xyz（纬度经度高程）在表面上的位置

Question

如何在由多个点创建的曲面上找到 xyz 位置。假设我测量了一个向两个方向倾斜的停车场的周界，不一定是在平面上创建一个表面。如果我走到点周边的任何区域，GPS 设备会告诉我纬度和经度？我将如何计算该点到地面的高程？ 使用 C#

Answer 1

The common method is a bilinear interpolation below:
 

using System;
using System.Linq;

class SurfaceInterpolation
{
    static void Main()
    {
        // Assume you have a list of survey points with latitude, longitude, and elevation
        var surveyPoints = new[]
        {
            new SurveyPoint(0, 0, 100),
            new SurveyPoint(0, 1, 150),
            new SurveyPoint(1, 0, 200),
            new SurveyPoint(1, 1, 250)
            // Add more survey points as needed
        };

        // Example: Calculate elevation at a specific point
        double latitude = 0.5;  // Example latitude
        double longitude = 0.5; // Example longitude

        double elevation = InterpolateElevation(surveyPoints, latitude, longitude);

        Console.WriteLine($"Elevation at ({latitude}, {longitude}): {elevation}");
    }

    static double InterpolateElevation(SurveyPoint[] surveyPoints, double targetLatitude, double targetLongitude)
    {
        // Find the four nearest survey points
        var nearestPoints = surveyPoints.OrderBy(p => Math.Pow(p.Latitude - targetLatitude, 2) + Math.Pow(p.Longitude - targetLongitude, 2)).Take(4).ToArray();

        // Bilinear interpolation
        double q11 = nearestPoints[0].Elevation;
        double q21 = nearestPoints[1].Elevation;
        double q12 = nearestPoints[2].Elevation;
        double q22 = nearestPoints[3].Elevation;

        double x1 = nearestPoints[0].Latitude;
        double x2 = nearestPoints[1].Latitude;
        double y1 = nearestPoints[0].Longitude;
        double y2 = nearestPoints[2].Longitude;

        double x = targetLatitude;
        double y = targetLongitude;

        double elevation = (1.0 / ((x2 - x1) * (y2 - y1))) *
                           (q11 * (x2 - x) * (y2 - y) +
                            q21 * (x - x1) * (y2 - y) +
                            q12 * (x2 - x) * (y - y1) +
                            q22 * (x - x1) * (y - y1));

        return elevation;
    }
}

class SurveyPoint
{
    public double Latitude { get; }
    public double Longitude { get; }
    public double Elevation { get; }

    public SurveyPoint(double latitude, double longitude, double elevation)
    {
        Latitude = latitude;
        Longitude = longitude;
        Elevation = elevation;
    }
}