It has been a while since I last blogged on dissertation stuff but there will be many dissertation entries coming from now to the deadline on Friday the 18^th of April.

This entry is celebrating the success of debugging a little C++ program to “Do_Magic() on a dish.” I should have finished this program a week ago but it has really foxed me. Anyway it is now done and I dare say will enable me to do far more for my dissertation, although I have to get the next part of it working.

Here is an image, early on, of the output, which for that stage of development was looking good.

In the last few days it has given outputs showing it just was not working:

Thankfully here it is looking lovely;

The program allows me to specify a dish (the top slice off a sphere) and run splines (initially straight batten but bent into shape) in three directions across it. The program finds the intersects and writes a file with this data. It also gives me all the points on a particular spline, ordered. It gives me the support points. The program allows me to use the intersections of the top and bottom layers or not.

In the development of this program I have run it 158 times. I know this as the program outputs four data files each starting with test144_ where 144 is the test run that I am up to.

Finding the intersection of any two splines took me a while to work out. I started by equating the equations of the splines but ended up with simultaneous equations that only had numerical solutions. It was vector analysis that proved to be easy in the end, much of which happens in the function (unimaginatively) called Do_Magic, part of which is shown below.

Gerald has helped me no end with this foxing little program and putting straight on some mathematics, and as such has been written into the acknowledgements of my working draft of the dissertation report.

I intend to do a variation on this program that will cut this dish in half and put a cylinder in between and map the splines over that shape. Wish me luck!