></span> +<span class="p">}</span><span class="w"></span> +</pre></div> +</div> +<p>So after the generic metadata, we define the input and output CRS (informative +only), and that the transformation affects horizontal components of +coordinates. We name the columns of the <code class="docutils literal notranslate"><span class="pre">vertices</span></code> and <code class="docutils literal notranslate"><span class="pre">triangles</span></code> arrays. +We defined the source and target coordinates of each vertex, and define a +triangle by referring to the index of its vertices in the <code class="docutils literal notranslate"><span class="pre">vertices</span></code> array.</p> +<p>More formally, the specific items for the triangulation file are:</p> +<dl class="simple"> +<dt>input_crs</dt><dd><p>String identifying the CRS of source coordinates +in the vertices. Typically <code class="docutils literal notranslate"><span class="pre">EPSG:XXXX</span></code>. If the transformation is for vertical +component, this should be the code for a compound CRS (can be EPSG:XXXX+YYYY +where XXXX is the code of the horizontal CRS and YYYY the code of the vertical CRS). +For example, for the KKJ->ETRS89 transformation, this is EPSG:2393 +(<code class="docutils literal notranslate"><span class="pre">KKJ</span> <span class="pre">/</span> <span class="pre">Finland</span> <span class="pre">Uniform</span> <span class="pre">Coordinate</span> <span class="pre">System</span></code>). The input coordinates are assumed +to be passed in the “normalized for visualisation” / “GIS friendly” order, +that is longitude, latitude for geographic coordinates and +easting, northing for projected coordinates.</p> +</dd> +<dt>output_crs</dt><dd><p>String identifying the CRS of target coordinates in the vertices. +Typically <code class="docutils literal notranslate"><span class="pre">EPSG:XXXX</span></code>. If the transformation is for vertical component, +this should be the code for a compound CRS (can be EPSG:XXXX+YYYY where +XXXX is the code of the horizontal CRS and YYYY the code of the vertical CRS). +For example, for the KKJ->ETRS89 transformation, this is EPSG:3067 +("ETRS89 / TM35FIN(E,N)"). The output coordinates will be returned in +the “normalized for visualisation” / “GIS friendly” order, +that is longitude, latitude for geographic coordinates and +easting, northing for projected coordinates.</p> +</dd> +<dt>transformed_components</dt><dd><p>Array which may contain one or two strings: “horizontal” when horizontal +components of the coordinates are transformed and/or “vertical” when the +vertical component is transformed.</p> +</dd> +<dt>fallback_strategy</dt><dd><p>String identifying how to treat points that do not fall into any of the +specified triangles. This item is available for <code class="docutils literal notranslate"><span class="pre">format_version</span></code> >= 1.1. +Possible values are <code class="docutils literal notranslate"><span class="pre">none</span></code>, <code class="docutils literal notranslate"><span class="pre">nearest_side</span></code> and <code class="docutils literal notranslate"><span class="pre">nearest_centroid</span></code>. The +default is <code class="docutils literal notranslate"><span class="pre">none</span></code> and signifies, that points that fall outside the +specified triangles are not transformed. This is also the behaviour for +<code class="docutils literal notranslate"><span class="pre">format_version</span></code> before 1.1. If <code class="docutils literal notranslate"><span class="pre">fallback_strategy</span></code> is set to +<code class="docutils literal notranslate"><span class="pre">nearest_side</span></code>, then points that do not fall into any triangle are +transformed according to the triangle closest to them by euclidean distance. +If <code class="docutils literal notranslate"><span class="pre">fallback_strategy</span></code> is set to <code class="docutils literal notranslate"><span class="pre">nearest_centroid</span></code>, then points that do +not fall into any triangle are transformed according to the triangle with the +closest centroid (intersection of its medians).