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transformation functions","contributors":[{"name":"Bert Spaan","email":"hello@bertspaan.nl","url":"https://bertspaan.nl"},{"name":"Manuel Claeys Bouuaert","email":"manuel.claeys.b@gmail.com","url":"https://manuelclaeysbouuaert.be"}],"maintainers":[{"name":"bertspaan","email":"hello@bertspaan.nl"}],"readme":"# @allmaps/transform\n\nThis module contains classes and methods to **transform Points, LineStrings, Polygons** and other spatial features from a 2D cartesian `(x, y)` source space to a destination space. The transformation function that accomplish this are constructed from **a set of Control Points**, who's coordinates are known in both spaces, and a specific **type of transformation** algorithm.\n\nThe classes in this module are further extended in the [@allmaps/project](../../packages/project/) module. If you're looking to build a *projected* transformer, transforming and projecting from the 'resource' space of a IIIF Image to the 'projected geospatial' space of a map projection, use the classes from that module. It can build Projected GCP Transformers from the Ground Control Points, transformation type and map projection definitions (e.g. defined in a map's Georeference Annotation).\n\n## How it works\n\nThis package exports the `GeneralGcpTransformer` and `GcpTransformer` classes.\n\n* A **General GCP Transformer** is useful in the general case: it takes in ground control points of the `GeneralGcp` type, with 'source' and 'destination' fields, and has methods `generalTransformer.transformForward()` to transform geometries from 'source' space to 'destination' space, and `generalTransformer.transformBackward()` to transform from 'destination' space to 'source' space.\n* A **GCP Transformer** it useful in the typical Allmaps case: it takes in ground control points of the `Gcp` type, with 'resource' and 'geo' fields, and has methods `transformer.transformToGeo()` to transform geometries from 'resource' space to 'geo' space, and `transformer.transformToResource()` to transform from 'geo' space to 'resource' space. Apart from naming, there is also one default option set for this type of transformer: `differentHandedness = true` by default, since the most common case is that the resource space had a downward y-axis.\n\nIn both cases, calling a transform method will build a transformation of the specified type using the input GCPs, or use it if it already exists. These transformations can then transform points one by one. For lineStrings and polygons the transform options can be used to **refine** the geometry during transformation as needed, i.e. add extra midpoints to assure sufficiently smooth results.\n\nAs an **example** for the georeferenced map *L'Angleterre Novissima Descriptio Angliae Scotiae et Hiberniae* ([Open in Allmaps Viewer](https://viewer.allmaps.org/?url=https%3A%2F%2Fannotations.allmaps.org%2Fmaps%2F135dfd2d58dc26ec)): based on the map's GCPs in resource and (projected) geo coordinates, a GCP Transformer can be built (visualized by the grid) allowing to transform any geometry from resource to geo space. Here, the resource mask is transformed from resource to (projected) geo space.\n\n![](https://github.com/allmaps/allmaps/blob/main/packages/transform/example.webp?raw=true)\n\n## Installation\n\nThis is an ESM-only module that works in browsers and in Node.js.\n\nInstall with pnpm:\n\n```sh\npnpm install @allmaps/transform\n```\n\n## Usage\n\n### Quickstart\n\nWhen starting from an **Annotation** or **Georeferenced Map**, the fastest way to build a GCP Transformer is:\n\n```js\nimport { parseAnnotation } from '@allmaps/annotation'\nimport { GcpTransformer } from '@allmaps/transform'\n\n// Fetch an annotation\nconst annotation = await fetch(annoationUrl).then((response) => response.json())\n\n// Create a georeferencedMap from the annotation\nconst georeferencedMaps = parseAnnotation(annotation)\nconst georeferencedMap = georeferencedMaps[0]\n\n// Build GCP Transformer\nconst transformer = GcpTransformer.fromGeoreferencedMap(georeferencedMap)\n\n// Use it to transform geometries, as below. E.g.:\nconst geoPoint = transformer.transformToGeo(resourcePoint)\n```\n\nThis is equivalent to constructing a transformer from the Annotation's or Georeferenced Map's GCPs and transformation type, as in the examples below.\n\nThis transformer can then be used to transform geometries between 'resource' space and 'geo' space.\n\nWhen **rendering** maps, another way to quickly obtain a transformer is to access it directly from a **Warped Map** in the renderer's Warped Map List:\n\n```js\n// Create a renderer from your canvas\nconst renderer = new WebGL2Renderer(gl)\n// Fetch and parse annotations, add them to the renderer ...\n\n// There are multiple ways to access the renderer's Warped Map List's Warped Maps, e.g.:\nconst warpedMap = renderer.warpedMapList.getWarpedMap(mapId)\n\n// Access the Projected GCP Transformer, in the Warped Map's current transformation type\nconst projectedTransformer = warpedMap.projectedTransformer\n// Or select or create the Projected GCP Transformer of a different transformation type\nconst projectedHelmertTransformer = warpedMap.getProjectedTransformer('helmert')\n```\n\nThe transformer obtained in this way is a Projected GCP Transformer as detailed in [@allmaps/project](../../packages/project/). See also the [@allmaps/render](../../packages/render/) module for more about working with renderers.\n\nNote: only GCP Transformers can be created in these ways. General GCP Transformers must be created using the constructor, as shown below.\n\n### Point\n\nIn this example we use a general transformer to transform forward.\n\n```js\nimport { GeneralGcpTransformer } from '@allmaps/transform'\n\nexport const generalGcps3 = [\n  {\n    source: [0, 0],\n    destination: [0, 0]\n  },\n  {\n    source: [0, 1],\n    destination: [1, 4]\n  },\n  {\n    source: [1, 0],\n    destination: [5, 10]\n  }\n]\n\nconst generalTransformer = new GeneralGcpTransformer(generalGcps3, 'polynomial')\n\nconst sourcePoint = [1, 1]\n\nconst destinationPoint = generalTransformer.transformForward(sourcePoint)\n// destinationPoint = [6, 14]\n```\n\n### LineString\n\nIn this example we use a transformer to transform backward.\n\n```js\nimport { GcpTransformer } from '@allmaps/transform'\n\nconst gcps7 = [\n  {\n    resource: [0, 0],\n    geo: [0, 0]\n  },\n  {\n    resource: [100, 0],\n    geo: [20, 0]\n  },\n  {\n    resource: [200, 100],\n    geo: [40, 20]\n  },\n  {\n    resource: [200, 200],\n    geo: [40, 40]\n  },\n  {\n    resource: [150, 250],\n    geo: [40, 100]\n  },\n  {\n    resource: [100, 200],\n    geo: [20, 40]\n  },\n  {\n    resource: [0, 100],\n    geo: [0, 20]\n  }\n]\n\nconst options = {\n  maxDepth: 2\n}\n\nconst transformer = new GcpTransformer(gcps7, 'polynomial')\n\nconst resourceLineString = [\n  [10, 50],\n  [50, 50]\n]\n\nconst geoLineString = transformer.transformBackward(resourceLineString, options)\n// geoLineString = [\n//   [31.06060606060611, 155.30303030303048],\n//   [82.57575757575762, 162.8787878787881],\n//   [134.09090909090912, 170.45454545454567],\n//   [185.60606060606065, 178.0303030303033],\n//   [237.12121212121218, 185.60606060606085]\n// ]\n\n// Notice how the result has two layers of midpoints!\n// In a first step the Point [134.09, 170.45] is added between the start and end Point\n// Then [82.57, 162.87] and [185.60, 178.03] are added in between.\n```\n\n### Polygon\n\nIn this example we use a transformer to build a Thin Plate Spline transformation.\n\n```js\nimport { GcpTransformer } from '@allmaps/transform'\n\nconst gcps6 = [\n  {\n    resource: [1344, 4098],\n    geo: [4.4091165, 51.9017125]\n  },\n  {\n    resource: [4440, 3441],\n    geo: [4.5029222, 51.9164451]\n  },\n  {\n    resource: [3549, 4403],\n    geo: [4.4764224, 51.897309]\n  },\n  {\n    resource: [1794, 2130],\n    geo: [4.4199066, 51.9391509]\n  },\n  {\n    resource: [3656, 2558],\n    geo: [4.4775683, 51.9324358]\n  },\n  {\n    resource: [2656, 3558],\n    geo: [4.4572643, 51.9143043]\n  }\n]\n\nconst options = {\n  minOffsetRatio: 0.00001,\n  maxDepth: 1\n}\n\nconst transformer = new GcpTransformer(gcps6, 'thinPlateSpline')\n\nconst resourcePolygon = [\n  [\n    [1000, 1000],\n    [1000, 2000],\n    [2000, 2000],\n    [2000, 1000]\n  ]\n]\n\nconst geoPolygon = transformer.transformForward(resourcePolygon, options)\n// geoPolygon = [\n//     [\n//       [4.388957777030093, 51.959084191571606],\n//       [4.390889520773774, 51.94984430356657],\n//       [4.392938913951547, 51.94062947962427],\n//       [4.409493277493718, 51.94119110133424],\n//       [4.425874493300959, 51.94172557475595],\n//       [4.4230497784967655, 51.950815146974556],\n//       [4.420666790347598, 51.959985351835975],\n//       [4.404906205946158, 51.959549039424715]\n//     ]\n//   ]\n```\n\n### MultiPoint\n\nIn this example we use a transformer to transform a multi-geometry.