I have a set of 'N' tags and their Euclidean distances. How do I plot this information on a 2D plane?
For 3 tags, the plot is a triangle where each corner is a tag.
I'm looking for an approximate algorithm to plot more than 3 tags on to X-Y plane which is indicative of the actual distances.
I'm attaching a screenshot of a seven tag matrix with their Euclidean distances
For every triplet of points A,B,C you need to solve equation system
Note that there are 6 unknowns for 3 equations. So you have some freedom in initial choice:
Assign (0,0) coordinates to the first point. Let's (BX, 0) are coordinates of the second point. Find BX, CX , CY. Note the quadratic equation gives two possible positions for CY - choose positive one.
Solve similar system for the next point D. To get right choice from two possible positions - check for distance dAD.
Repeat process for all next points.
Example for 3 points with distances
dAB=1, dBC=1, dCD=1, dDA=1, dAC=1.414, dBD=1.414