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+# XYZ and projection math
+
+[NZTM2000Quad](https://github.com/linz/NZTM2000TileMatrixSet) is not supported by many third party tools especially inside the Vector Tile space. Often tools expect tiles to be served as `/{z}/{x}/{y}.mvt` and assume the projection is [WebMercatorQuad](https://docs.ogc.org/is/17-083r2/17-083r2.html#63).
+
+Basemaps uses the lack of built in projection information to allow tools to work with NZTM2000Quad tiles without knowing they are in a different tile matrix set.
+
+This is how basemaps provides [NZTM2000 EPSG:2193](https://epsg.io/2193) support to Aerial imagery on https://basemaps.linz.govt.nz using custom projection logic [basemaps/landing](https://github.com/linz/basemaps/blob/master/packages/landing/src/tile.matrix.ts#L56)
+
+## Background
+
+Tile mapping services use a [TileMatrixSet](https://docs.ogc.org/is/17-083r2/17-083r2.html) to describe where the tiles are meant to be positioned on the globe using a origin point and scale information per zoom level, most web mapping systems assume the tile matrix set is [WebMercatorQuad](https://docs.ogc.org/is/17-083r2/17-083r2.html#63).
+
+Assuming the target tile matrix set is similar to WebMercatorQuad, which has a square tile grid, with zoom levels increasing at a factor of 2 and starting with a single tile z:0, x:0, y:0 points can be projected into a "fake" version of the tile matrix set and then used with any tool that supports [EPSG:4326](https://epsg.io/4326) to [EPSG:3857](https://epsg.io/3857) math such as tippecanoe.
+
+## Process
+
+To create a fake projection from a tile grid the process is
+
+- Take a lat, lon pair ([EPSG:4326](https://epsg.io/4326) degrees) and project into the target projection (eg [EPSG:2193](https://epsg.io/2193))
+- Take the target x,y pair ([EPSG:2193](https://epsg.io/2193) metres) and project where in the tile grid the point would be located (px)
+- Take the x,y pixels pair and assume it is now a WebMercatorQuad tile then project it to [EPSG:3857](https://epsg.io/3857)
+- Take the x,y ([EPSG:3857](https://epsg.io/3857) metres) and project it into lat, lon ([EPSG:4326](https://epsg.io/4326))
+
+The point is now in the fake projection and can be combined with applications that consume XYZ tiles
+
+## Example
+
+To convert an example point, such as the [Beehive](<https://en.wikipedia.org/wiki/Beehive_(New_Zealand)>) is located at `-41.2784°`, `174.7767°` ([EPSG:4326](https://epsg.io/4326)) ![Beehive NZTM2000Quad](./static/projection_beehive_nztm2000quad.webp)
+
+Converting to [NZTM2000 EPSG:2193](https://epsg.io/2193) `x: 1748795.82...`, `y: 5428814.899...`
+
+Using NZTM2000Quad to convert to pixel cooridantes of tile z:0, x:0, y:0 yields `x:128.0001..., y:127.999...`
+
+![Beehive NZTM2000Quad](./static/projection_nztm2000quad_0_0_0.webp)
+
+converting to metres EPSG:3857 x: `21.883...`, y: `7.2815...` and then into lat,lon ([EPSG:4326](https://epsg.io/4326)) `0.0001...`, `0.0000...` as NZTM2000Quad is centred on the beehive the result of lat,lon approx 0,0 is expected!
+
+![Beehive FakeNZTM2000Quad](./static/projection_beehive_fakenztm2000.webp)
+
+These lat,lon coordinates can now be used in a system that works with XYZ tiles but assumes that they are in WebMercatorQuad
+
+### Example Code
+
+Using [@basemaps/geo](https://github.com/linz/basemaps/tree/master/packages/geo)
+
+````typescript
+import {NZTM2000QuadTms, GoogleTms, Projection} from '@basemaps/geo'
+
+// Convert to NZTMQuad pixel location
+const nztmXy = Projection.get(Nztm2000QuadTms).fromWgs84([174.7767, -41.2784])
+const nztmPixels = Nztm2000QuadTms.sourceToPixels(nztmXy[0], nztmXy[1],0)
+
+// Convert from pixels assuming EPSG:3857 WebMercatorQuad
+const googleXy = GoogleTms.pixelsToSource(nztmPixels.x, nztmPixels.y, 0)
+const latLon = Projection.get(GoogleTms).toWgs84([googleXy.x, googleXy.y])```
+````