\n\n```js\nimport { GcpTransformer } from '@allmaps/transform'\n\nconst gcps7 = // see above\n\n// The option `isMultiGeometry` assures the transform method recognises the input (an array of points) as a multiPoint, instead of a lineString\nconst options = {\n  isMultiGeometry: true\n}\n\nconst transformer = new GcpTransformer(gcps7, 'polynomial')\n\nconst resourceMultiPoint = [\n  [10, 50],\n  [50, 50]\n]\n\nconst geoMultiPoint = transformer.transformForward(resourceMultiPoint, options)\n// const geoMultiPoint = [\n//   [31.06060606060611, 155.30303030303048],\n//   [237.12121212121218, 185.60606060606085]\n// ]\n// Note: if the input would have been recognised as a lineString, more points would have been added!\n```\n\n## Creating a transformer\n\nLet's go over the different steps of using this package: creating a transformer and using transformer methods.\n\nA transformer is created from a set of **GCPs**, a **transformation type** and some optional **options**.\n\n### GCPs\n\nGCPs follow the `GeneralGcp` or `Gcp` type (see below) respectively. Each transformation type has a minimum number of GCPs.\n\nOnly **linearly independent control points** should be considered when checking if the criterion for the minimum number of control points is met. For example, three control points that are collinear (one the same line) only count as two linearly independent points. The current implementation doesn't check such linear (in)dependance, but building a transformer with insufficient linearly independent control points will result in a badly conditioned matrix (no error but diverging results) or non-invertible matrix (**error when inverting matrix**). See [@allmaps/analyse](../../packages/analyse/) for ways to analyse and check GCP properties.\n\n### Transformation types\n\nThe following transformation types are supported.\n\n|                                                                                                                                                                                          | Type                                       | Description                                                              | Properties                                                                                                                           | Minimum number of GCPs |\n|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------|--------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------|------------------------|\n| <img width=\"100\" src=\"https://raw.githubusercontent.com/allmaps/allmaps/refs/heads/main/packages/ui/src/lib/shared/images/transformations/straight.svg\" alt=\"straight\">                  | `straight`                                 | Straight transformation                                                  | Applies translation and scaling. Preserves shapes and angles.                                                                        | 2                      |\n| <img width=\"100\" src=\"https://raw.githubusercontent.com/allmaps/allmaps/refs/heads/main/packages//ui/src/lib/shared/images/transformations/helmert.svg\" alt=\"helmert\">                   | `helmert`                                  | Helmert transformation or 'similarity transformation'                    | Applies translation, scaling and rotation. Preserves shapes and angles.                                                              | 2                      |\n| <img width=\"100\" src=\"https://raw.githubusercontent.com/allmaps/allmaps/refs/heads/main/packages//ui/src/lib/shared/images/transformations/polynomial-1.svg\" alt=\"polynomial\">           | `polynomial` (default), also `polynomial1` | First order polynomial transformation                                    | Applies translation, scaling, rotation and shearing. Preserves lines and parallelism.                                                | 3                      |\n| <img width=\"100\" src=\"https://raw.githubusercontent.com/allmaps/allmaps/refs/heads/main/packages//ui/src/lib/shared/images/transformations/polynomial-2.svg\" alt=\"polynomial2\">          | `polynomial2`                              | Second order polynomial transformation.                                  | Applies second order effects. Adds some bending flexibility.                                                                         | 6                      |\n| <img width=\"100\" src=\"https://raw.githubusercontent.com/allmaps/allmaps/refs/heads/main/packages//ui/src/lib/shared/images/transformations/polynomial-3.svg\" alt=\"polynomial3\">          | `polynomial3`                              | Third order polynomial transformation                                    | Applies third order effects. Adds more bending flexibility.                                                                          | 10                     |\n| <img width=\"100\" src=\"https://raw.githubusercontent.com/allmaps/allmaps/refs/heads/main/packages//ui/src/lib/shared/images/transformations/thin-plate-spline.svg\" alt=\"thinPlateSpline\"> | `thinPlateSpline`                          | Thin Plate Spline transformation or 'rubber sheeting' (with affine part) | Applies smooth transformation. Transformation is 'exact' at GPCs. (see [this notebook](https://observablehq.com/d/0b57d3b587542794)) | 3                      |\n| <img width=\"100\" src=\"https://raw.githubusercontent.com/allmaps/allmaps/refs/heads/main/packages//ui/src/lib/shared/images/transformations/projective.svg\" alt=\"projective\">             | `projective`                               | Projective or 'perspective' transformation, used for aerial images       | Follow perspective rules. Preserves lines and cross-ratios.                                                                          | 4                      |\n\n### Transformer options\n\nWhen creating a transformer, 'transformer options' can be specified. Apart from the options below, any 'transform options' (e.g. `maxDepth`) specified when creating a transformer will become the default options, used when calling a transform method.\n\n| Option | Description | Type | Default |\n|:-------|:------------|:-----|:--------|\n| `differentHandedness`     | Whether one of the axes should be flipped (internally) while computing the transformation parameters. Should be true if the handedness differs between the source and destination coordinate spaces. This makes a difference for specific transformation types like the Helmert transform. (Flipping will not alter the axis orientation of the output (use the 'return type function' for this)). | `boolean`             | `false` for General GCP Transformer, `true` for GCP Transformer\n\n#### Handedness\n\nFor some transformation types, it is important that the source and destination planes have the same *handedness*.\n\nWhen we consider 2D Cartesian planes, there are two types of 'handedness'. A Cartesian plane with the positive x-axis pointing right and the positive y-axis pointing up (and the x-axis being the 'first' and the y-axis the 'second' axis) is said to have *right-handed* orientation (also called *standard*, *positive* or *counter-clockwise*). This is for example the case in the equirectangular projection - at least if the coordinate order is (lon, lat). Alternatively, if the y-axis points downwards, we say the orientation is *left-handed* (or *negative* or *clock-wise*). This is for example the case for typical pixel coordinates, which have their origin in the top left corner.