Sunday, March 07, 2010

Answer: How to find a set of coordinates in a bounded 2D space?

3 days ago, I posted a Mathematics problem on finding a set of coordinates in a bounded 2D space. I promised to offer my solution to the problem on the coming Sunday which is today.

Question
Given 4 known coordinates, length and breadth of a bounded 2D space, find the set of coordinates (in RED) with its x and y offset in units as shown above.

Answer

Using the method of interpolation,
lon
= (103.69926-103.72147)*263/1000 + (103.708975-103.72147)*2017/4000 + 103.72147
= 103.70932816625

lat
= (1.34192-1.34504)*263/1000 + (1.433975-1.34504)*2017/4000) + 1.34504
= 1.38906491375

It took me quite some time before I recalled there exists a method called interpolation to come out with the answer myself. BTW, this problem is work-related and not school-related.

References to interpolation
http://en.wikipedia.org/wiki/Interpolation
http://www.mathworks.com/moler/interp.pdf

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