</p> +</dd> +<dt>vertices_columns</dt><dd><p>Specify the name of the columns of the rows in the <code class="docutils literal notranslate"><span class="pre">vertices</span></code> +array. There must be exactly as many elements in <code class="docutils literal notranslate"><span class="pre">vertices_columns</span></code> as in a +row of <code class="docutils literal notranslate"><span class="pre">vertices</span></code>. The following names have a special meaning: <code class="docutils literal notranslate"><span class="pre">source_x</span></code>, +<code class="docutils literal notranslate"><span class="pre">source_y</span></code>, <code class="docutils literal notranslate"><span class="pre">target_x</span></code>, <code class="docutils literal notranslate"><span class="pre">target_y</span></code>, <code class="docutils literal notranslate"><span class="pre">source_z</span></code>, <code class="docutils literal notranslate"><span class="pre">target_z</span></code> and +<code class="docutils literal notranslate"><span class="pre">offset_z</span></code>. <code class="docutils literal notranslate"><span class="pre">source_x</span></code> and <code class="docutils literal notranslate"><span class="pre">source_y</span></code> are compulsory. +<code class="docutils literal notranslate"><span class="pre">source_x</span></code> is for the source longitude (in degree) or easting. +<code class="docutils literal notranslate"><span class="pre">source_y</span></code> is for the source latitude (in degree) or northing. +<code class="docutils literal notranslate"><span class="pre">target_x</span></code> and <code class="docutils literal notranslate"><span class="pre">target_y</span></code> are compulsory when <code class="docutils literal notranslate"><span class="pre">horizontal</span></code> is specified +in <code class="docutils literal notranslate"><span class="pre">transformed_components</span></code>. (<code class="docutils literal notranslate"><span class="pre">source_z</span></code> and <code class="docutils literal notranslate"><span class="pre">target_z</span></code>) or +<code class="docutils literal notranslate"><span class="pre">offset_z</span></code> are compulsory when <code class="docutils literal notranslate"><span class="pre">vertical</span></code> is specified in <code class="docutils literal notranslate"><span class="pre">transformed_components</span></code></p> +</dd> +<dt>triangles_columns</dt><dd><p>Specify the name of the columns of the rows in the +<code class="docutils literal notranslate"><span class="pre">triangles</span></code> array. There must be exactly as many elements in <code class="docutils literal notranslate"><span class="pre">triangles_columns</span></code> +as in a row of <code class="docutils literal notranslate"><span class="pre">triangles</span></code>. The following names have a special meaning: +<code class="docutils literal notranslate"><span class="pre">idx_vertex1</span></code>, <code class="docutils literal notranslate"><span class="pre">idx_vertex2</span></code>, <code class="docutils literal notranslate"><span class="pre">idx_vertex3</span></code>. They are compulsory.</p> +</dd> +<dt>vertices</dt><dd><p>An array whose items are themselves arrays with as many columns as +described in <code class="docutils literal notranslate"><span class="pre">vertices_columns</span></code>.</p> +</dd> +<dt>triangles</dt><dd><p>An array whose items are themselves arrays with as many columns as +described in <code class="docutils literal notranslate"><span class="pre">triangles_columns</span></code>. +The value of the <code class="docutils literal notranslate"><span class="pre">idx_vertexN</span></code> columns must be indices +(between 0 and len(<code class="docutils literal notranslate"><span class="pre">vertices</span></code>-1) of items of the <code class="docutils literal notranslate"><span class="pre">vertices</span></code> array.</p> +</dd> +</dl> +<p>A <a class="reference external" href="https://proj.org/schemas/triangulation.schema.json">JSON schema</a> is available +for this file format.</p> +</section> +</section> +</section> + + + </div> + </div> + <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer"> + <a href="hgridshift.html" class="btn btn-neutral float-left" title="Horizontal grid shift" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a> + <a href="vgridshift.html" class="btn btn-neutral float-right" title="Vertical grid shift" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a> + </div> + + <hr/> + + <div role="contentinfo"> + <p>© Copyright 1983-2022. + <span class="lastupdated">Last updated on 22 Mar 2022. + </span></p> + </div> + + Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a + <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a> + provided by <a href="https://readthedocs.org">Read the Docs</a>. + + +</footer> + </div> + </div> + </section> + </div> + <script> + jQuery(function () { + SphinxRtdTheme.Navigation.enable(true); + }); + </script> + +</body> +</html>
\ No newline at end of file |