Niveles de zoom y cuadrícula de mosaico

2025-05-07

Azure Maps usa el sistema de coordenadas de proyección Spherical Mercator (EPSG:3857). Una proyección es el modelo matemático que se usa para transformar el globo esférico en un mapa plano. La proyección Spherical Mercator amplía el mapa en los polos para crear un mapa cuadrado. Esta proyección distorsiona significativamente la escala y el área del mapa, pero tiene dos propiedades importantes que superan esta distorsión:

Es una proyección conforme, lo que significa que conserva la forma de objetos relativamente pequeños. Conservar la forma de objetos pequeños es especialmente importante al mostrar imágenes aéreas. Por ejemplo, queremos evitar distorsionar la forma de los edificios. Los edificios cuadrados deben parecerse a un cuadrado, no a un rectángulo.
Es una proyección cilíndrica. Norte y sur siempre están arriba y abajo, y el oeste y este siempre están a la izquierda y a la derecha.

Para optimizar el rendimiento de la recuperación y visualización del mapa, el mapa se divide en mosaicos cuadrados. El SDK de Azure Maps usa iconos que tienen un tamaño de 512 x 512 píxeles para mapas de carreteras y 256 x 256 píxeles más pequeños para imágenes satélite. Azure Maps proporciona mosaicos rasterizados y vectoriales para 23 niveles de zoom, numerados entre 0 y 22. En el nivel de zoom 0, todo el mundo encaja en un solo icono:

Icono de mapa mundial

El nivel de zoom 1 usa cuatro iconos para representar el mundo: un cuadrado de 2 x 2

Distribución de mosaico de mapa 2x2

Cada nivel de zoom adicional divide en cuatro los mosaicos del anterior, creando una cuadrícula de 2 ^zoom x 2 ^zoom. El nivel de zoom 22 es una cuadrícula de 2²² x 2²² o 4 194 304 x 4 194 304 mosaicos (17 592 186 044 416 mosaicos en total).

Los controles de mapa interactivo de Azure Maps para el soporte web admiten 25 niveles de zoom, numerados entre 0 y 24. Aunque los datos de la carretera solo están disponibles en los niveles de zoom en cuando los mosaicos están disponibles.

En la tabla siguiente se proporciona la lista completa de valores para los niveles de zoom en los que el tamaño del icono es de 256 píxeles cuadrados:

Nivel de zoom	Metros/píxel	Metros/lado de mosaico
0	156543	40075017
1	78271,5	20037508
2	39.135,8	10018754
3	19567.88	5009377.1
4	9783.94	2504688.5
5	4891.97	1252344.3
6	2445.98	626172.1
7	1222.99	313086.1
8	611.5	156543
9	305.75	78271,5
10	152.87	39.135,8
11	76.44	19567,9
12	38.219	9783.94
13	19.109	4891.97
14	9,555	2445.98
15	4.777	1222.99
16	2.3887	611.496
17	1.1943	305.748
18	0.5972	152.874
19	0.2986	76.437
20	0.14929	38.2185
Veintiuno	0.074646	19.10926
22	0.037323	9.55463
23	0.0186615	4.777315
veinticuatro	0.00933075	2.3886575

Coordenadas de píxeles

Después de elegir la proyección y la escala que se van a usar en cada nivel de zoom, podemos convertir las coordenadas geográficas en coordenadas de píxeles. El ancho y alto de píxeles completos de una imagen de mapa del mundo para un nivel de zoom determinado se calcula como:

var mapWidth = tileSize * Math.pow(2, zoom);

var mapHeight = mapWidth;

Dado que el ancho y alto del mapa son diferentes en cada nivel de zoom, también lo son las coordenadas de píxel. El píxel de la esquina superior izquierda del mapa siempre tiene coordenadas de píxel (0, 0). El píxel de la esquina inferior derecha del mapa tiene las coordenadas de píxel (ancho-1, alto-1), o como en las ecuaciones de la sección anterior, (tileSize * 2^zoom–1, tileSize * 2^zoom–1). Por ejemplo, al usar 512 mosaicos cuadrados en el nivel 2, las coordenadas de píxeles oscilan entre (0, 0) y (2047, 2047), de la siguiente manera:

Mapa que muestra dimensiones de píxeles

Dada la latitud y la longitud en grados, y el nivel de detalle, las coordenadas XY de píxel se calculan de la siguiente manera:

var sinLatitude = Math.sin(latitude * Math.PI/180);

var pixelX = ((longitude + 180) / 360) * tileSize * Math.pow(2, zoom);

var pixelY = (0.5 – Math.log((1 + sinLatitude) / (1 – sinLatitude)) / (4 * Math.PI)) * tileSize * Math.pow(2, zoom);

Se supone que los valores de latitud y longitud están en el datum WGS 84. Aunque Azure Maps usa una proyección esférica, es importante convertir todas las coordenadas geográficas en un dato común. WGS 84 es el valor de referencia seleccionado. Se supone que el valor de longitud va desde -180 grados a +180 grados, y el valor de latitud debe recortarse hasta oscilar entre -85,05112878 y 85,05112878. La adhesión a estos valores evita una singularidad en los polos y garantiza que el mapa proyectado sea una forma cuadrada.