\n\nThe handedness of the source and destination can differ, for example if the source are pixels of an image and the destination are (lon, lat) coordinates (which is the typical case for Allmaps). For most transformation types solving the transformation happens independently for the x- and y-axis is, and hence it does not matter whether the source and destination are considered to have the same handedness or not: the same transformation parameters are obtained. For some transformations, like the Helmert transformation, the transformation of x- and y- coordinates are computed jointly (they are said to be 'coupled') and the difference matters. The algorithms won't produce the desired results unless action is taken to align the handedness.\n\nTherefore, in case the handedness differs and this could matter, one can set the `differentHandedness` parameter to `true`. This will (not change the data itself, but) during computation of the transformation parameters and during evaluation of new inputs flip the y-axis of the source so as to align the handedness of both.\n\nIn addition, it is also possible to *explicitly* flip the y-axis of the output. This can be useful for example when transforming features backward from (lon, lat) coordinates to image coordinates (with `differentHandedness` set to `true` as it should be): when inspecting the resulting features in image space in an HTML-canvas, the results will display correctly since both the image and features are rendered according to the downward y-axis of the canvas. Some applications will, however, load images and vector features differently: QGIS (with the 'no-CRS' setting) for example loads vector features with an upward y-axis but images with a downward y-axis. For these special cases, (still set the `differentHandedness` set to `true` but also) use the 'return type function' as follows to make your resulting features overlap the image in the application you are using:\n\n```ts\nimport { GeneralGcpTransformer } from '@allmaps/transform'\n\nconst generalGcps3 = ... // see above\n\nconst transformer = new GeneralGcpTransformer(generalGcps3, 'helmert', {\n    differentHandedness: true\n  })\nconst destinationPoint = [4.925027120153211, 52.46506809004473]\n\nconst sourcePoint = transformer.transformBackward(destinationPoint, {}, (generalGcp) => [\n  generalGcp.source[0],\n  -generalGcp.source[1]\n])\n// sourcePoint = [146.25183291709982, -122.59989116975339]\n// instead of [146.25183291709982, 122.59989116975339]\n```\n\n## Using transformer methods\n\nOnce a transformer is built, its methods can be used to transform geometries from one space to the other. Transformer methods take a **Geometry**, some optional **options** and an optional **'return type function'**.\n\nThere are separate methods for transforming one way or the other between the two spaces: a General GCP Transformer has methods `transformForward()` and `transformBackward()`, a GCP Transformer has methods `transformToGeo()` and `transformToResource()`.\n\nThese methods accepts Points, LineStrings as well as Polygons (and MultiPoints, MultiLineStrings and MultiPolygons) geometries (as defined in [@allmaps/types](../../packages/types/)).\n\nNote that the 'backward' (or 'toResource') methods are in general **not the exact inverse** of the 'forward' (or 'toGeo') methods. They are different function created by interpreting the GCPs in the one sense or the other. In some exceptional cases (like for 1st order polynomial transformations with exactly 3 GCPs) the backwards method is the exact inverse. In some cases, the exact inverse can be computed using some simple math from the transformation parameters (like for general 1st order polynomial transformations). In other cases, an exact inverse function could be obtained by implementing stepwise approximation of the inverse function (e.g. gradient descent).\n\n### Handling GeoJSON input and output\n\nWhile this package takes Geometries as input and output (as defined in [@allmaps/types](../../packages/types/)) it is also possible to handle GeoJSON Geometries or SVG Geometries, by converting to and from these geometry types using the functions available in [@allmaps/stdlib](../../packages/stdlib/):\n\n```ts\nimport { GcpTransformer } from '@allmaps/transform'\nimport { geojsonGeometryToGeometry, geometryToGeojsonGeometry } from '@allmaps/stdlib'\n\nconst gcps7 = ... // see above\n\nconst transformer = new GcpTransformer(gcps7, 'polynomial')\n\nconst geojsonLineString = {\n  type: 'LineString',\n  coordinates: [\n    [10, 50],\n    [50, 50]\n  ]\n}\nconst geoLineString = geojsonGeometryToGeometry(geojsonLineString)\n// geoLineString = [[10, 50],[50, 50]]\n\nconst resourceLineString = transformer.transformToResource(\n  geoLineString,\n  options\n)\nconst resourceLineStringAsGeojson = geometryToGeojsonGeometry(resourceLineString)\n```\n\nFor faster transformation between SVG Geometries and GeoJSON Geometries, the following shortcut methods are available as static methods of the GcpTransformer class: `transformSvgToGeojson()`, `transformSvgStringToGeojsonFeatureCollection()`, `transformGeojsonToSvg()`, `transformGeojsonFeatureCollectionToSvgString()`. Example usage:\n\n```ts\nimport { GcpTransformer } from '@allmaps/transform'\n\nconst geojsonFeatureCollection = ... // A feature collection\n\nconst svg = GcpTransformer.transformGeojsonFeatureCollectionToSvgString(\n  transformer,\n  geojsonFeatureCollection,\n  transformOptions\n)\n// svg = ... an SVG string\n```\n\n### Transform options\n\nSome 'transform options' are available when we transform geometries:\n\nThe 'transform options' for a General GCP Transformer methods and a GCP Transformer methods are similar but may have different names. When this is the case this is reflected in the table below.\n\n| Option                                                                                                       | Description                                                                                                                                                                                                                                                                  | Type                  | Default                                            |\n|:-------------------------------------------------------------------------------------------------------------|:-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:----------------------|:---------------------------------------------------|\n| `maxDepth`                                                                                                   | Maximum recursion depth when recursively refining (higher means more midpoints)                                                                                                                                                                                              | `number`              | `0`                                                |\n| `minSourceDistance`                                                                                          | Minimum distance of a source segment when recursively refining (lower means more midpoints)                                                                                                                                                                                  | `number`              | `0`                                                |\n| `minDestinationDistance`                                                                                     | Minimum distance of a destination segment when recursively refining (lower means more midpoints)                                                                                                                                                                             | `number`              | `0`                                                |\n| `minOffsetRatio`                                                                                             | Minimum offset ratio when recursively refining (lower means more midpoints)                                                                                                                                                                                                  | `number`              | `0`                                                |\n| `minOffsetDistance`                                                                                          | Minimum offset distance when recursively refining (lower means more midpoints)                                                                                                                                                                                               | `number`              | `Infinity` (i.e. condition not applied by default) |\n| `distortionMeasures`                                                                                         | A list of distortion measures to compute. E.g. `['log2sigma', 'twoOmega']`. Use in combination with a 'return type function' to find the distortion values in the output.                                                                                                    | `DistortionMeasure[]` | `[]`                                               |\n| `referenceScale`                                                                                             | The reference area scaling (sigma) to take into account for certain distortion measures, notably `'log2sigma'`.                                                                                                                                                              | `number`              | `1`                                                |\n| `isMultiGeometry`                                                                                            | Whether the input should be considered as a MultiPoint, MultiLineString or MultiPolygon. This is necessary since the standard geometry types are not deterministic: the types of LineString and MultiPoint are identical.                                                    | `boolean`             | `false`                                            |\n| `preForward` (not available for GCP Transformer methods)                                                     | A projection function to be applied to the General GCP 'source' (GCP 'resource') points before building a transformation, and to be applied during a 'forward' transform before evaluating the 'forward' transformation at the input points.                                 | `Projection Function` | Identity projection `(point: Point) => point`      |\n| `postForward` for General GCP Transformer methods, `postToGeo` for GCP Transformer methods                   | A projection function to be applied during a 'forward' ('toGeo') transform after evaluating the 'forward' ('toGeo') transformation.                                                                                                                                          | `Projection Function` | Identity projection `(point: Point) => point`      |\n| `preBackward` for General GCP Transformer methods, `preToResource` for GCP Transformer methods               | A projection function to be applied to the General GCP 'destination' (GCP 'geo') points before building a transformation, and to be applied during a 'backward' ('toResource') transform before evaluating the 'backward' ('toResource') transformation at the input points. | `Projection Function` | Identity projection `(point: Point) => point`      |\n| `postBackward` (not available for GCP Transformer methods)                                                   | A projection function to be applied during a 'backward' transform after evaluating the 'backward' transformation.                                                                                                                                                            | `Projection Function` | Identity projection `(point: Point) => point`      |\n\n#### Recursively refining (adding midpoints)\n\nWhen transforming LineStrings and Polygons, it can happen that simply transforming every Point is not sufficient.\n\nTwo factors are at play which may require a more granular transformation: the transformation (which can be non-shape preserving, as is the case with all transformation in this package except for Helmert and 1st degree polynomial) or the geographic nature of the coordinates (where lines are generally meant as 'great arcs' but could be interpreted as lon-lat cartesian lines).\n\nAn algorithm will therefore recursively add midpoints in each segment (i.e. between two Points) to make the line more granular. A midpoint is added at the transformed middle Point of the original segment if **all of the following conditions** are met:\n\n* The number of iterations is smaller than or equal to `maxDepth`\n* The length of the considered segment, in source space, is larger than `minSourceDistance`\n* The length of the considered segment, in destination space, is larger than `minDestinationDistance`\n\nand **at least one of the following conditions** are met:\n\n* The ratio of (the distance between the middle Point of the transformed segment and the transformed middle Point of the original segment) to the length of the transformed segment, is larger than or equal to the specified `minOffsetRatio`.\n* The distance between the middle Point of the transformed segment and the transformed middle Point of the original segment is larger than or equal to the specified `minOffsetDistance`.\n\nBy default, `maxDepth = 0` and no refinement is applied. If it would be set to `1`, then all three conditions (on `maxDepth`, `minSourceDistance` and `minDestinationDistance`) are true and the default value `minOffsetRatio = 0` will trigger one refinement check of each segment.\n\n#### Distortions\n\nSome transformations may induce distortions. Let's consider transforming an image to make this more visual. It we take a Helmert transformation of an image, we will see that it doesn't distort the image much: it will scale, rotate and translate the image, but not shear it (angles are preserved) - the only distortion applied is the scaling, and that scaling is the same everywhere across the image. If, on the other hand, we take a Thin Plate Spline transformation (with many GCPs) of that same image, we will see that the image will be distorted much, and will look like a rubber sheet which has been pulled and deformed in many different locations. Every pixel will be distorted in a unique way, such that both the areas and angles of the original image are not preserved.\n\nWe can compute these distortions locally, at every point. The approach implemented here is based on the theory of **'Differential Distortion Analysis'**: by evaluating the partial derivatives of the transformation function at every point we can compute local distortion measures from these derivatives, such as the **area distortion** `log2sigma` and **angular distortion** `twoOmega`. These will tell us how much the area and angles are distortion at every point. Thereafter averaging over all points can give un an indication of the overall distortion.\n\n'Differential Distortion Analysis' was earlier implemented in [this](https://github.com/mclaeysb/distortionAnalysis) Matlab/Octave package following peer reviewed publications of both the theoretical approach an an application to a historical map.\n\nThe supported distortion measures are available via the exported `supportedDistortionMeasures` constant. These include:\n\n| Key         | Type                               | Description                                                                                                                                                                                                                              | Example                                                                                                              |\n|-------------|------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------|\n| `log2sigma` | Area distortion measure            | The base-2 logarithm of the area scale factor σ, which indicates how much a local infinitesimal surface element is enlarged on the map (relative to the map’s scale).                                                                    | `0` for no area distortion, `1` if the area is twice as big, `-1` if the are is twice as small after transformation. |\n| `twoOmega`  | Angular distortion measure         | The maximum angular distortion 2Ω, which indicated the maximal (taken over all possible angles between two direction from that point) difference between an angle before and after the transformation, making it a measure for shearing. | `0` for no angular distortion, `>0` for angular distortion.                                                          |\n| `airyKavr`  | Airy-Kavrayskiy distortion measure | A measure combining the effects of areal and angular distortion.                                                                                                                                                                         | `0` for no distortion, `>0` for distortion.                                                                          |\n| `signDetJ`  | Flip measure                       | The transformation's Jacobian determinant flipping sign, describing 'fold-over' of the transformation.                                                                                                                                   | `1` for no flip, `-1` for flip.                                                                                      |\n| `thetaa`    | Tissot indicatrix axis             | The angle between the major axis of the Tissot indicatrix and the cartesian x-axis.                                                                                                                                                      | `0` for no rotation, `>0` for rotation.                                                                              |\n\nTo compute distortion measures, specify the requested measures in the transform options and read the values using the 'return type function':\n\n```js\nimport { GcpTransformer } from '@allmaps/transform'\n\nconst gcps6 = ... // See above\n\n// Obtain the referenceScale\nconst helmertTransformer = new GcpTransformer(gcps6, 'helmert')\nconst toGeoHelmertTransformation = helmertTransformer.getToGeoTransformation()\nconst referenceScale = toGeoHelmertTransformation.getMeasures().scale\n\nconst transformer = new GcpTransformer(gcps6, 'thinPlateSpline')\nconst resourcePoint = [1000, 1000]\nconst distortion = transformer.transformToGeo(\n    resourcePoint,\n    {\n      distortionMeasures: ['log2sigma'],\n      referenceScale\n    },\n    (gcpAndDistortions) => gcpAndDistortions.distortions.get('log2sigma')\n)\n// distortion = -0.2140907145956012\n// => At this resource location the area has slightly contracted after the transformation\n```\n\n### Projections\n\nThe (forward and backward) transformations underlying the the General GCP Transformer and GCP Transformer are map-projection agnostic: they describe a transformation for one cartesian `(x, y)` plane to another.\n\nIf you need to deal with simple map projection situation, e.g. when you are given GCPs in a lon-lat WGS84 geographic projection but want to build a GCP Transformer to WebMercator (as a guess for the map's projection and as the projection of the viewport to render in), you could simply project your GCPs from WGS84 to WebMercator first and build a projected transformed from these projected GCPs.\n\nTo deal with more complex general projection situations, the transform options includes optional projection functions. This is useful when the transformation should be computed between 'internal' projected spaces that are different than the 'source' and 'destination' spaces of the GCPs. These functions are `preForward`, `postForward` (`postToGeo`), `preBackward` (`preToResource`) and `postBackward`. When set, these are applied when reading the GCPs to form the 'internal' GCPs (`preForward` is applied to the source coordinates and `preBackward` to destination coordinates). They are also applied on each corresponding transform call before and after the transformation is evaluated: a `transformForward()` call thus applies `preForward`, evaluates the forward transformation, and finally applies `postForward`.\n\nTo make this general case more concrete, here's how this is works **in the Allmaps case**. Allmaps uses a GCP Transformer and transforms from the 'resource' space of an image of a map to a 'projected geo' space of the viewport to render the map. Not only is the viewport a projected space, but it is also possible that the user knows or supposes the geographic projection in which the map is made, and that this geographic projection is different than the geographic projection of the viewport. In that case one wants to build a transformation between the 'resource' space of pixels and an 'internal projected geo' space of the maps geographic projection. When transforming to geo, one wants to first evaluate this transformation (from 'resource' to 'internal projected geo') and then apply a `postForward` projection function from 'internal projected geo' space to 'projected geo' space.\n\nThe crucial insight here is that the map's geographic projection *can* be different than the rendered geographic projection. The first inspires a internal projected space to use when computing the transformation, which will assure that the transformation only takes into account the warping between these two spaces, and ideally, when our information or guess about the map's geographic projection is correct, does not account for warping due to the projections. The latter must be taken into account later, and handles the warping due to the difference in geographic projections. By doing *both within* a transformer, one can use the transformer methods to transform geometries forward or backward (or compute a resolution), and know that our geometries will be refined both by the transformation and the projection functions!\n\nTo simplify the computation of these optional projection functions from the map's geographic projection and viewport geographic projection, use the class **Projected GCP Transformer** from the [@allmaps/project](../../packages/project/) module.\n\nThe optional projection functions are part of the transform options to allow them to be specified not just at the construction of a transformer but for any transform call. Since they are also applied at construction when reading the GCPs, be careful when specifying such a function in a transform call. In a Projected GCP Transformer, the use-case for specifying a different projection in a transform call (and reusing existing the transformation!) has been implemented with care and can be used safely.\n\n### Return Type Function\n\nThe 'return type function' (internally named `generalGcpToP` or `GcpToP`) allows to modify the type of data returned for each point.\n\nAn example will make this more clear: when using a General GCP Transformer to forward-transform a LineString, the input is a LineString in the source space and the (default) output is a LineString in the destination space (i.e. an Array of destination points). Using the 'return type function', you can make this output to be an Array of any function of objects of type GeneralGcpAndDistortions, which include the destination points, but also the corresponding source points and (if computed) the distortion information. By default this function selects the destination points, and hence returns an Array of Points, but you can pass a function `(generalGcpToP) => generalGcpToP` to return an Array of GcpAndDistortions objects, or you can pass more complex function on this object as well. This can be useful in several cases:\n\n* When you want to refine an input geometry using a transformation but are interested in the coordinates of the refined geometry in the input domain more than those in the output domain.\n* When you want to read out distortion information at each point (see the options for how to specify which distortions measures to compute).\n* When you want to apply a transformation on the outputs point, e.g. flip the output points around their y-axis (see the notes on handedness for example of the latter).\n\n## Typing\n\nFor geometries and other types, the same types as in [@allmaps/types](../../packages/types/) are used.