# Features of WebGL map scaling

We released style editor… You can read more about how you can customize the map for the tasks of the service with it. on vc.ru… On Habré, we want to talk about the StyleZoom concept, which we also use in the style editor.

Below the cut – a short story about zoom levels: why they are not suitable for large areas in the standard form and how the scale affects the loading of tiles and the appearance of the map.

## Zoom-level

To indicate the scale in the 2GIS WebGL map, as in many other maps, a number is used – zoom-level or just zoom. A zoom of zero corresponds to a map scale that fits the entire world into a 256 × 256 px square.

World map at zoom = 0

Increasing the zoom by one corresponds to stretching the map twice. At the first zoom, the whole world will be 256 × 2 = 512 px. On the fourth, we get the size 256 × 2 × 2 × 2 × 2 = 4096 px.

This system allows you to designate the range of scales with easy-to-understand numbers. For example, zoom = 11 is about one large city on the screen, zoom = 19 allows you to see buildings and passages between them in detail.

## Mercator projection

2GIS maps use the Mercator cartographic projection. A cartographic projection is a way of displaying a spherical surface of the Earth on a flat map.

Since a plane and a ball are not the same thing, any cartographic projection distorts the shape or size of objects. In the Mercator projection, objects at high latitudes on the map appear larger than objects at the equator. Therefore, on such maps, Greenland looks the size of Africa, although in fact its area is 14 times less than Africa. Here you can see how the projection distorts the size of the countries.

If Russia is brought closer to the equator, its size on the map is significantly reduced

The stretching of objects is proportional to 1 / cos (lat), where lat is the latitude of the object. From this formula it follows that objects at the latitude of St. Petersburg (lat = 60 °) on the map will be stretched twice. And objects at the North or South Poles (lat = 90 °) will stretch indefinitely. That is why the poles are never drawn on the maps in the Mercator projection – they cut off everything north and south of ≈85 ° latitude.

You can read more about the Mercator projection in this visual and fascinating material

## Problems with zoom and Mercator projection

The main problem with zooms follows from the properties of the Mercator projection: the same zoom-level at different latitudes corresponds to different actual map scales.

Let’s compare screenshots of the map at the 14th zoom in Murmansk (latitude 69 °) and Tashkent (latitude 41 °).

15th zoom in Murmansk

15th zoom in Tashkent

You can see how much the house size is different. In Murmansk, they are large, in Tashkent, the map is shallow.

When styling the map, we want to give it a specific look and feel. To do this, we set the width of the roads in pixels depending on the zoom or the zoom from which we start showing houses. Styles written for one latitude will look very different on another. The meaning inherent in them will be distorted, since the zooms will mean a different actual scale.

## Decision

To solve this problem, we introduced the concept of styleZoom, which may differ from the usual zoom.

 Normal zoom StyleZoom Defines the scaling of objects Determines which tiles to load Written in url Determines which scale to apply styles to Used in the familiar getZoom / setZoom methods Used in the getStyleZoom / setStyleZoom methods Matches bitmap tiles

styleZoom is calculated from zoom and latitude using the following formula: styleZoom = zoom + log2 (1 / (2 * cos (lat)).

The following styleZoom properties follow from the formula:

• At 60 ° latitude styleZoom = zoom. Since the styles were originally written for Novosibirsk and Moscow, we decided to take this latitude as the base.
• At latitudes <60 ° styleZoom
• At latitudes> 60 ° styleZoom> zoom.

Now let’s see how Tashkent and Murmansk will look with styleZoom = 15.

Tashkent, styleZoom = 15 (zoom ≈ 15.59)

Murmansk, styleZoom = 15 (zoom ≈ 14.53)

You can clearly see that styleZoom corresponds to the real scale of the map regardless of the latitude: the houses do not visually differ in size, the map looks the same in two different cities.

## Limitations

The correction mechanism has drawbacks that appear in two scenarios for working with the map.

zoom <9

At small zooms, when the whole world or most of it is visible on the screen, dragging the map up and down leads to large changes in latitude and, accordingly, styleZoom.

While dragging and dropping, this can lead to loading new tiles, switching styles, appearing or disappearing objects, etc. To avoid this effect, at zoom <9 the correction is disabled and styleZoom is set to zoom.lat> 60 °

At very high latitudes, styleZoom becomes much larger zoom. Since styleZoom is responsible for which tiles to load, it may turn out, for example, that at the 14th zoom we will load and display the tiles of the 16th zoom. The 16th zoom tile is 16 times smaller in area than the 14th zoom tile. And if usually ≈30 tiles fall on the screen, then in this case there will be 480. And the number of tiles greatly affects performance. In order not to load the video card at these latitudes, at lat> 60 ° the correction is disabled, and styleZoom is also set to zoom.