Coordenadas de mosaicos

Para optimizar el rendimiento de la recuperación y visualización del mapa, el mapa representado se corta en mosaicos. El número de píxeles y el número de iconos difieren en cada nivel de zoom:

var numberOfTilesWide = Math.pow(2, zoom);

var numberOfTilesHigh = numberOfTilesWide;

Cada mosaico recibe coordenadas XY que van desde (0, 0) en la parte superior izquierda hasta (2^zoom–1, 2^zoom–1) en la parte inferior derecha. Por ejemplo, en el nivel de zoom 3, las coordenadas de mosaico oscilan entre (0, 0) y (7, 7) como se indica a continuación:

Mapa de coordenadas de mosaico

Dado un par de coordenadas XY de píxeles, puede determinar fácilmente las coordenadas XY del mosaico que contiene ese píxel:

var tileX = Math.floor(pixelX / tileSize);

var tileY = Math.floor(pixelY / tileSize);

El nivel de zoom determina los mosaico. Las coordenadas x e y corresponden a la posición del icono en la cuadrícula para ese nivel de zoom.

Al determinar el nivel de zoom que se va a usar, recuerde que cada ubicación está en una posición fija en su mosaico. Como resultado, el número de mosaicos necesarios para mostrar una extensión determinada de territorio depende de la ubicación específica de la cuadrícula de zoom en el mapa mundial. Por ejemplo, si hay dos puntos a 900 metros de distancia, podría requerir solo tres mosaicos para mostrar una ruta entre ellos en el nivel de zoom 17. Sin embargo, si el punto occidental está a la derecha de su mosaico y el punto oriental a la izquierda, puede ocupar cuatro mosaicos:

Escala de demostración de zoom

Una vez determinado el nivel de zoom, se pueden calcular los valores x e y. El icono de la parte superior izquierda de cada cuadrícula de zoom es x=0, y=0; el icono de la parte inferior derecha está en x=2^zoom-1, y=2^zoom-1.

Esta es la cuadrícula de zoom para el nivel de zoom 1:

Cuadrícula de zoom para el nivel de zoom 1

Índices de quadkeys

Algunas plataformas de mapas usan una convención de nomenclatura de indexación de quadkey que combina las coordenadas ZY de un mosaico en una cadena de una sola dimensión llamada "claves de quadtree" o simplemente "quadkeys". Cada quadkey identifica de forma inequívoca un único mosaico con un nivel de detalle determinado y se puede usar como clave en los índices comunes de árbol B de la base de datos. Los SDK de Azure Maps admiten la superposición de capas de mosaico que usan quadkey la convención de nomenclatura, además de otras convenciones de nomenclatura, tal como se documenta en el documento Agregar una capa de mosaico .

Nota:

La quadkeys convención de nomenclatura solo funciona para los niveles de zoom de uno o más. El SDK de Azure Maps admite el nivel de zoom 0, que es un icono de mapa único para todo el mundo.

Para convertir las coordenadas de mosaico en quadkey, los bits de las coordenadas Y y X se intercalan y el resultado se interpreta como un número en base 4 (manteniendo los ceros iniciales) y se convierte en una cadena. Por ejemplo, dadas las coordenadas XY (3, 5) de un mosaico de nivel 3, el valor de quadkey se calcula de la siguiente manera:

tileX = 3 = 011 (base 2)

tileY = 5 = 101 (base 2)

quadkey = 100111 (base 2) = 213 (base 4) = "213"

Qquadkeys tienen varias propiedades interesantes. En primer lugar, la longitud de un quadkey (el número de dígitos) es igual al nivel de zoom del icono correspondiente. En segundo lugar, el quadkey de cualquier icono comienza con el quadkey de su icono primario (el icono contenedor en el nivel anterior). Como se muestra en el ejemplo siguiente, el icono 2 es el elemento primario de los iconos de 20 a 23:

Pirámide de mosaicos Quadkey

Por último, los quadkeys proporcionan una clave de índice unidimensional que normalmente respeta la proximidad de los mosaicos en el espacio XY. En otras palabras, normalmente, dos mosaicos que tengan coordenadas XY cercanas tendrán quadkeys que estarán relativamente cerca. Esto es importante para optimizar el rendimiento de la base de datos, ya que los iconos vecinos a menudo se solicitan en grupos y es conveniente mantener esos iconos en los mismos bloques de disco, con el fin de minimizar el número de lecturas de disco.

Código fuente de la matemática de los mosaicos

En el código de ejemplo siguiente se muestra cómo implementar las funciones descritas en este documento. Estas funciones se pueden traducir fácilmente a otros lenguajes de programación según sea necesario.

C#
Mecanografiado

using System;
using System.Text;

namespace AzureMaps
{
    /// <summary>
    /// Tile System math for the Spherical Mercator projection coordinate system (EPSG:3857)
    /// </summary>
    public static class TileMath
    {
        //Earth radius in meters.
        private const double EarthRadius = 6378137;

        private const double MinLatitude = -85.05112878;
        private const double MaxLatitude = 85.05112878;
        private const double MinLongitude = -180;
        private const double MaxLongitude = 180;

        /// <summary>
        /// Clips a number to the specified minimum and maximum values.
        /// </summary>
        /// <param name="n">The number to clip.</param>
        /// <param name="minValue">Minimum allowable value.</param>
        /// <param name="maxValue">Maximum allowable value.</param>
        /// <returns>The clipped value.</returns>
        private static double Clip(double n, double minValue, double maxValue)
        {
            return Math.Min(Math.Max(n, minValue), maxValue);
        }

