Calculating the average of two angles (two bearings actually)

I recently needed to find the average of two angles.  I was programmatically creating a irregular polygon. I wanted to draw a small square at the points of the polygon, and I wanted the squares to be rotated to the average of the two lines that met at that point.

The issue is that if you have two bearings, one at 20° and one at 350°, or one at 15° and one at 315°. If you just average the two numbers, you get 185°, but the more appropriate number is 5°.  This is called by some a “Wraparound issue” and if you search the web you will see lots of ways to solve this problem. Unfortunately they mostly try to solve it using a mathematical equation.  Now for people that have read this blog for awhile know that I am not allergic to math, but if we can solve this problem simply with an algorithm, we should … that’s what computers are for, right?

So, here is my algorithm and the thought behind it.

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(Assumptions: 0 >= bearings < 360)

First if you look at the difference between the two bearings, you will see that there are two possibilities, the actual difference is greater than 180° or less than 180°.  Since we are only concerned about “fixing” the issue when the difference is greater than 180°, that is the first thing we will check.

We will call the smaller value bearing bearingA and the larger value bearing bearingB.

Since we know that bearingB has a larger value and that the difference is greater than 180, so bearingB > 180.

So, if we subtract 360  –  bearingB, then just add bearingA + bearingB and divide the total in half, we are 90% there.

One last check. If the result is less than 0, we need to add 360 back in.

So, example #1 20° & 350° 350 – 20 > 180 350 – 360 = –10 (–10 + 20) / 2 = 5 5 ≥ 0 = 5 °

So, example #2 15° & 315° 315 – 15 > 180 315 – 360 = –45 (-45 + 15) / 2 = –30 –30 < 0–30 + 360 = 354°

And here is the code:

Code Snippet

1. private static double GetAverageBearing(double bearingA, double bearingB)
2.         {
3.             if (bearingA > bearingB)
4.             {


5.                 var temp = bearingA;
6.                 bearingA = bearingB;


7.                 bearingB = temp;
8.             }
9.  
10.             if (bearingB - bearingA > 180) bearingB -= 360;
11.  
12.             var finalBearing = (bearingB + bearingA)/2;
13.  
14.             if (finalBearing < 0) finalBearing += 360;
15.             
16.             return finalBearing;
17.         }

Scripting C++/cli with IronPython (Visual Studio 2008 & IronPython 2.6.1)

Even though there has been a lot of talk about IronPython, there has been very little info about how to use it with C++/cli.  I’ve actually found posts claiming that it is not possible to use IronPython with C++/cli.

Well, it is possible and easy, once you have a working example.  If, not then … well, lets just hope your hair will grow back.

Ok, I’m never one to take the easy way out, but I started by creating a C# dll that called my IronPython script and then called the C# dll from C++/cli.  That worked but seemed overly complicated.  If you do not mind a middleman then I guess it is ok, but if you want to go straight from C++/cli to IronPython, read on.

When I first tried to write a call to an IronPython script from  C++/cli, I tried a direct conversion of C# code into C++/cli code.  That didn’t work, so I then tried using RedGate’s .Net Reflector and the C++/cli add-in for .Net Reflector.  This got me 70% there.  Combining both with some trial and error got me the rest of the way. 

Funny, but when you look at the code, it seems so simple – yet getting there was not easy.

So, the following snippet shows a simple usage of IronPython as a scripting language.  It takes the first parameter passed in prints it to the console, passes it to the IronPython script: ipyStrings.ipy, then prints to the console the value of the same parameter that was passed back.  The IronPython code takes the string, prints it, reverses it, then sends it back.

C++/cli code:

Code Snippet

1. int main(array<System::String ^> ^args)
2. {
3.     try
4.     {
5.         if(args->Length>0)
6.         {   
7.             String^ filename = "ipyStrings";
8.             String^ path = Assembly::GetExecutingAssembly()->Location;
9.  
10.             ScriptEngine^ engine = Python::CreateEngine();
11.             ScriptScope^ scope = engine->CreateScope();
12.             ScriptSource^ source = engine->CreateScriptSourceFromFile
13.             (String::Concat(Path::GetDirectoryName(path), "\\", filename, ".ipy"));
14.        
15.             Console::WriteLine(args[0]);
16.  
17.             scope->SetVariable("passedArgs", args[0]);           
18.             source->Execute(scope);
19.  
20.             Console::WriteLine(scope->GetVariable<String ^>("passedArgs"));
21.         }                                   
22.     }
23.     catch(Exception ^e)
24.     {
25.         Console::WriteLine(e->ToString());
26.     }
27.  
28.     Console::ReadLine();
29.  
30.     return 0;
31. }

Python code:

Code Snippet

1. import clr
2.  
3. print "Passed in: " + passedArgs
4. passedArgs = passedArgs[::-1]
5.  
6. print "Sending back: " + passedArgs

Random Numbers on a Bell Curve in C#

Have you ever wanted to generate some random numbers but with a distribution pattern other than the normal even pattern?

Well in a recent project I did.  I wanted a weighted distribution pattern that looked like a bell curve. 

I looked around yes there were some answers, but most got a lot deeper into math than I wanted or needed.  I simply wanted to generate a number with the probability that it was in the center of the range be greater than the probability that it was on the edges – in other words, it fit on a Bell Curve.

I cannot credit what post where gave me the simple solution, or I would post a link.  Here is a simple Extension Method to the Random class. 

It takes two parameters:

1. Steps: How many numbers in each “Chunk” do you want.  If you want a number between 0 & 600 and set the Steps equal to 50, then the midpoint value (300) will be much more likely than 0 or 300.
2. MaxValue: The possible range for the random number will be 0 to MaxValue - 1.

Now keep in mind that this is not mathematically perfect.  If you do not choose a step value that is a divisor of your MaxValue then you will not get the full range.  But, having said that, this is a great “Quick & Dirty” way to get a good approximation of a random bell curve.

Code Snippet

1. public static class RandomExtender
2. {
3.     public static int NormalNext(this Random rnd, int Steps, int MaxValue)
4.     {
5.         int count = 0;
6.         int val = 0;
7.  
8.         if (Steps < 1) return 0;
9.  
10.         while (++count * Steps <= MaxValue) val += rnd.Next(Steps);
11.  
12.         return val;
13.     }
14. }

Here is a picture of 20,000 random numbers with Steps = 50 & MaxValue = 600.