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I need some help figuring out how to make this post more clear. I've addressed the comments for clarification, but it looks like people still don't understand my question?

I stated the question originally in terms of five known points, from which one can interpolate a curve. I am trying to determine how to match the curve to four basic shapes.

Given five points on a face, determine if the "face shape" is closest to a circle, oval, square, or triangle

Any insight on how to make my question more clear is appreciated.

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    $\begingroup$ I'd say the biggest problem is that you don't have a good definition (in the question, at least) of what "closest" means. As in: if I hand you a list of five points, you ought to be able to tell me some specific number quantifying how far it is from a circle/triangle/oval/square and be able to make a choice about what the best number is. This is close to the idea of Ross Millikan's comment about the metric you're using. $\endgroup$ – user296602 Mar 29 '18 at 21:13
  • $\begingroup$ I personally think it's rather clear what's being asked (then again, I was just at an optometrist, and saw a similar face-shape chart, recommending lens shapes based on face shapes). I could perhaps see "too broad" as a valid close reason. The fact that you don't have a method/formula for measuring "closeness" seems to be exactly the point of the question... $\endgroup$ – pjs36 Mar 29 '18 at 21:36
  • $\begingroup$ @pjs36 what a great coincidence. i am as an indie developer building a product for optometrists (or primarily end-users who purchase a lot of eyewear online, such as myself). i've used a variety of just 2D graph curves to try measuring the face shape but was hoping for more advanced insight here $\endgroup$ – ina Mar 30 '18 at 0:31
  • $\begingroup$ @user296602 i've heard of metric in definition to things with jacobians and also in relativity. are they suggesting that i first need to define some sort of eigenspace for each of these shapes? it isn't clear to me how the metric applies here $\endgroup$ – ina Mar 30 '18 at 0:32
  • $\begingroup$ @user296602 do you think i should ask a corollary or pre-ceding question for metrics that define these basic shapes? $\endgroup$ – ina Mar 30 '18 at 0:36
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    $\begingroup$ @ina "Metric" is just another word for "Distance Function". It doesn't have to be defined on a vector space. $\endgroup$ – Dylan Mar 30 '18 at 15:52
  • $\begingroup$ Read the comment of @user296602 more closely, particularly the emphasis on a number (the word "metric" refers to the method of specifying this number, not to eigenspaces are jacobians etc.). One reason why your question was closed is that without specifying such a number, nor acknowledging the importance of such a number to your question, the mathematical basis of your question was deficient. $\endgroup$ – Lee Mosher Mar 30 '18 at 16:08
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    $\begingroup$ I think that inventing a suitable metric is the whole point of the question. Once you have a metric, the rest is just boring calculation. $\endgroup$ – bubba Apr 6 '18 at 10:36
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I think partly your question is "how do I make my question clear?". I.e. you are asking how can you define closeness.

Maybe restate your question as "how can I define closeness of geometric shapes, and using that definition how do I find the closest shape?".

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    $\begingroup$ Better: ask a question "how can I define closeness of geometric shapes?", get an answer, try and implement it yourself, and then if you get stuck ask a second question: "using this definition, how do I find the closest shape?" $\endgroup$ – John Gowers Apr 6 '18 at 22:14
  • $\begingroup$ thanks for this idea! posted an initial metrics question - i feel like there could be more advanced ways than just the simple plane geometry methods i know of, so really looking forward to answers. math.stackexchange.com/questions/2731477/… $\endgroup$ – ina Apr 10 '18 at 22:56

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