        /// <summary>
        /// Calculates width and height of the map in pixels at a specific zoom level from -180 degrees to 180 degrees.
        /// </summary>
        /// <param name="zoom">Zoom Level to calculate width at</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param>
        /// <returns>Width and height of the map in pixels</returns>
        public static double MapSize(double zoom, int tileSize)
        {
            return Math.Ceiling(tileSize * Math.Pow(2, zoom));
        }

        /// <summary>
        /// Calculates the Ground resolution at a specific degree of latitude in meters per pixel.
        /// </summary>
        /// <param name="latitude">Degree of latitude to calculate resolution at</param>
        /// <param name="zoom">Zoom level to calculate resolution at</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param>
        /// <returns>Ground resolution in meters per pixels</returns>
        public static double GroundResolution(double latitude, double zoom, int tileSize)
        {
            latitude = Clip(latitude, MinLatitude, MaxLatitude);
            return Math.Cos(latitude * Math.PI / 180) * 2 * Math.PI * EarthRadius / MapSize(zoom, tileSize);
        }

        /// <summary>
        /// Determines the map scale at a specified latitude, level of detail, and screen resolution.
        /// </summary>
        /// <param name="latitude">Latitude (in degrees) at which to measure the map scale.</param>
        /// <param name="zoom">Level of detail, from 1 (lowest detail) to 23 (highest detail).</param>
        /// <param name="screenDpi">Resolution of the screen, in dots per inch.</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param>
        /// <returns>The map scale, expressed as the denominator N of the ratio 1 : N.</returns>
        public static double MapScale(double latitude, double zoom, int screenDpi, int tileSize)
        {
            return GroundResolution(latitude, zoom, tileSize) * screenDpi / 0.0254;
        }

        /// <summary>
        /// Global Converts a Pixel coordinate into a geospatial coordinate at a specified zoom level. 
        /// Global Pixel coordinates are relative to the top left corner of the map (90, -180)
        /// </summary>
        /// <param name="pixel">Pixel coordinates in the format of [x, y].</param>  
        /// <param name="zoom">Zoom level</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param>
        /// <returns>A position value in the format [longitude, latitude].</returns>
        public static double[] GlobalPixelToPosition(double[] pixel, double zoom, int tileSize)
        {
            var mapSize = MapSize(zoom, tileSize);

            var x = (Clip(pixel[0], 0, mapSize - 1) / mapSize) - 0.5;
            var y = 0.5 - (Clip(pixel[1], 0, mapSize - 1) / mapSize);

            return new double[] {
                360 * x,    //Longitude
                90 - 360 * Math.Atan(Math.Exp(-y * 2 * Math.PI)) / Math.PI  //Latitude
            };
        }

        /// <summary>
        /// Converts a point from latitude/longitude WGS-84 coordinates (in degrees) into pixel XY coordinates at a specified level of detail.
        /// </summary>
        /// <param name="position">Position coordinate in the format [longitude, latitude]</param>
        /// <param name="zoom">Zoom level.</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param> 
        /// <returns>A global pixel coordinate.</returns>
        public static double[] PositionToGlobalPixel(double[] position, int zoom, int tileSize)
        {
            var latitude = Clip(position[1], MinLatitude, MaxLatitude);
            var longitude = Clip(position[0], MinLongitude, MaxLongitude);

            var x = (longitude + 180) / 360;
            var sinLatitude = Math.Sin(latitude * Math.PI / 180);
            var y = 0.5 - Math.Log((1 + sinLatitude) / (1 - sinLatitude)) / (4 * Math.PI);

            var mapSize = MapSize(zoom, tileSize);

            return new double[] {
                 Clip(x * mapSize + 0.5, 0, mapSize - 1),
                 Clip(y * mapSize + 0.5, 0, mapSize - 1)
            };
        }

        /// <summary>
        /// Converts pixel XY coordinates into tile XY coordinates of the tile containing the specified pixel.
        /// </summary>
        /// <param name="pixel">Pixel coordinates in the format of [x, y].</param>  
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param>
        /// <param name="tileX">Output parameter receiving the tile X coordinate.</param>
        /// <param name="tileY">Output parameter receiving the tile Y coordinate.</param>
        public static void GlobalPixelToTileXY(double[] pixel, int tileSize, out int tileX, out int tileY)
        {
            tileX = (int)(pixel[0] / tileSize);
            tileY = (int)(pixel[1] / tileSize);
        }

        /// <summary>
        /// Performs a scale transform on a global pixel value from one zoom level to another.
        /// </summary>
        /// <param name="pixel">Pixel coordinates in the format of [x, y].</param>  
        /// <param name="oldZoom">The zoom level in which the input global pixel value is from.</param>  
        /// <returns>A scale pixel coordinate.</returns>
        public static double[] ScaleGlobalPixel(double[] pixel, double oldZoom, double newZoom)
        {
            var scale = Math.Pow(2, oldZoom - newZoom);

            return new double[] { pixel[0] * scale, pixel[1] * scale };
        }

        /// <summary>
        /// Performs a scale transform on a set of global pixel values from one zoom level to another.
        /// </summary>
        /// <param name="pixels">A set of global pixel value from the old zoom level. Points are in the format [x,y].</param>
        /// <param name="oldZoom">The zoom level in which the input global pixel values is from.</param>
        /// <param name="newZoom">The new zoom level in which the output global pixel values should be aligned with.</param>
        /// <returns>A set of global pixel values that has been scaled for the new zoom level.</returns>
        public static double[][] ScaleGlobalPixels(double[][] pixels, double oldZoom, double newZoom)
        {
            var scale = Math.Pow(2, oldZoom - newZoom);

