Making graph from coordinates when we don't know which curve it is

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amolaher750

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I got some coordinates from doing some optics calculation on aspheric lense and from that i got some coordinates which makes a graph which is not know now i want to make equation from those points, can anybody help me by telling me how to make it?
 
amolaher750 said:
I got some coordinates from doing some optics calculation on aspheric lense and from that i got some coordinates which makes a graph which is not know now i want to make equation from those points, can anybody help me by telling me how to make it?
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Use MS-EXCEL to get the best fit curve.
 
Subhotosh Khan said:
Use MS-EXCEL to get the best fit curve.
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i want to make equation from the coordinates not just want to get graph, and when i got graph it was irregular , can you tell me how to find it? i am also attaching my excel sheet with it in that at bottom there are columns coordinates x and y, can you help to nake equation for those coordinates
 
amolaher750 said:
i want to make equation from the coordinates not just want to get graph, and when i got graph it was irregular , can you tell me how to find it? i am also attaching my excel sheet with it in that at bottom there are columns coordinates x and y, can you help to nake equation for those coordinates
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Excel lets you calculate "trend-line" and it will provide equations accordingly.

Do you know the "expected" equations from those points?

I do not see any excel attached to your note above.
 
Given any finite number of points there exist an infinite number of curves through them and therefore an infinite number of "equations" that will give those points. You will have to first decide what kind of function (polynomial, trigonometric, exponential, etc.) you think it will be then do a "best fit" algorithm appropriate for that kind.
 
Subhotosh Khan said:
Excel lets you calculate "trend-line" and it will provide equations accordingly.

Do you know the "expected" equations from those points?

I do not see any excel attached to your note above.
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give me your email id i will mail you cause this is not working here because its saying file type not supported
 
amolaher750 said:
give me your email id i will mail you cause this is not working here because its saying file type not supported
Click to expand...
Subhotosh Khan said:
Excel lets you calculate "trend-line" and it will provide equations accordingly.

Do you know the "expected" equations from those points?

I do not see any excel attached to your note above.
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i dont know which equation it will give but it should satisfy all coordinates that i got
 
Subhotosh Khan said:
Excel lets you calculate "trend-line" and it will provide equations accordingly.

Do you know the "expected" equations from those points?

I do not see any excel attached to your note above.
Click to expand...
This are coordinates i got can you help me to find out equation for these coordinates
 

Attachments

  • coordinates_i_got.txt
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HallsofIvy said:
Given any finite number of points there exist an infinite number of curves through them and therefore an infinite number of "equations" that will give those points. You will have to first decide what kind of function (polynomial, trigonometric, exponential, etc.) you think it will be then do a "best fit" algorithm appropriate for that kind.
Click to expand...
this are cordinates i got from that i want to make equation that will satisfy all these points. it does not have any known shape when i get curve from excel. Sorry but i am new in this so need help of you guys.
 

Attachments

  • coordinates_i_got.txt
    8.9 KB · Views: 1
amolaher750 said:
This are coordinates i got can you help me to find out equation for these coordinates
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What does 'x' and 'y' mean in your case?

What is the Physiscs (or Chemistry or science) behind your hypothesis that - x & y are co-related?
 
When I put that into Excel, the graph looks a lot like a square root. When I swap x and y and plot x as a function of y, the polynomial trendline (quadratic) is a pretty close fit, and a cubic fit is essentially perfect. So I'd go with that as a hypothesized relationship.

Of course, if you use the cubic, it won't be practical to invert it to get y as a function of x; but the inverse of the quadratic could be good enough.
 
Dr.Peterson said:
When I put that into Excel, the graph looks a lot like a square root. When I swap x and y and plot x as a function of y, the polynomial trendline (quadratic) is a pretty close fit, and a cubic fit is essentially perfect. So I'd go with that as a hypothesized relationship.

