/// <summary>
/// Calculates the approximate area of a point on a map projection with the given
/// characteristics, by transforming the point and its nearest neighbors to latitude and
/// longitude, calculating the midpoints between them, and calculating the area of the
/// region enclosed within those midpoints.
/// </summary>
/// <param name="region">The mapped region.</param>
/// <param name="planet">The mapped planet.</param>
/// <param name="x">The x coordinate of a point on a map projection, with zero as the
/// westernmost point.</param>
/// <param name="y">The y coordinate of a point on a map projection, with zero as the
/// northernmost point.</param>
/// <param name="resolution">The vertical resolution of the projection.</param>
/// <param name="options">
/// The map projection options used to generate the map used.
/// </param>
/// <returns>The area of the given point, in m².</returns>
public static HugeNumber GetAreaOfLocalPoint(
this SurfaceRegion region,
Planetoid planet,
int x, int y,
int resolution,
MapProjectionOptions options) => SurfaceMap.GetAreaOfPointFromRadiusSquared(
planet.RadiusSquared,
x, y,
(int)Math.Floor(resolution * options.AspectRatio),
resolution,
region.GetProjection(planet, options.EqualArea));
/// <summary>
/// Gets the elevation at the given <paramref name="latitude"/> and <paramref
/// name="longitude"/>, in meters.
/// </summary>
/// <param name="region">The mapped region.</param>
/// <param name="planet">The mapped planet.</param>
/// <param name="elevationMap">An elevation map.</param>
/// <param name="latitude">The latitude at which to determine elevation.</param>
/// <param name="longitude">The longitude at which to determine elevation.</param>
/// <param name="equalArea">
/// If <see langword="true"/> the projection is a cylindrical equal-area projection.
/// Otherwise, an equirectangular projection will be used.
/// </param>
/// <returns>
/// The elevation at the given <paramref name="latitude"/> and <paramref name="longitude"/>,
/// in meters. Or <see cref="double.NaN"/> if the given <paramref name="latitude"/> and
/// <paramref name="longitude"/> are not contained within this region.
/// </returns>
public static double GetElevationAt(
this SurfaceRegion region,
Planetoid planet,
Image <L16> elevationMap,
double latitude,
double longitude,
bool equalArea = false) => region.IsPositionWithin(planet, latitude, longitude)
? (elevationMap.GetValueFromImage(
latitude,
longitude,
region.GetProjection(planet, equalArea),
true)
- planet.NormalizedSeaLevel)
* planet.MaxElevation
: double.NaN;
/// <summary>
/// Produces an elevation map projection of this region.
/// </summary>
/// <param name="region">The mapped region.</param>
/// <param name="planet">The planet being mapped.</param>
/// <param name="resolution">The vertical resolution of the projection.</param>
/// <param name="equalArea">
/// If <see langword="true"/> the projection will be a cylindrical equal-area projection.
/// Otherwise, an equirectangular projection will be used.
/// </param>
/// <returns>
/// A projected map of elevation. Pixel luminosity indicates elevation relative to <see
/// cref="Planetoid.MaxElevation"/>, with values below the midpoint indicating elevations
/// below the mean surface.
/// </returns>
public static Image <L16> GetElevationMap(
this SurfaceRegion region,
Planetoid planet,
int resolution,
bool equalArea = false) => planet.GetElevationMap(resolution, region.GetProjection(planet, equalArea));