            var output = new System.Collections.Generic.List<double[]>();
            foreach (var p in pixels)
            {
                output.Add(new double[] { p[0] * scale, p[1] * scale });
            }

            return output.ToArray();
        }

        /// <summary>
        /// Converts tile XY coordinates into a global pixel XY coordinates of the upper-left pixel of the specified tile.
        /// </summary>
        /// <param name="tileX">Tile X coordinate.</param>
        /// <param name="tileY">Tile Y coordinate.</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param>
        /// <param name="pixelX">Output parameter receiving the X coordinate of the point, in pixels.</param>  
        /// <param name="pixelY">Output parameter receiving the Y coordinate of the point, in pixels.</param>  
        public static double[] TileXYToGlobalPixel(int tileX, int tileY, int tileSize)
        {
            return new double[] { tileX * tileSize, tileY * tileSize };
        }

        /// <summary>
        /// Converts tile XY coordinates into a quadkey at a specified level of detail.
        /// </summary>
        /// <param name="tileX">Tile X coordinate.</param>
        /// <param name="tileY">Tile Y coordinate.</param>
        /// <param name="zoom">Zoom level</param>
        /// <returns>A string containing the quadkey.</returns>
        public static string TileXYToQuadKey(int tileX, int tileY, int zoom)
        {
            var quadKey = new StringBuilder();
            for (int i = zoom; i > 0; i--)
            {
                char digit = '0';
                int mask = 1 << (i - 1);
                if ((tileX & mask) != 0)
                {
                    digit++;
                }
                if ((tileY & mask) != 0)
                {
                    digit++;
                    digit++;
                }
                quadKey.Append(digit);
            }
            return quadKey.ToString();
        }

        /// <summary>
        /// Converts a quadkey into tile XY coordinates.
        /// </summary>
        /// <param name="quadKey">Quadkey of the tile.</param>
        /// <param name="tileX">Output parameter receiving the tile X coordinate.</param>
        /// <param name="tileY">Output parameter receiving the tile Y coordinate.</param>
        /// <param name="zoom">Output parameter receiving the zoom level.</param>
        public static void QuadKeyToTileXY(string quadKey, out int tileX, out int tileY, out int zoom)
        {
            tileX = tileY = 0;
            zoom = quadKey.Length;
            for (int i = zoom; i > 0; i--)
            {
                int mask = 1 << (i - 1);
                switch (quadKey[zoom - i])
                {
                    case '0':
                        break;

                    case '1':
                        tileX |= mask;
                        break;

                    case '2':
                        tileY |= mask;
                        break;

                    case '3':
                        tileX |= mask;
                        tileY |= mask;
                        break;

                    default:
                        throw new ArgumentException("Invalid QuadKey digit sequence.");
                }
            }
        }

        /// <summary>
        /// Calculates the XY tile coordinates that a coordinate falls into for a specific zoom level.
        /// </summary>
        /// <param name="position">Position coordinate in the format [longitude, latitude]</param>
        /// <param name="zoom">Zoom level</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param>
        /// <param name="tileX">Output parameter receiving the tile X position.</param>
        /// <param name="tileY">Output parameter receiving the tile Y position.</param>
        public static void PositionToTileXY(double[] position, int zoom, int tileSize, out int tileX, out int tileY)
        {
            var latitude = Clip(position[1], MinLatitude, MaxLatitude);
            var longitude = Clip(position[0], MinLongitude, MaxLongitude);

            var x = (longitude + 180) / 360;
            var sinLatitude = Math.Sin(latitude * Math.PI / 180);
            var y = 0.5 - Math.Log((1 + sinLatitude) / (1 - sinLatitude)) / (4 * Math.PI);

            //tileSize needed in calculations as in rare cases the multiplying/rounding/dividing can make the difference of a pixel which can result in a completely different tile. 
            var mapSize = MapSize(zoom, tileSize);
            tileX = (int)Math.Floor(Clip(x * mapSize + 0.5, 0, mapSize - 1) / tileSize);
            tileY = (int)Math.Floor(Clip(y * mapSize + 0.5, 0, mapSize - 1) / tileSize);
        }

        /// <summary>
        /// Calculates the tile quadkey strings that are within a specified viewport.
        /// </summary>
        /// <param name="position">Position coordinate in the format [longitude, latitude]</param>
        /// <param name="zoom">Zoom level</param>
        /// <param name="width">The width of the map viewport in pixels.</param>
        /// <param name="height">The height of the map viewport in pixels.</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param>
        /// <returns>A list of quadkey strings that are within the specified viewport.</returns>
        public static string[] GetQuadkeysInView(double[] position, int zoom, int width, int height, int tileSize)
        {
            var p = PositionToGlobalPixel(position, zoom, tileSize);

            var top = p[1] - height * 0.5;
            var left = p[0] - width * 0.5;

            var bottom = p[1] + height * 0.5;
            var right = p[0] + width * 0.5;

            var tl = GlobalPixelToPosition(new double[] { left, top }, zoom, tileSize);
            var br = GlobalPixelToPosition(new double[] { right, bottom }, zoom, tileSize);

