# Calculating points on the curve

I want to get the x and y coordinates of a curve..How can i do that...

In the above image.Is it possible to calculate the intermediate points(one side) by knowing starting and ending point

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At least you have to have a model for the curve, and knowledge of extremities will let you pin down parameters of that model. Without the model, your question is incomplete. – Sasha Sep 8 '11 at 15:51
To add to Sasha: are you assuming it's a circle arc? A Bézier arc? What? – J. M. Sep 8 '11 at 15:56
I just point out the arc. I know starting point(i.e)top left and ending point (i.e)Bottom left. It is a bezier arc.. – Anish Sep 8 '11 at 16:04
Then your problem is underdetermined. Remember that a Bézier arc requires four control points to determine it. – J. M. Sep 8 '11 at 16:10
Ok...if it's is a parabolic arc...is is possible to find x and y coordinates.. – Anish Sep 8 '11 at 16:13

## 1 Answer

I surely observe that the given curve on the bi-concave lens is a parabola , so take the coordinate axes ,and then fix the lens at origin ,so that the mid-point(center) of the lens coincide with the origin ,

so then eccentricity of the lens is known or can be calculated,so one can find each corresponding $y$ for each $x$,

for more details about parabola see this

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Actually this one seems to be a programmatic and mathematical question...My curve is an image that shown above...so i can't trac the exact curve..there will be free space infront of curve where the arrows are placed.... – Anish Sep 8 '11 at 16:16
oh,fantastic ,i just now read about you,i felt very happy that you are a good programmer,and all the best for your iphone project,@anish – Iyengar Sep 8 '11 at 16:17
may be if you are interested in programming i suggest you to join this too,: superuser.com, there are many people,programmers there,with whom you can share and exchange your knowledge,thank you – Iyengar Sep 8 '11 at 16:19
How can you "surely observe that the given curve on the bi-concave lens is a parabola"? According to Wikipedia (granted, not the most authoritative source) "most lenses are spherical" so even if we knew that the picture represents a bi-concave lens (which is still a reasonable guess), a circle arc would be more likely (and, again, a guess). – A.P. Apr 2 '15 at 16:13