Of course, if you use the cubic, it won't be practical to invert it to get y as a function of x; but the inverse of the quadratic could be good enough.
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so do i assume it as a cubic fit and go with its equation formation?
 
Do you have a prediction of what the data represent? (Such as x/y or a quadratic or cubic as Dr.Peterson recommends.) Saying that x and y are coordinates of the lens doesn't say much. Perhaps it would help if you could provide a brief description of what you are doing.

-Dan
 
topsquark said:
Do you have a prediction of what the data represent? (Such as x/y or a quadratic or cubic as Dr.Peterson recommends.) Saying that x and y are coordinates of the lens doesn't say much. Perhaps it would help if you could provide a brief description of what you are doing.

-Dan
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i am tracking light which is falling on the aspheric lense and i want to find out as perfect aspheric lense shape that will make every light parallel when it come out of lense i also made whole algorithm on excel but this system not supporting its extension so that i am unable to post it here if you want i can personal send you my sheet if you give your mail id.
 
It might be more helpful if, as requested, you give a brief description of what you are doing, rather than a large, hard-to-interpret spreadsheet. For example, are you measuring locations on an actual lens, as I initial thought, or have you made a theoretical model from which you calculated these pairs, but without a formula that directly relates the coordinates? It's possible that we could derive a formula from the calculations you did, if you describe them to us.

Or, you can take your work as demonstrating that this cubic equation describes the shape of this particular lens, and perhaps enabling you to make this particular lens. (This would not provide a general way to find an equation for the shape of any lens of the type you are studying.)
 
Dr.Peterson said:
It might be more helpful if, as requested, you give a brief description of what you are doing, rather than a large, hard-to-interpret spreadsheet. For example, are you measuring locations on an actual lens, as I initial thought, or have you made a theoretical model from which you calculated these pairs, but without a formula that directly relates the coordinates? It's possible that we could derive a formula from the calculations you did, if you describe them to us.

Or, you can take your work as demonstrating that this cubic equation describes the shape of this particular lens, and perhaps enabling you to make this particular lens. (This would not provide a general way to find an equation for the shape of any lens of the type you are studying.)
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i was finding lense's curve equaion so that i will come that i will comed to know that this curve of lense makes light path parallel to x-axis
aspheric track.png
The r2 should be almost parallel. in this the i1 changes but r2 should be almost parallel every time so that i need that i want the equation of this lens's curve. i also tried cubic equation but takes only one coordinate so it just satisfy that point only, i want equation that will satisfy all coordinates that i got from tracking light path using snell's law at changing medium. and got coordinates of curve using simple geometry rules. can you tell me the way to find out this curve equation?
 
How did you obtain the numbers in your list? Evidently you did it by ray tracing; but how did you decide at what point along a ray the surface should lie?

And have you studied optics to find how such lenses are designed, or are you trying to do this directly from Snell's Law without using existing knowledge in the field? I know that a lot has been done about designing lenses; I also know that there are reasons that no lens can be perfect (e.g. if it focuses rays parallel to the axis, it will not exactly focus rays in other directions). I don't know much more than that.
 
Dr.Peterson said:
How did you obtain the numbers in your list? Evidently you did it by ray tracing; but how did you decide at what point along a ray the surface should lie?

And have you studied optics to find how such lenses are designed, or are you trying to do this directly from Snell's Law without using existing knowledge in the field? I know that a lot has been done about designing lenses; I also know that there are reasons that no lens can be perfect (e.g. if it focuses rays parallel to the axis, it will not exactly focus rays in other directions). I don't know much more than that.
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actually it will not not give exact parallel but can give the approx parallel rays and yes i just decided the what i1 should be and max thickness of lens so that i am able to get h1 other can be solved just by using the snells law and simple trigonometry and geometry formulas and i am doing this ray tracking because the lens formulas fails when lens is too much thick for very thin lens this lens formula can be use.. if you see my excelsheet and diagram you will get to know how i did it
 
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