            //Bounding box in the format: [west, south, east, north];
            var bounds = new double[] { tl[0], br[1], br[0], tl[1] };

            return GetQuadkeysInBoundingBox(bounds, zoom, tileSize);
        }

        /// <summary>
        /// Calculates the tile quadkey strings that are within a bounding box at a specific zoom level.
        /// </summary>
        /// <param name="bounds">A bounding box defined as an array of numbers in the format of [west, south, east, north].</param>
        /// <param name="zoom">Zoom level to calculate tiles for.</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param>
        /// <returns>A list of quadkey strings.</returns>
        public static string[] GetQuadkeysInBoundingBox(double[] bounds, int zoom, int tileSize)
        {
            var keys = new System.Collections.Generic.List<string>();

            if (bounds != null && bounds.Length >= 4)
            {
                PositionToTileXY(new double[] { bounds[3], bounds[0] }, zoom, tileSize, out int tlX, out int tlY);
                PositionToTileXY(new double[] { bounds[1], bounds[2] }, zoom, tileSize, out int brX, out int brY);

                for (int x = tlX; x <= brX; x++)
                {
                    for (int y = tlY; y <= brY; y++)
                    {
                        keys.Add(TileXYToQuadKey(x, y, zoom));
                    }
                }
            }

            return keys.ToArray();
        }

        /// <summary>
        /// Calculates the bounding box of a tile.
        /// </summary>
        /// <param name="tileX">Tile X coordinate</param>
        /// <param name="tileY">Tile Y coordinate</param>
        /// <param name="zoom">Zoom level</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid.</param>
        /// <returns>A bounding box of the tile defined as an array of numbers in the format of [west, south, east, north].</returns>
        public static double[] TileXYToBoundingBox(int tileX, int tileY, double zoom, int tileSize)
        {
            //Top left corner pixel coordinates
            var x1 = (double)(tileX * tileSize);
            var y1 = (double)(tileY * tileSize);

            //Bottom right corner pixel coordinates
            var x2 = (double)(x1 + tileSize);
            var y2 = (double)(y1 + tileSize);

            var nw = GlobalPixelToPosition(new double[] { x1, y1 }, zoom, tileSize);
            var se = GlobalPixelToPosition(new double[] { x2, y2 }, zoom, tileSize);

            return new double[] { nw[0], se[1], se[0], nw[1] };
        }

        /// <summary>
        /// Calculates the best map view (center, zoom) for a bounding box on a map.
        /// </summary>
        /// <param name="bounds">A bounding box defined as an array of numbers in the format of [west, south, east, north].</param>
        /// <param name="mapWidth">Map width in pixels.</param>
        /// <param name="mapHeight">Map height in pixels.</param>
        /// <param name="latitude">Output parameter receiving the center latitude coordinate.</param>
        /// <param name="longitude">Output parameter receiving the center longitude coordinate.</param>
        /// <param name="zoom">Output parameter receiving the zoom level</param>
        /// <param name="padding">Width in pixels to use to create a buffer around the map. This is to keep markers from being cut off on the edge. Default: 0</param>
        /// <param name="tileSize">The size of the tiles in the tile pyramid. Default: 512</param>
        /// <param name="maxZoom">Optional maximum zoom level to return. Useful when the bounding box represents a very small area. Default: 24</param>
        /// <param name="allowFloatZoom">Specifies if the returned zoom level should be a float or rounded down to an whole integer zoom level. Default: true</param>
        public static void BestMapView(BoundingBox bounds, double mapWidth, double mapHeight, out double centerLat, out double centerLon, out double zoom, int padding = 0, int tileSize = 512, double maxZoom = 24, bool allowFloatZoom = true)
        {
        	centerLat = 0;
        	centerLon = 0;
        	zoom = 0;
        
        	if (bounds != null && mapWidth > 0 && mapHeight > 0)
        	{
        		//Ensure padding is valid.
        		padding = Math.Abs(padding);
        
        		//Ensure max zoom is within valid range.
        		maxZoom = Clip(maxZoom, 0, 24);
        
        		//Do pixel calculations at zoom level 24 as that will provide a high level of visual accuracy.
        		int pixelZoom = 24;
        
        		//Calculate mercator pixel coordinate at zoom level 24.
        		var wnPixel = PositionToGlobalPixel(new double[] { bounds[0], bounds[3] }, pixelZoom, tileSize);
        		var esPixel = PositionToGlobalPixel(new double[] { bounds[2], bounds[1] }, pixelZoom, tileSize);
        
        		//Calculate the pixel distance between pixels for each axis.
        		double dx = esPixel[0] - wnPixel[0];
        		double dy = esPixel[1] - wnPixel[1];
        
        		//Calculate the average pixel positions to get the visual center.
        		double xAvg = (esPixel[0] + wnPixel[0]) / 2;
        		double yAvg = (esPixel[1] + wnPixel[1]) / 2;
        
        		//Determine if the bounding box crosses the antimeridian. (West pixel will be greater than East pixel).
        		if (wnPixel[0] > esPixel[0])
        		{
        			double mapSize = MapSize(24, tileSize);
        
        			//We are interested in the opposite area of the map. Calculate the opposite area and visual center.
        			dx = mapSize - Math.Abs(dx);
        
        			//Offset the visual center by half the global map width at zoom 24 on the x axis.
        			xAvg += mapSize / 2;
        		}
        
        		//Convert visual center pixel from zoom 24 to lngLat.
        		center = GlobalPixelToPosition(new Pixel(xAvg, yAvg), pixelZoom, tileSize);
        
        		//Calculate scale of screen pixels per unit on the Web Mercator plane.
        		double scaleX = (mapWidth - padding * 2) / Math.Abs(dx) * Math.Pow(2, pixelZoom);
        		double scaleY = (mapHeight - padding * 2) / Math.Abs(dy) * Math.Pow(2, pixelZoom);
        