\n\nFor GCPs, some generalisations have been added:\n\nFor a General GCP Transformer, control points can be supplied as an array of objects containing `source` and `destination` coordinates:\n\n```ts\ntype GeneralGcp = {\n  source: [number, number]\n  destination: [number, number]\n}\n```\n\nFor a GCP Transformer, supply the control points as an array of objects containing `resource` and `geo` coordinates. This is the format used in [Georeference Annotations](https://iiif.io/api/extension/georef/):\n\n```ts\ntype Gcp = {\n  resource: [number, number]\n  geo: [number, number]\n}\n```\n\nThe return type functions work on the types `GeneralGcpAndDistortions` and `GcpAndDistortions`, defined as follows:\n\n```ts\nexport type Distortions = {\n  partialDerivativeX: Point\n  partialDerivativeY: Point\n  distortions: Map<DistortionMeasure, number>\n  distortion: number\n}\n\nexport type GeneralGcpAndDistortions = GeneralGcp & Partial<Distortions>\nexport type GcpAndDistortions = Gcp & Partial<Distortions>\n```\n\nProjection functions are defined as follows\n\n```ts\nexport type ProjectionFunction = (point: Point) => Point\n```\n\n## Transform vs. GDAL\n\nThe transformation algorithms of this package correspond to those of **GDAL** and the results are (nearly) identical. See the [tests](./test/test-transform.js) for details.\n\nFor a little history: this library started out as a JavaScript port of [gdaltransform](https://gdal.org/programs/gdaltransform.html) (as described in [this notebook](https://observablehq.com/@bertspaan/gdaltransform?collection=@bertspaan/iiif-maps)) and initially only implemented polynomial transformations of order 1. Later Thin Plate Spline transformations were added (see [this notebook](https://observablehq.com/d/0b57d3b587542794)) amongst other transformations, which lead to a refactoring using the [`ml-matrix`](https://github.com/mljs/matrix) library. This library is used for creating and solving the linear systems of equations that are at the heart of each of each of these transformations.\n\n## CLI\n\nThe [@allmaps/cli](../../apps/cli/) package creates and interface for some specific use cases:\n\n* Transforming **coordinates** from point to point.\n* Transforming **SVG** geometries from the resource coordinates space of a IIIF resource to GeoJSON objects in the geo coordinate space of an interactive map, using the GCPs and transformation type specified in a Georeference Annotation.\n* Transforming **GeoJSON** objects from the geo coordinate space of an interactive map to SVG objects in the resource coordinates space of a IIIF resource, using the GCPs and transformation type specified in a Georeference Annotation.\n* Transforming the **resource mask** of a Georeference Annotation from the resource coordinates space to a GeoJSON polygon in the geo coordinate space.\n\n## Benchmark\n\nHere are some benchmarks on building and using a transformer, as computed on a 2023 MacBook Air M2 with 16 GB RAM.\n\nThis benchmark can be run with `pnpm run bench`. For more information, see [`./bench/index.js`](`./bench/index.js`).\n\nTo create a transformer (with 10 points) and compute its 'toGeo' transformation:\n\n| Type            | Ops/s  |\n|-----------------|--------|\n| helmert         | 68455  |\n| polynomial1     | 117899 |\n| polynomial2     | 68981  |\n| polynomial3     | 30239  |\n| thinPlateSpline | 32927  |\n| projective      | 28530  |\n\nTo use a transformer (with 10 points, and its 'toGeo' transformation already computed) and transform a point 'toGeo':\n\n| Type            | Ops/s    |\n|-----------------|----------|\n| helmert         | 17049083 |\n| polynomial1     | 17568448 |\n| polynomial2     | 17007445 |\n| polynomial3     | 3774792  |\n| thinPlateSpline | 2933006  |\n| projective      | 16462262 |\n\n## License\n\nMIT\n\n## API\n\n### `new BaseIndependentLinearWeightsTransformation(sourcePoints, destinationPoints, type, pointCountMinimum)`\n\n###### Parameters\n\n* `sourcePoints` (`Array<Point>`)\n* `destinationPoints` (`Array<Point>`)\n* `type` (`  | 'straight'\n    | 'helmert'\n    | 'polynomial'\n    | 'polynomial1'\n    | 'polynomial2'\n    | 'polynomial3'\n    | 'thinPlateSpline'\n    | 'projective'\n    | 'linear'`)\n* `pointCountMinimum` (`number`)\n\n###### Returns\n\n`BaseIndependentLinearWeightsTransformation`.\n\n###### Extends\n\n* `BaseLinearWeightsTransformation`\n\n### `BaseIndependentLinearWeightsTransformation#coefsArrayMatrices`\n\n###### Type\n\n```ts\n[Array<Array<number>>, Array<Array<number>>]\n```\n\n### `BaseIndependentLinearWeightsTransformation#coefsArrayMatricesSize`\n\n###### Type\n\n```ts\n[Size, Size]\n```\n\n### `BaseIndependentLinearWeightsTransformation#coefsArrayMatrix`\n\n###### Type\n\n```ts\nArray<Array<number>>\n```\n\n### `BaseIndependentLinearWeightsTransformation#coefsArrayMatrixSize`\n\n###### Type\n\n```ts\n[number, number]\n```\n\n### `BaseIndependentLinearWeightsTransformation#getCoefsArrayMatrices()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`[Array<Array<number>>, Array<Array<number>>]`.\n\n### `BaseIndependentLinearWeightsTransformation#getCoefsArrayMatrix()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`Array<Array<number>>`.\n\n### `BaseIndependentLinearWeightsTransformation#getSourcePointCoefsArray(sourcePoint)`\n\n###### Parameters\n\n* `sourcePoint` (`[number, number]`)\n\n###### Returns\n\n`Array<number>`.\n\n### `BaseIndependentLinearWeightsTransformation#getSourcePointCoefsArrays(sourcePoint)`\n\n###### Parameters\n\n* `sourcePoint` (`[number, number]`)\n\n###### Returns\n\n`[Array<number>, Array<number>]`.\n\n### `new BaseLinearWeightsTransformation(sourcePoints, destinationPoints, type, pointCountMinimum)`\n\n###### Parameters\n\n* `sourcePoints` (`Array<Point>`)\n* `destinationPoints` (`Array<Point>`)\n* `type` (`  | 'straight'\n    | 'helmert'\n    | 'polynomial'\n    | 'polynomial1'\n    | 'polynomial2'\n    | 'polynomial3'\n    | 'thinPlateSpline'\n    | 'projective'\n    | 'linear'`)\n* `pointCountMinimum` (`number`)\n\n###### Returns\n\n`BaseLinearWeightsTransformation`.\n\n###### Extends\n\n* `BaseTransformation`\n\n### `BaseLinearWeightsTransformation#destinationPointsArrays`\n\n###### Type\n\n```ts\n[Array<number>, Array<number>]\n```\n\n### `BaseLinearWeightsTransformation#getCoefsArrayMatrices()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`[Array<Array<number>>, Array<Array<number>>]`.\n\n### `BaseLinearWeightsTransformation#getDestinationPointsArrays()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`[Array<number>, Array<number>]`.\n\n### `BaseLinearWeightsTransformation#getSourcePointCoefsArrays(sourcePoint)`\n\n###### Parameters\n\n* `sourcePoint` (`[number, number]`)\n\n###### Returns\n\n`[Array<number>, Array<number>]`.\n\n### `BaseLinearWeightsTransformation#weightsArrays?`\n\n###### Type\n\n```ts\n[Array<number>, Array<number>]\n```\n\n### `new BasePolynomialTransformation(sourcePoints, destinationPoints, order)`\n\n###### Parameters\n\n* `sourcePoints` (`Array<Point>`)\n* `destinationPoints` (`Array<Point>`)\n* `order?` (`number | undefined`)\n\n###### Returns\n\n`BasePolynomialTransformation`.\n\n###### Extends\n\n* `BaseIndependentLinearWeightsTransformation`\n\n### `BasePolynomialTransformation#coefsArrayMatrices`\n\n###### Type\n\n```ts\n[Array<Array<number>>, Array<Array<number>>]\n```\n\n### `BasePolynomialTransformation#coefsArrayMatricesSize`\n\n###### Type\n\n```ts\n[Size, Size]\n```\n\n### `BasePolynomialTransformation#coefsArrayMatrix`\n\n###### Type\n\n```ts\nArray<Array<number>>\n```\n\n### `BasePolynomialTransformation#coefsArrayMatrixSize`\n\n###### Type\n\n```ts\n[number, number]\n```\n\n### `BasePolynomialTransformation#getCoefsArrayMatrix()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`Array<Array<number>>`.\n\n### `BasePolynomialTransformation#getDestinationPointsArrays()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`[Array<number>, Array<number>]`.\n\n### `BasePolynomialTransformation#getTransformationDataAsFloat64Array()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`{weights: Float64Array; sourcePoints: Float64Array}`.\n\n### `BasePolynomialTransformation#order`\n\n###### Type\n\n```ts\nnumber\n```\n\n### `BasePolynomialTransformation#solve()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`void`.\n\n### `BasePolynomialTransformation#weightsArrays?