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I am trying to write a program which will render tiles from EPSG2180-based WMTS server. Given coordinates of a point (WSG84 or EPSG2180, I can convert from one to another) I want to render a tile containing it.

Each TileMatrix has info about TileWidth/Height, MatrixWidth/Height, TopLeftCorner and I understand what they mean. However, they don't seem sufficient to translate lat/lon to row/column. Apart from those each TileMatrix has mysterious ScaleDenominator value.

What is ScaleDenominator and what is the relationship between it and other values describing TileMatrix? How can I use it to translate lat/lon to tile's row/column?

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    The standard portal.opengeospatial.org/files/?artifact_id=35326 tries to give an answer to both of your questions. Please quote the parts that remains unclear for you.
    – user30184
    Commented Mar 18, 2019 at 19:54
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    Everything is clear now, thank you very much! As an amateur I didn't even think of googling "wmts standard", I didn't expect such doc to be so human-friendly. Thanks again!
    – hugo
    Commented Mar 18, 2019 at 20:54
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    @hugo please add and accept an answer to help out future users who have the sam equestion
    – Ian Turton
    Commented Mar 19, 2019 at 8:34

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Standard linked by @user30184 (portal.opengeospatial.org/files/?artifact_id=35326) explicitly and precisely defines ScaleDenominator in section 6.1 "Tile matrix set – the geometry of the tiled space":

The scale denominator is defined with respect to a "standardized rendering pixel size" of 0.28 mm × 0.28 mm (millimeters).

Scale of tiled map is 1:ScaleDenominator. Each pixel is assumed to be 0.28mm, which allows to calculate span of each tile in meters by multiplying TileWidth (or TileHeight) by ScaleDenominator * 0.00028.

Knowing real-world size of each tile in meters (and knowing that the CRS used is EPSG 2180, which uses meter as its base unit), I was finally able to determine size of the whole matrix and choose appropriate tile for given coordinates.

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  • For those of us using EPSG:27700 (British National Grid): to get the row take the TopLeftCorner[1] and subtract the Northings before floor dividing (//) by TileHeight*ScaleDenominator*0.00028. To get the column take the Eastings and subtract the TopLeftCorner[0] before floor dividing by TileWidth*ScaleDenominator*0.00028.
    – Ari Cooper-Davis
    Commented Mar 18, 2022 at 15:16

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