        		//Calculate zoom levels based on the x/y scales. Choose the most zoomed out value.
        		zoom = Math.Max(0, Math.Min(maxZoom, Math.Log2(Math.Abs(Math.Min(scaleX, scaleY)))));
        
        		//Round down zoom level if float values are not desired.
        		if (!allowFloatZoom)
        		{
        			zoom = Math.Floor(zoom);
        		}
        	}
        
        	return new CameraOptions
        	{
        		Center = center,
        		Zoom = zoom
        	};
        }
    }
}

module AzureMaps {

    /** Tile System math for the Spherical Mercator projection coordinate system (EPSG:3857) */
    export class TileMath {
        //Earth radius in meters.
        private static EarthRadius = 6378137;

        private static MinLatitude = -85.05112878;
        private static MaxLatitude = 85.05112878;
        private static MinLongitude = -180;
        private static MaxLongitude = 180;

        /**
         * Clips a number to the specified minimum and maximum values.
         * @param n The number to clip.
         * @param minValue Minimum allowable value.
         * @param maxValue Maximum allowable value.
         * @returns The clipped value.
         */
        private static Clip(n: number, minValue: number, maxValue: number): number {
            return Math.min(Math.max(n, minValue), maxValue);
        }

        /**
         * Calculates width and height of the map in pixels at a specific zoom level from -180 degrees to 180 degrees.
         * @param zoom Zoom Level to calculate width at.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns Width and height of the map in pixels.
         */
        public static MapSize(zoom: number, tileSize: number): number {
            return Math.ceil(tileSize * Math.pow(2, zoom));
        }

        /**
         * Calculates the Ground resolution at a specific degree of latitude in the meters per pixel.
         * @param latitude Degree of latitude to calculate resolution at.
         * @param zoom Zoom level.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns Ground resolution in meters per pixels.
         */
        public static GroundResolution(latitude: number, zoom: number, tileSize: number): number {
            latitude = this.Clip(latitude, this.MinLatitude, this.MaxLatitude);
            return Math.cos(latitude * Math.PI / 180) * 2 * Math.PI * this.EarthRadius / this.MapSize(zoom, tileSize);
        }

        /**
         * Determines the map scale at a specified latitude, level of detail, and screen resolution.
         * @param latitude Latitude (in degrees) at which to measure the map scale.
         * @param zoom Zoom level.
         * @param screenDpi Resolution of the screen, in dots per inch.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns The map scale, expressed as the denominator N of the ratio 1 : N.
         */
        public static MapScale(latitude: number, zoom: number, screenDpi: number, tileSize: number): number {
            return this.GroundResolution(latitude, zoom, tileSize) * screenDpi / 0.0254;
        }

        /**
         * Global Converts a Pixel coordinate into a geospatial coordinate at a specified zoom level.
         * Global Pixel coordinates are relative to the top left corner of the map (90, -180).
         * @param pixel Pixel coordinates in the format of [x, y].
         * @param zoom Zoom level.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns A position value in the format [longitude, latitude].
         */
        public static GlobalPixelToPosition(pixel: number[], zoom: number, tileSize: number): number[] {
            var mapSize = this.MapSize(zoom, tileSize);

            var x = (this.Clip(pixel[0], 0, mapSize - 1) / mapSize) - 0.5;
            var y = 0.5 - (this.Clip(pixel[1], 0, mapSize - 1) / mapSize);

            return [
                360 * x,    //Longitude
                90 - 360 * Math.atan(Math.exp(-y * 2 * Math.PI)) / Math.PI  //Latitude
            ];
        }

        /**
         * Converts a point from latitude/longitude WGS-84 coordinates (in degrees) into pixel XY coordinates at a specified level of detail.
         * @param position Position coordinate in the format [longitude, latitude].
         * @param zoom Zoom level.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns A pixel coordinate 
         */
        public static PositionToGlobalPixel(position: number[], zoom: number, tileSize: number): number[] {
            var latitude = this.Clip(position[1], this.MinLatitude, this.MaxLatitude);
            var longitude = this.Clip(position[0], this.MinLongitude, this.MaxLongitude);

            var x = (longitude + 180) / 360;
            var sinLatitude = Math.sin(latitude * Math.PI / 180);
            var y = 0.5 - Math.log((1 + sinLatitude) / (1 - sinLatitude)) / (4 * Math.PI);

            var mapSize = this.MapSize(zoom, tileSize);

            return [
                this.Clip(x * mapSize + 0.5, 0, mapSize - 1),
                this.Clip(y * mapSize + 0.5, 0, mapSize - 1)
            ];
        }

        /**
         * Converts pixel XY coordinates into tile XY coordinates of the tile containing the specified pixel.
         * @param pixel Pixel coordinates in the format of [x, y].
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns Tile XY coordinates.
         */
        public static GlobalPixelToTileXY(pixel: number[], tileSize: number): { tileX: number, tileY: number } {
            return {
                tileX: Math.round(pixel[0] / tileSize),
                tileY: Math.round(pixel[1] / tileSize)
            };
        }

