Question

I’m moving through the atmosphere with Microsoft Virtual Earth 3D and I can descend smoothly, but I don’t know the math to ascend smoothly.

I’m descending like this:

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

This works by decreasing the size of the jump the closer I get to the earth (lower altitude). I need a solution that would do similar, just in reverse, while still keeping the smaller jumps at the lower altitude.

How can I do this? Or is what I am doing unacceptable and should be done differently (say with logarithms)?

Answer 1

An even better solution might be to use a function like the Logistic function.

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; } 

Because the current altitude is explicitly calculated you do not have to rely on a iterative calculation introducing all sorts of precision releated errors.

See the sample code for how to tune the function shape.

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Here is a sample console application that displays the function. You can play a bit with the parameters to get a feeling for the behavior.

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();         }     } }