Níveis de zoom e grade lado a lado

2025-06-22

O Azure Mapas usa o sistema de coordenadas de projeção esférica de Mercator (EPSG:3857). Uma projeção é o modelo matemático usado para transformar o globo esférico em um mapa plano. A projeção esférica de Mercator estica o mapa nos pólos para criar um mapa quadrado. Essa projeção distorce significativamente a escala e a área do mapa, mas tem duas propriedades importantes que superam essa distorção:

É uma projeção conforme, o que significa que preserva a forma de objetos relativamente pequenos. Preservar a forma de pequenos objetos é especialmente importante ao mostrar imagens aéreas. Por exemplo, queremos evitar distorcer a forma dos edifícios. Edifícios quadrados devem parecer quadrados, não retangulares.
É uma projeção cilíndrica. Norte e sul estão sempre para cima e para baixo, e oeste e leste estão sempre para a esquerda e para a direita.

Para otimizar o desempenho da recuperação e exibição do mapa, o mapa é dividido em blocos quadrados. Os SDKs do Azure Mapas usam blocos com um tamanho de 512 x 512 pixels para mapas rodoviários e menores de 256 x 256 pixels para imagens de satélite. O Azure Mapas fornece blocos de varredura e vetor para 23 níveis de zoom, numerados de 0 a 22. No nível de zoom 0, o mundo inteiro cabe em um único bloco:

Bloco do mapa do mundo

O nível de zoom 1 usa quatro blocos para renderizar o mundo: um quadrado 2 x 2

Layout de bloco de mapa 2x2

Cada nível de zoom adicional divide quádruplo os blocos do anterior, criando uma grade de^{zoom de 2} x zoom de^2. O nível de zoom 22 é uma grade 2²² x 2²² ou 4.194.304 x 4.194.304 blocos (17.592.186.044.416 blocos no total).

Os controles de mapa interativo do Azure Mapas para Web dão suporte a 25 níveis de zoom, numerados de 0 a 24. Embora os dados da estrada só estejam disponíveis nos níveis de zoom quando os blocos estiverem disponíveis.

A tabela a seguir fornece a lista completa de valores para níveis de zoom em que o tamanho do bloco é de 256 pixels quadrados:

Nível de zoom	Metros/pixel	Medidores/lado do ladrilho
0	156543	40075017
1	78271.5	20037508
2	39135.8	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
oito	611.5	156543
9	305.75	78271.5
10	152.87	39135.8
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
21	0.074646	19.10926
22	0.037323	9.55463
vinte e três	0.0186615	4.777315
24	0.00933075	2.3886575

Coordenadas de pixel

Tendo escolhido a projeção e a escala a serem usadas em cada nível de zoom, podemos converter coordenadas geográficas em coordenadas de pixel. A largura e a altura totais de pixel de uma imagem de mapa do mundo para um determinado nível de zoom são calculadas como:

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

var mapHeight = mapWidth;

Como a largura e a altura do mapa são diferentes em cada nível de zoom, as coordenadas de pixel também são. O pixel no canto superior esquerdo do mapa sempre tem coordenadas de pixel (0, 0). O pixel no canto inferior direito do mapa tem coordenadas de pixel (largura-1, altura-1) ou referindo-se às equações na seção anterior, (tileSize * 2^zoom–1, tileSize * 2^zoom–1)). Por exemplo, ao usar 512 blocos quadrados no nível 2, as coordenadas de pixel variam de (0, 0) a (2047, 2047), assim:

Mapa mostrando dimensões de pixel

Dada a latitude e longitude em graus e o nível de detalhe, as coordenadas XY do pixel são calculadas da seguinte forma:

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);

Os valores de latitude e longitude são considerados no datum WGS 84. Embora o Azure Mapas use uma projeção esférica, é importante converter todas as coordenadas geográficas em um dado comum. WGS 84 é o datum selecionado. Supõe-se que o valor de longitude varie de -180 graus a +180 graus, e o valor de latitude deve ser recortado para variar de -85,05112878 a 85,05112878. A adesão a esses valores evita uma singularidade nos pólos e garante que o mapa projetado tenha uma forma quadrada.

