In class we also reviewed the concept of reducing a geodetic or ellipsoid distance to the mapping plane.

Step 1: Implement the reduction

I would like you to create a C++ function, Matlab function, or Excel spreadsheet that implements this correction for the distances measured in the first part of this lab. In other words, I want you to compute and apply the appropriate grid scale factors. Use the latitude and longitude of each point provided here.

Point \phi \lambda
A N 51^o04^{'}32.590018^{"} W 115^o19^{'}14.550907^{"}
B N 51^o01^{'}49.349105^{"} W 115^o12^{'}38.636068^{"}
C N 51^o05^{'}52.502023^{"} W 115^o22^{'}19.169935^{"}

You are required to use the process outlined in this paper by Charles Karney ». I’d encourage you to make simple(r) work of this by looking at the code for the same thing found here ».

Use the parameters of the GRS80 ellipsoid for your calculations.

Step 2: Check your implementation

Although you don’t need to hand anything in for this step, I would encourage you to check your implementation for at least one point using the online calculator found at the second link above.

Step 3: Reduce the measured distances

Use your implementation to reduce the three measured distances that were provided in the first part of this lab. You may need to calculate a scale factor for the line(s). Provide:

1. The scale factor you applied in each case

2. The reduced distance

Step 4: Prepare and submit a suitable summary of your input and output

If you used Excel this might just mean your Excel file.

In C++ this would mean submitting your input and output files. I’d also like to see your full C++ project files again so we can provide you with feedback.

In Matlab I’d like to see your functions and some capture of the input and output.

Step 5: Draw some conclusions

I’d like you to comment in your submission on the magnitude of the reductions being made here. How big are they? On what do they seem to depend? When would you recommend doing them?

Step 6: Submit your work

When you’ve completely finished the lab you need to submit it as usual. Include with this:

1. A PDF of your report scanned using an app such as Genius Scan (for iOSn or for Android). Or using the scanner / printer available in your lab. This should include all of the requested elements.

2. Your full project file / solution or spreadsheet(s)