        /**
         * Performs a scale transform on a global pixel value from one zoom level to another.
         * @param pixel Pixel coordinates in the format of [x, y].
         * @param oldZoom The zoom level in which the input global pixel value is from.
         * @param newZoom The new zoom level in which the output global pixel value should be aligned with.
         */
        public static ScaleGlobalPixel(pixel: number[], oldZoom: number, newZoom: number): number[] {
            var scale = Math.pow(2, oldZoom - newZoom);

            return [pixel[0] * scale, pixel[1] * scale];
        }

        /// <summary>
        /// Performs a scale transform on a set of global pixel values from one zoom level to another.
        /// </summary>
        /// <param name="points">A set of global pixel value from the old zoom level. Points are in the format [x,y].</param>
        /// <param name="oldZoom">The zoom level in which the input global pixel values is from.</param>
        /// <param name="newZoom">The new zoom level in which the output global pixel values should be aligned with.</param>
        /// <returns>A set of global pixel values that has been scaled for the new zoom level.</returns>
        public static ScaleGlobalPixels(pixels: number[][], oldZoom: number, newZoom: number): number[][] {
            var scale = Math.pow(2, oldZoom - newZoom);

            var output: number[][] = [];
            for (var i = 0, len = pixels.length; i < len; i++) {
                output.push([pixels[i][0] * scale, pixels[i][1] * scale]);
            }

            return output;
        }

        /**
         * Converts tile XY coordinates into a global pixel XY coordinates of the upper-left pixel of the specified tile.
         * @param tileX Tile X coordinate.
         * @param tileY Tile Y coordinate.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns Pixel coordinates in the format of [x, y].
         */
        public static TileXYToGlobalPixel(tileX, tileY, tileSize): number[] {
            return [tileX * tileSize, tileY * tileSize];
        }

        /**
         * Converts tile XY coordinates into a quadkey at a specified level of detail.
         * @param tileX Tile X coordinate.
         * @param tileY Tile Y coordinate.
         * @param zoom Zoom level.
         * @returns A string containing the quadkey.
         */
        public static TileXYToQuadKey(tileX: number, tileY: number, zoom: number): string {
            var quadKey: number[] = [];
            for (var i = zoom; i > 0; i--) {
                var digit = 0;
                var mask = 1 << (i - 1);

                if ((tileX & mask) != 0) {
                    digit++;
                }

                if ((tileY & mask) != 0) {
                    digit += 2
                }

                quadKey.push(digit);
            }
            return quadKey.join('');
        }

        /**
         * Converts a quadkey into tile XY coordinates.
         * @param quadKey Quadkey of the tile.
         * @returns Tile XY coordinates and zoom level for the specified quadkey.
         */
        public static QuadKeyToTileXY(quadKey: string): { tileX: number, tileY: number, zoom: number } {
            var tileX = 0;
            var tileY = 0;
            var zoom = quadKey.length;

            for (var i = zoom; i > 0; i--) {
                var mask = 1 << (i - 1);
                switch (quadKey[zoom - i]) {
                    case '0':
                        break;

                    case '1':
                        tileX |= mask;
                        break;

                    case '2':
                        tileY |= mask;
                        break;

                    case '3':
                        tileX |= mask;
                        tileY |= mask;
                        break;

                    default:
                        throw "Invalid QuadKey digit sequence.";
                }
            }

            return {
                tileX: tileX,
                tileY: tileY,
                zoom: zoom
            };
        }

        /**
         * Calculates the XY tile coordinates that a coordinate falls into for a specific zoom level.
         * @param position Position coordinate in the format [longitude, latitude].
         * @param zoom Zoom level.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns Tile XY coordinates.
         */
        public static PositionToTileXY(position: number[], zoom: number, tileSize: number): { tileX: number, tileY: number } {
            var latitude = this.Clip(position[1], this.MinLatitude, this.MaxLatitude);
            var longitude = this.Clip(position[0], this.MinLongitude, this.MaxLongitude);

            var x = (longitude + 180) / 360;
            var sinLatitude = Math.sin(latitude * Math.PI / 180);
            var y = 0.5 - Math.log((1 + sinLatitude) / (1 - sinLatitude)) / (4 * Math.PI);

            //tileSize needed in calculations as in rare cases the multiplying/rounding/dividing can make the difference of a pixel which can result in a completely different tile. 
            var mapSize = this.MapSize(zoom, tileSize);

            return {
                tileX: Math.floor(this.Clip(x * mapSize + 0.5, 0, mapSize - 1) / tileSize),
                tileY: Math.floor(this.Clip(y * mapSize + 0.5, 0, mapSize - 1) / tileSize)
            };
        }

        /**
         * Calculates the tile quadkey strings that are within a specified viewport.
         * @param position Position coordinate in the format [longitude, latitude].
         * @param zoom Zoom level.
         * @param width The width of the map viewport in pixels.
         * @param height The height of the map viewport in pixels.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns A list of quadkey strings that are within the specified viewport.
         */
        public static GetQuadkeysInView(position: number[], zoom: number, width: number, height: number, tileSize: number): string[] {
            var p = this.PositionToGlobalPixel(position, zoom, tileSize);

            var top = p[1] - height * 0.5;
            var left = p[0] - width * 0.5;

            var bottom = p[1] + height * 0.5;
            var right = p[0] + width * 0.5;

            var tl = this.GlobalPixelToPosition([left, top], zoom, tileSize);
            var br = this.GlobalPixelToPosition([right, bottom], zoom, tileSize);