`\n\n###### Type\n\n```ts\n[Array<number>, Array<number>]\n```\n\n### `new BaseTransformation(sourcePoints, destinationPoints, type, pointCountMinimum)`\n\nCreate a transformation\n\n###### Parameters\n\n* `sourcePoints` (`Array<Point>`)\n  * The source points\n* `destinationPoints` (`Array<Point>`)\n  * The destination points\n* `type` (`  | 'straight'\n    | 'helmert'\n    | 'polynomial'\n    | 'polynomial1'\n    | 'polynomial2'\n    | 'polynomial3'\n    | 'thinPlateSpline'\n    | 'projective'\n    | 'linear'`)\n  * The transformation type\n* `pointCountMinimum` (`number`)\n  * The minimum number of points for the transformation type\n\n###### Returns\n\n`BaseTransformation`.\n\n### `BaseTransformation#destinationPoints`\n\n###### Type\n\n```ts\nArray<Point>\n```\n\n### `BaseTransformation#destinationRmse?`\n\n###### Type\n\n```ts\nnumber\n```\n\n### `BaseTransformation#destinationTransformedSourcePoints?`\n\n###### Type\n\n```ts\nArray<Point>\n```\n\n### `BaseTransformation#errors?`\n\n###### Type\n\n```ts\nArray<number>\n```\n\n### `BaseTransformation#evaluateFunction(newSourcePoint)`\n\nEvaluate the transformation function at a new point\n\n###### Parameters\n\n* `newSourcePoint` (`[number, number]`)\n  * a source point\n\n###### Returns\n\nthe source point, transformed to destination space (`[number, number]`).\n\n### `BaseTransformation#evaluatePartialDerivativeX(newSourcePoint)`\n\nEvaluate the transformation function's partial derivative to x at a new point\n\n###### Parameters\n\n* `newSourcePoint` (`[number, number]`)\n  * a source point\n\n###### Returns\n\nthe x and y component of the partial derivative to x at the source point (`[number, number]`).\n\n### `BaseTransformation#evaluatePartialDerivativeY(newSourcePoint)`\n\nEvaluate the transformation function's partial derivative to y at a new point\n\n###### Parameters\n\n* `newSourcePoint` (`[number, number]`)\n  * a source point\n\n###### Returns\n\nthe x and y component of the partial derivative to y at the source point (`[number, number]`).\n\n### `BaseTransformation#getDestinationRmse()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`number`.\n\n### `BaseTransformation#getDestinationTransformedSourcePoints()`\n\nGet the destination-transformed source points.\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\nsource points, transformed to destination domain (`Array<Point>`).\n\n### `BaseTransformation#getErrors()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`Array<number>`.\n\n### `BaseTransformation#getMeasures()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`Partial<HelmertMeasures> | Partial<Polynomial1Measures>`.\n\n### `BaseTransformation#getTransformationDataAsFloat64Array()`\n\nGet transformation weights in a format suitable for WASM rendering.\nThis provides a standardized way to extract internal transformation parameters\nfor use in WebAssembly-based rendering pipelines.\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\nAn object containing: (`{weights: Float64Array; sourcePoints: Float64Array}`).\n\n* weights: Transformation-specific weight parameters as Float64Array\n* sourcePoints: Flattened source control points as Float64Array (for TPS only, empty otherwise)\n\n### `BaseTransformation#pointCount`\n\n###### Type\n\n```ts\nnumber\n```\n\n### `BaseTransformation#pointCountMinimum`\n\n###### Type\n\n```ts\nnumber\n```\n\n### `BaseTransformation#processWeightsArrays()`\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`void`.\n\n### `BaseTransformation#setWeightsArrays(weightsArrays)`\n\nSet weights.\n\nThe weights might be obtained in other ways then through solving\n(e.g. through solving multiple transformation together when staping).\nThis function can be used to set weights computed elsewhere.\n\n###### Parameters\n\n* `weightsArrays` (`object`)\n\n###### Returns\n\n`void`.\n\n### `BaseTransformation#solve()`\n\nNote: since (writing to and) reading from matrices is expensive,\nwe convert to and convert from ml-matrix Matrix types in this function,\nin order not to use them in the evaluate functions.\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`void`.\n\n### `BaseTransformation#sourcePoints`\n\n###### Type\n\n```ts\nArray<Point>\n```\n\n### `BaseTransformation#type`\n\n###### Type\n\n```ts\n  | 'straight'\n  | 'helmert'\n  | 'polynomial'\n  | 'polynomial1'\n  | 'polynomial2'\n  | 'polynomial3'\n  | 'thinPlateSpline'\n  | 'projective'\n  | 'linear'\n```\n\n### `BaseTransformation#weightsArrays?`\n\n###### Type\n\n```ts\nobject\n```\n\n### `DistortionMeasure`\n\n###### Type\n\n```ts\n'log2sigma' | 'twoOmega' | 'airyKavr' | 'signDetJ' | 'thetaa'\n```\n\n### `Distortions`\n\n###### Fields\n\n* `distortion` (`number`)\n* `distortions` (`Map<DistortionMeasure, number>`)\n* `partialDerivativeX` (`[number, number]`)\n* `partialDerivativeY` (`[number, number]`)\n\n### `GcpAndDistortions`\n\n###### Type\n\n```ts\nGcp & Partial<Distortions>\n```\n\n### `GcpTransformOptions`\n\n###### Type\n\n```ts\n{\n  maxDepth: number\n  minSourceDistance: number\n  minDestinationDistance: number\n  minOffsetRatio: number\n  minOffsetDistance: number\n  distortionMeasures: DistortionMeasure[]\n  referenceScale: number\n  postToGeo: ProjectionFunction\n  preToResource: ProjectionFunction\n} & MultiGeometryOptions\n```\n\n### `new GcpTransformer(gcps, type, partialGcpTransformerOptions)`\n\nCreate a GcpTransformer\n\n###### Parameters\n\n* `gcps` (`Array<Gcp>`)\n  * An array of Ground Control Points (GCPs)\n* `type` (`TransformationType | undefined`)\n  * The transformation type\n* `partialGcpTransformerOptions?` (`Partial<GcpTransformerOptions> | undefined`)\n  * GCP Transformer options\n\n###### Returns\n\n`GcpTransformer`.\n\n###### Extends\n\n* `BaseGcpTransformer`\n\n### `GcpTransformer#gcps`\n\nGet GCPs as they were inputed to the GCP Transformer (`Array<Gcp>`).\n\n### `GcpTransformer#getToGeoTransformation()`\n\nGet the forward transformation. Create if it doesn't exist yet.\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`BaseTransformation`.\n\n### `GcpTransformer#getToGeoTransformationResolution(resourceBbox, partialGcpTransformOptions)`\n\nGet the resolution of the toGeo transformation in resource space, within a given bbox.\n\nThis informs you in how fine the warping is, in resource space.\nIt can be useful e.g. to create a triangulation in resource space\nthat is fine enough for this warping or set the minSourceDistance options.\n\nIt is obtained by transforming toGeo two linestring,\nnamely the horizontal and vertical midlines of the given bbox.\nThe toGeo transformation will refine these lines:\nit will break them in small enough pieces to obtain a near continuous result.\n\nResolution returned in the length of the shortest piece, measured in resource coordinates,\nor undefined if no refinements were needed.\n\n###### Parameters\n\n* `resourceBbox?` (`Bbox | undefined`)\n  * BBox in resource space where the resolution is requested, or undefined to get this from the GCPs\n* `partialGcpTransformOptions?` (`Partial<GcpTransformOptions> | undefined`)\n  * GCP Transform options to consider during the transformation\n\n###### Returns\n\nResolution of the toGeo transformation in resource space (`number | undefined`).\n\n### `GcpTransformer#getToResourceTransformation()`\n\nGet the backward transformation. Create if it doesn't exist yet.\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`BaseTransformation`.\n\n### `GcpTransformer#getToResourceTransformationResolution(geoBbox, partialGcpTransformOptions)`\n\nGet the resolution of the toResource transformation in geo space, within a given bbox.\n\nThis informs you in how fine the warping is, in geo space.\nIt can be useful e.g. to create a triangulation in geo space\nthat is fine enough for this warping or set the minDestionationDistance options.\n\nIt is obtained by transforming toResource two linestring,\nnamely the horizontal and vertical midlines of the given bbox.\nThe toResource transformation will refine these lines:\nit will break them in small enough pieces to obtain a near continuous result.\n\nResolution returned in the length of the shortest piece, measured in geo coordinates,\nor undefined if no refinements were needed.\n\n###### Parameters\n\n* `geoBbox?` (`Bbox | undefined`)\n  * BBox in geo space where the resolution is requested, or undefined to get this from the GCPs\n* `partialGcpTransformOptions?