c# - 流畅的运动上升穿过大气层

Question

我正在使用 Microsoft Virtual Earth 3D 穿越大气层，我可以平稳下降，但我不知道如何顺利​​上升。

我是这样下降的:

for(int curAlt = startAlt; curAlt < endAlt; curAlt--){
    //do something
    curAlt -= curAlt/150
}

当我离地球越近(海拔越低)时，跳跃的幅度就越小。我需要一个类似的解决方案，只是相反，同时仍将较小的跳跃保持在较低的高度。

我该怎么做？或者我正在做的事情是 Not Acceptable ，应该以不同的方式来做(比如用对数)？

Answer 1

更好的解决方案可能是使用类似 Logistic function 的函数.

Double minAlt = 0.0;
Double maxAlt = 500000.0;

Int32 numberSteps = 1000;

Double boundary = +6.0;

for (Int32 step = 0; step < numberSteps; step++)
{
   Double t = -boundary + 2.0 * boundary * step / (numberSteps - 1);
   Double correction = 1.0 / (1.0 + Math.Exp(Math.Abs(boundary)));
   Double value = 1.0 / (1.0 + Math.Exp(-t));
   Double correctedValue = (value - correction) / (1.0 - 2.0 * correction);
   Double curAlt = correctedValue * (maxAlt - minAlt) + minAlt;
}

因为当前高度是明确计算的，所以您不必依赖引入各种精度相关错误的迭代计算。

有关如何调整函数形状的示例代码。

---

这是一个显示函数的示例控制台应用程序。您可以稍微调整一下参数以感受一下行为。

using System;

namespace LogisticFunction
{
    class Program
    {
        static void Main(string[] args)
        {
            Double minAlt = 5.0;
            Double maxAlt = 95.0;

            Int32 numberSteps = 60;

            // Keep maxAlt and numberSteps small if you don't want a giant console window.
            Console.SetWindowSize((Int32)maxAlt + 12, numberSteps + 1);

            // Positive values produce ascending functions.
            // Negative values produce descending functions.
            // Values with smaller magnitude produce more linear functions.
            // Values with larger magnitude produce more step like functions.
            // Zero causes an error.
            // Try for example +1.0, +6.0, +20.0 and -1.0, -6.0, -20.0
            Double boundary = +6.0;

            for (Int32 step = 0; step < numberSteps; step++)
            {
                Double t = -boundary + 2.0 * boundary * step / (numberSteps - 1);
                Double correction = 1.0 / (1.0 + Math.Exp(Math.Abs(boundary)));
                Double value = 1.0 / (1.0 + Math.Exp(-t));
                Double correctedValue = (value - correction) / (1.0 - 2.0 * correction);
                Double curAlt = correctedValue * (maxAlt - minAlt) + minAlt;

                Console.WriteLine(String.Format("{0, 10:N4} {1}", curAlt, new String('#', (Int32)Math.Round(curAlt))));
            }

            Console.ReadLine();
        }
    }
}