@Ronan 

Thanks for the speedy reply and solution. I appreciate this.

I have originally used your same recommended procedure - but the problem persists.

I suspect it is connected to Powerpoint (when I exported the file to another machine, it worked fine!)

Again .. I appreciate the help.

@dharr 

Thank you!

This adds another useful insight into this problem. Very useful, indeed.

I appreciate this.

@mmcdara 

I am extremely pleased with this proposal - both the content and the turnaround are impressive! 

Thanks so much for sharing this.

@acer 

A nice alternative to the mmcdara solution ... much appreciated. Thanks for broadening my knowledge on this matter.

@mmcdara 

This is truly impressive ... I would never have figured this out! 

Your solution and response time to this request is very much appreciated, so thanks once again for the dig-out.

@tomleslie 

This is an approach I never thought of ... it's great to get this and the visual output is welcomed.

Many thanks for this. 

@mmcdara 

I did not realise the nature of my question was connected to this subject.

These insights are intriguing and I'll certainly research this subject further. Thank you for shining a light on this ... I appreciate your guidance .. it's very generous.

@Kitonum 

This is a nice routine and I thank you for sharing this solution - especially as a quick response.

Looking at your structure, do you think that it is possible to adapt this routine for the general case of n points so that it avoids the need to input all coordinates in the distance formula p[1], p[2], ..., p[n]?

I'm obliged!

@tomleslie 

Thanks very much for this.

I can now start to explore this subject in greater depth.

@mmcdara 

I appreciate your spline model and solutions - these are indeed, quite useful.

Basically, I sought an approximation to this repeatable pattern (point 13 being the same as point 1, and so on), however, I can certainly make use of this approach to expand the work.

Thanks again!

@dharr 

Thank you for this - I'm obliged.

I wouldn't have considered this approach - it seems to provide a good fit. I will use this procedure and trial various scenarios.

@acer 

This response is truly comprehensive - and covers all my requirements ... and then some!

Many thanks for this - I'm obliged.

@Carl Love 

Thanks for this, Carl - I like this approach.

Re-thinking this, I seek a contour plot;  curves that represents the relationship between x and z for different k-values. I do like your 3d solution, so I will certainly make good use of this.

@acer 

Despite being content with the assistance so far,  did try dialling values to reduce the jagged edges - with no luck.

Thanks for this.

This makes a great difference to the visuals.

@Kitonum 

That's also very convenient.

Thank you!