Coordenadas do bloco

Para otimizar o desempenho da recuperação e exibição do mapa, o mapa renderizado é cortado em blocos. O número de pixels e o número de blocos diferem em cada nível de zoom:

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

var numberOfTilesHigh = numberOfTilesWide;

Cada bloco recebe coordenadas XY que variam de (0, 0) no canto superior esquerdo a (2^zoom–1, 2^zoom–1) no canto inferior direito. Por exemplo, no nível de zoom 3, as coordenadas do bloco variam de (0, 0) a (7, 7) da seguinte maneira:

Mapa de coordenadas de bloco

Dado um par de coordenadas XY de pixel, você pode determinar facilmente as coordenadas XY do bloco que contém esse pixel:

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

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

Os blocos são chamados pelo nível de zoom. As coordenadas x e y correspondem à posição do bloco na grade para esse nível de zoom.

Ao determinar qual nível de zoom usar, lembre-se de que cada local está em uma posição fixa em seu bloco. Como resultado, o número de blocos necessários para exibir uma determinada extensão de território depende do posicionamento específico da grade de zoom no mapa do mundo. Por exemplo, se houver dois pontos separados por 900 metros, podem ser necessários apenas três blocos para exibir uma rota entre eles no nível de zoom 17. No entanto, se o ponto oeste estiver à direita de seu ladrilho e o ponto leste à esquerda de seu ladrilho, ele pode levar quatro ladrilhos:

Escala de demonstração de zoom

Depois que o nível de zoom é determinado, os valores x e y podem ser calculados. O bloco superior esquerdo em cada grade de zoom é x=0, y=0; O bloco inferior direito está em x=2^zoom-1, y=2^zoom-1.

Aqui está a grade de zoom para o nível de zoom 1:

Grade de zoom para o nível de zoom 1

Índices Quadkey

Algumas plataformas de mapeamento usam uma quadkey convenção de nomenclatura de indexação que combina as coordenadas ZY do bloco em uma cadeia de caracteres unidimensional chamada quadtree chaves ou quadkeys abreviadamente. Cada quadkey um identifica exclusivamente um único bloco em um determinado nível de detalhe e pode ser usado como uma chave em índices comuns de árvore B de banco de dados. Os SDKs do Azure Mapas dão suporte à sobreposição de camadas de bloco que usam quadkey a convenção de nomenclatura, além de outras convenções de nomenclatura, conforme documentado no documento Adicionar uma camada de bloco .

Observação

A quadkeys convenção de nomenclatura só funciona para níveis de zoom de um ou mais. O SDK do Azure Mapas dá suporte ao nível de zoom 0, que é um único bloco de mapa para o mundo inteiro.

Para converter as coordenadas do bloco em um quadkey, os bits das coordenadas Y e X são intercalados e o resultado é interpretado como um número de base 4 (com zeros à esquerda mantidos) e convertido em uma cadeia de caracteres. Por exemplo, dadas as coordenadas XY do bloco (3, 5) no nível 3, o quadkey é determinado da seguinte forma:

tileX = 3 = 011 (base 2)

tileY = 5 = 101 (base 2)

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

Qquadkeys têm várias propriedades interessantes. Primeiro, o comprimento de a quadkey (o número de dígitos) é igual ao nível de zoom do bloco correspondente. Em segundo lugar, o quadkey de qualquer bloco começa com o quadkey bloco pai (o bloco que contém no nível anterior). Conforme mostrado no exemplo a seguir, o bloco 2 é o pai dos blocos 20 a 23:

Pirâmide de peças Quadkey

Por fim, quadkeys forneça uma chave de índice unidimensional que geralmente preserva a proximidade dos blocos no espaço XY. Em outras palavras, dois blocos que têm coordenadas XY próximas geralmente têm quadkeys que estão relativamente próximos. Isso é importante para otimizar o desempenho do banco de dados, pois os blocos vizinhos geralmente são solicitados em grupos e é desejável manter esses blocos nos mesmos blocos de disco, a fim de minimizar o número de leituras de disco.

Código-fonte matemático do bloco

O código de exemplo a seguir ilustra como implementar as funções descritas neste documento. Essas funções podem ser facilmente traduzidas para outras linguagens de programação, conforme necessário.

C#
Máquina

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
        	};
        }
    }
}

Observação

Os controles de mapa interativo no SDK do Azure Mapas têm funções auxiliares para converter entre posições geoespaciais e pixels do visor