            //Bounding box in the format: [west, south, east, north];
            var bounds = [tl[0], br[1], br[0], tl[1]];

            return this.GetQuadkeysInBoundingBox(bounds, zoom, tileSize);
        }

        /**
         * Calculates the tile quadkey strings that are within a bounding box at a specific zoom level.
         * @param bounds A bounding box defined as an array of numbers in the format of [west, south, east, north].
         * @param zoom Zoom level to calculate tiles for.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns A list of quadkey strings.
         */
        public static GetQuadkeysInBoundingBox(bounds: number[], zoom: number, tileSize: number): string[] {
            var keys: string[] = [];

            if (bounds != null && bounds.length >= 4) {
                var tl = this.PositionToTileXY([bounds[0], bounds[3]], zoom, tileSize);
                var br = this.PositionToTileXY([bounds[2], bounds[1]], zoom, tileSize);

                for (var x = tl[0]; x <= br[0]; x++) {
                    for (var y = tl[1]; y <= br[1]; y++) {
                        keys.push(this.TileXYToQuadKey(x, y, zoom));
                    }
                }
            }

            return keys;
        }

        /**
         * Calculates the bounding box of a tile.
         * @param tileX Tile X coordinate.
         * @param tileY Tile Y coordinate.
         * @param zoom Zoom level.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @returns A bounding box of the tile defined as an array of numbers in the format of [west, south, east, north].
         */
        public static TileXYToBoundingBox(tileX: number, tileY: number, zoom: number, tileSize: number): number[] {
            //Top left corner pixel coordinates
            var x1 = tileX * tileSize;
            var y1 = tileY * tileSize;

            //Bottom right corner pixel coordinates
            var x2 = x1 + tileSize;
            var y2 = y1 + tileSize;

            var nw = this.GlobalPixelToPosition([x1, y1], zoom, tileSize);
            var se = this.GlobalPixelToPosition([x2, y2], zoom, tileSize);

            return [nw[0], se[1], se[0], nw[1]];
        }

        /**
         * Calculates the best map view (center, zoom) for a bounding box on a map.
         * @param bounds A bounding box defined as an array of numbers in the format of [west, south, east, north]. 
         * @param mapWidth Map width in pixels.
         * @param mapHeight Map height in pixels.
         * @param padding Width in pixels to use to create a buffer around the map. This is to keep markers from being cut off on the edge.
         * @param tileSize The size of the tiles in the tile pyramid.
         * @param maxZoom Optional maximum zoom level to return. Useful when the bounding box represents a very small area.
         * @param allowFloatZoom Specifies if the returned zoom level should be a float or rounded down to an whole integer zoom level. 
         * @returns The center and zoom level to best position the map view over the provided bounding box.
         */
        public static BestMapView(bounds: number, mapWidth: number, mapHeight: number, padding: number = 0, tileSize: number = 512, maxZoom: number = 24, allowFloatZoom: boolean = true): { center: number[], zoom: number } {
        	//Ensure valid bounds and map dimensions are provided.
        	if (bounds == null || bounds.length < 4 || !mapWidth || !mapHeight || mapWidth <= 0 || mapHeight <= 0) {
        		return {
        			center: [0, 0],
        			zoom: 0
        		};
        	}
        
        	//Ensure padding is valid.
        	padding = Math.abs(padding || 0);
        	
        	//Ensure max zoom is within valid range.
        	maxZoom = this.Clip(maxZoom, 0, 24);
        	
        	//Do pixel calculations at zoom level 24 as that will provide a high level of visual accuracy.
        	const pixelZoom = 24;
        
        	//Calculate mercator pixel coordinate at zoom level 24.
        	const wnPixel = this.PositionToGlobalPixel([bounds[0], bounds[3]], pixelZoom, tileSize);
        	const esPixel = this.PositionToGlobalPixel([bounds[2], bounds[1]], pixelZoom, tileSize);
        	
        	//Calculate the pixel distance between pixels for each axis.
        	let dx = esPixel[0] - wnPixel[0];
        	const dy = esPixel[1] - wnPixel[1];
        	
        	//Calculate the average pixel positions to get the visual center.
        	let xAvg = (esPixel[0] + wnPixel[0]) / 2;
        	const yAvg = (esPixel[1] + wnPixel[1]) / 2;
        		
        	//Determine if the bounding box crosses the antimeridian. (West pixel will be greater than East pixel).
        	if(wnPixel[0] > esPixel[0]) {
        		const mapSize = this.MapSize(24, tileSize);
		
        		//We are interested in the opposite area of the map. Calculate the opposite area and visual center.
        		dx = mapSize - Math.abs(dx);
        		
        		//Offset the visual center by half the global map width at zoom 24 on the x axis.
        		xAvg += mapSize / 2;		
        	}
        
        	//Convert visual center pixel from zoom 24 to lngLat.
        	const centerLngLat = this.GlobalPixelToPosition([xAvg, yAvg], pixelZoom, tileSize);
        
        	//Calculate scale of screen pixels per unit on the Web Mercator plane.
        	const scaleX = (mapWidth - padding * 2) / Math.abs(dx) * Math.pow(2, pixelZoom);
        	const scaleY = (mapHeight - padding * 2) / Math.abs(dy) * Math.pow(2, pixelZoom);
        
        	//Calculate zoom levels based on the x/y scales. Choose the most zoomed out value.
        	let zoom = Math.max(0, Math.min(maxZoom, Math.log2(Math.abs(Math.min(scaleX, scaleY)))));
        
        	//Round down zoom level if float values are not desired.
        	if(!allowFloatZoom) {
        		zoom = Math.floor(zoom);
        	}
        
        	return {
        		center: centerLngLat,
        		zoom
        	};
        }
    }
}

Nota:

Los controles de mapa interactivos del SDK de Azure Maps tienen funciones auxiliares para convertir entre posiciones geoespaciales y píxeles de ventanilla.