` (`Partial<GcpTransformOptions> | undefined`)\n  * GCP Transform options to consider during the transformation\n\n###### Returns\n\nResolution of the toResource transformation in geo space (`number | undefined`).\n\n### `GcpTransformer#getTransformerOptions()`\n\nGet the transformer options.\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`{ differentHandedness: boolean; } & { maxDepth: number; minSourceDistance: number; minDestinationDistance: number; minOffsetRatio: number; minOffsetDistance: number; distortionMeasures: DistortionMeasure[]; ... 4 more ...; postBackward: ProjectionFunction; } & MultiGeometryOptions`.\n\n### `GcpTransformer#setTransformerOptions(partialGcpTransformerOptions)`\n\nSet the transformer options.\n\nUse with caution, especially for options that have effects in the constructor.\n\n###### Parameters\n\n* `partialGcpTransformerOptions` (`{ differentHandedness?: boolean | undefined; maxDepth?: number | undefined; minSourceDistance?: number | undefined; minDestinationDistance?: number | undefined; minOffsetRatio?: number | undefined; ... 5 more ...; isMultiGeometry?: boolean | undefined; }`)\n\n###### Returns\n\n`void`.\n\n### `GcpTransformer#transformToGeo(resourcePoint, partialGcpTransformOptions, gcpToP)`\n\n###### Parameters\n\n* `resourcePoint` (`[number, number]`)\n* `partialGcpTransformOptions?` (`Partial<GcpTransformOptions> | undefined`)\n* `gcpToP?` (`((gcp: GcpAndDistortions) => P) | undefined`)\n\n###### Returns\n\n`P`.\n\n### `GcpTransformer#transformToResource(geoPoint, partialGcpTransformOptions, gcpToP)`\n\n###### Parameters\n\n* `geoPoint` (`[number, number]`)\n* `partialGcpTransformOptions?` (`Partial<GcpTransformOptions> | undefined`)\n* `gcpToP?` (`((gcp: GcpAndDistortions) => P) | undefined`)\n\n###### Returns\n\n`P`.\n\n### `GcpTransformer.fromGeoreferencedMap(georeferencedMap, options)`\n\nCreate a Projected GCP Transformer from a Georeferenced Map\n\n###### Parameters\n\n* `georeferencedMap` (`{ type: \"GeoreferencedMap\"; resource: { id: string; type: \"ImageService1\" | \"ImageService2\" | \"ImageService3\" | \"Canvas\"; height?: number | undefined; width?: number | undefined; partOf?: Array<PartOfItemType> | undefined; provider?: Array<{ ...; }> | undefined; }; ... 8 more ...; _allmaps?: unknown; }`)\n  * A Georeferenced Map\n* `options?` (`Partial<{ differentHandedness: boolean; } & { maxDepth: number; minSourceDistance: number; minDestinationDistance: number; minOffsetRatio: number; minOffsetDistance: number; distortionMeasures: DistortionMeasure[]; referenceScale: number; postToGeo: ProjectionFunction; preToResource: ProjectionFunction; } & MultiGeo...`)\n  * Options, including GCP Transformer Options, and a transformation type to overrule the type defined in the Georeferenced Map\n\n###### Returns\n\nA Projected GCP Transformer (`GcpTransformer`).\n\n### `GcpTransformer.transformGeojsonFeatureCollectionToSvgString(transformer, geojson, partialGcpTransformOptions)`\n\nTransform a GeoJSON FeatureCollection from geo space to resource space to a SVG string\n\nThis is a shortcut method, available as static method in order not to overpopulate intellisense suggestions\nNote: Multi-geometries are not supported\n\n###### Parameters\n\n* `transformer` (`GcpTransformer`)\n  * A GCP Transformer defining the transformation\n* `geojson` (`{type: 'FeatureCollection'; features: GeojsonFeature[]}`)\n  * GeoJSON FeatureCollection to transform\n* `partialGcpTransformOptions?` (`Partial<GcpTransformOptions> | undefined`)\n  * GCP Transform options\n\n###### Returns\n\nInput GeoJSON FeaturesCollection transformed to resource space, as SVG string (`string`).\n\n### `GcpTransformer.transformGeojsonToSvg(transformer, geojsonGeometry, partialGcpTransformOptions)`\n\nTransform a GeoJSON Geometry from geo space to resource space to a SVG geometry\n\nThis is a shortcut method, available as static method in order not to overpopulate intellisense suggestions\nNote: Multi-geometries are not supported\n\n###### Parameters\n\n* `transformer` (`GcpTransformer`)\n  * A GCP Transformer defining the transformation\n* `geojsonGeometry` (`  | GeojsonPoint\n    | GeojsonLineString\n    | GeojsonPolygon\n    | GeojsonMultiPoint\n    | GeojsonMultiLineString\n    | GeojsonMultiPolygon`)\n  * GeoJSON Geometry to transform\n* `partialGcpTransformOptions?` (`Partial<GcpTransformOptions> | undefined`)\n  * GCP Transform options\n\n###### Returns\n\nInput GeoJSON Geometry transform to resource space, as SVG geometry (`SvgCircle | SvgLine | SvgPolyLine | SvgRect | SvgPolygon`).\n\n### `GcpTransformer.transformSvgStringToGeojsonFeatureCollection(transformer, svg, partialGcpTransformOptions)`\n\nTransform an SVG string from resource space to geo space to a GeoJSON FeatureCollection\n\nThis is a shortcut method, available as static method in order not to overpopulate intellisense suggestions\nNote: Multi-geometries are not supported\n\n###### Parameters\n\n* `transformer` (`GcpTransformer`)\n  * A GCP Transformer defining the transformation\n* `svg` (`string`)\n  * An SVG string to transform\n* `partialGcpTransformOptions?` (`Partial<GcpTransformOptions> | undefined`)\n  * GCP Transform options\n\n###### Returns\n\nInput SVG string transformed to geo space, as a GeoJSON FeatureCollection (`{type: 'FeatureCollection'; features: GeojsonFeature[]}`).\n\n### `GcpTransformer.transformSvgToGeojson(transformer, svgCircle, partialGcpTransformOptions)`\n\n###### Parameters\n\n* `transformer` (`GcpTransformer`)\n* `svgCircle` (`{type: 'circle'; attributes?: SvgAttributes; coordinates: Point}`)\n* `partialGcpTransformOptions?` (`Partial<GcpTransformOptions> | undefined`)\n\n###### Returns\n\n`{type: 'Point'; coordinates: number[]}`.\n\n### `GcpTransformerInputs`\n\n###### Type\n\n```ts\nGcpsInputs & TransformationTypeInputs\n```\n\n### `GcpTransformerOptions`\n\n###### Type\n\n```ts\n{ differentHandedness: boolean; } & { maxDepth: number; minSourceDistance: number; minDestinationDistance: number; minOffsetRatio: number; minOffsetDistance: number; distortionMeasures: DistortionMeasure[]; referenceScale: number; postToGeo: ProjectionFunction; preToResource: ProjectionFunction; } & MultiGeometryOpt...\n```\n\n### `GcpsInputs`\n\n###### Fields\n\n* `gcps` (`Array<Gcp>`)\n\n### `GeneralGcp`\n\n###### Fields\n\n* `destination` (`[number, number]`)\n* `source` (`[number, number]`)\n\n### `GeneralGcpAndDistortions`\n\n###### Type\n\n```ts\nGeneralGcp & Partial<Distortions>\n```\n\n### `GeneralGcpTransformOptions`\n\n###### Type\n\n```ts\n{ maxDepth: number; minSourceDistance: number; minDestinationDistance: number; minOffsetRatio: number; minOffsetDistance: number; distortionMeasures: DistortionMeasure[]; referenceScale: number; preForward: ProjectionFunction; postForward: ProjectionFunction; preBackward: ProjectionFunction; postBackward: Projection...\n```\n\n### `new GeneralGcpTransformer(generalGcps, type, partialGeneralGcpTransformerOptions)`\n\nCreate a GeneralGcpTransformer\n\n###### Parameters\n\n* `generalGcps` (`Array<GeneralGcp>`)\n  * An array of General Ground Control Points (GCPs)\n* `type` (`TransformationType | undefined`)\n  * The transformation type\n* `partialGeneralGcpTransformerOptions?` (`Partial<GeneralGcpTransformerOptions> | undefined`)\n  * General GCP Transformer options\n\n###### Returns\n\n`GeneralGcpTransformer`.\n\n###### Extends\n\n* `BaseGcpTransformer`\n\n### `GeneralGcpTransformer#generalGcps`\n\n###### Type\n\n```ts\nArray<GeneralGcp>\n```\n\n### `GeneralGcpTransformer#getBackwardTransformation()`\n\nGet the backward transformation. Create if it doesn't exist yet.\n\n###### Parameters\n\nThere are no parameters.\n\n###### Returns\n\n`BaseTransformation`.\n\n### `GeneralGcpTransformer#getBackwardTransformationResolution(destinationBbox, partialGeneralGcpTransformOptions)`\n\nGet the resolution of the backward transformation in destination space, within a given bbox.\n\nThis informs you in how fine the warping is, in destination space.\nIt can be useful e.g. to create a triangulation in destination space\nthat is fine enough for this warping.\n\nIt is obtained by transforming backward two linestring,\nnamely the horizontal and vertical midlines of the given bbox.\nThe backward transformation will refine these lines:\ni","readmeFilename":"README.md"}