# Optical Forums > Ophthalmic Optics >  Contact Lens Tricurve Lens?

## HarryChiling

If I wanted to create a tricurve lens and I knew the Base Curve, Optic Zone Diameter, Overall Diameter, and the Edge Lift needed, is their a formula out their or research that would help me to determine the best options for the diameter and radius of the secondary and tertiary curves.

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## fjpod

Normally you just specify the overall lens diameter, the OZ diameter, and the tertiary curve width. The lab will calculate the secondary curve width for you. 

You can determine it yourself by 

total diam = OZ diam + 2 x sec curve width + 2 x ter curve width

As far as what secondary and tertiary curve diameters and widths are best?...well that depends.

On a normal cornea I usually make the secondary curve radius 1 to 1.5 mm flatter than the primary. Depending on the total diameter of the lens, I might make the tertiary curve radius somewhere between 9.5 and 12 mm. (larger diameter, larger radius of curvature.). From there I judge the fit by fluorescein patterns.  I usually stick to a .3 or .4 mm width on my tertiary, and let the secondary fall where it may.

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## chip anderson

There are or have been many many nomograms, etc. published for this. My rules of thumb for HGP (for PMMA add .2 to P.C. Width).
Lens dia/pc width 9.5/.8(7.7 Oz) 9.2/.7(7.8 Oz.) 8.8/.6(7.6 Oz)
8.6/.5(7.6 Oz.) 8.4/.5(7.4 Oz.) 8.0/.4(7.2 Oz.)
Peripheral curve radii used, usually 1 mm, longer than central posterior curve.
I also use a .2 bevel on the periphery of all lenses except those with extreemly flat or extreemly steep bases.

Do I vary this? You bet. If the P.C. looks too close I flatten it, if it looks too flat I either remake lens with steeper P.C. or reduce lens size if I want to try to use same lens. If central clearance is excessive, I widen and/or flatten the P.C. Note; Keep notes in record of all modifications, no need to find you need to do them over again when replacements needed.

While in today's world not all labs will follow such instructions, I specify all lens perameters. Why: Because I like to do my own thinking, make my own decisions and do my own fitting. I don't like leaving this up to someone who has never seen the (or sometimes any) patient. Or someone who may or may not be there tommarrow.

Chip

More tips: The steeper the base curve the smaller the diameter/Oz.. The flatter the base the larger the diameter/Oz.

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## HarryChiling

I think I have come up with some formulas for a tricurve lens and can be expanded for additional or less curves. I don't have a picture so see if you can follow.

The equation of a circle:

*(x-h)2+(y-k)2=r2*

The first curve I would determine would be the central curve, to simplify things a bit we will make point {h,k} the center of our grid and the first set of coordinates will be where the secondary curve begins {a,b} so the equation boils down to:

*{h,k} = {0,0)*
*r = base curve radius*
*a2+b2=r2*

Now in the equation we have the (r), and we can determine the (a) as 1/2 of our OZ diameter so the only unknown is the (b) and by rearrangeing the equation:

*a = 1/2 OZ Diam.*

*b = Sqrt(r2-b2)*

So now we have the point {a,b} that we know lies on both the Base Curve (r) and the secondary curve wich we will call (r2) so then we would need to find the center of our secondary curve, whih we will call point {i,j} so our equation becomes:

*(a-i)2+(b-j)2=r22*

we know what our {a,b} pont is because we determined that in the previous steps, the secondary curve we specify (r2) and we know the (i) in our equation lies on the y axis so it is equal to 0, so our equation now becomes:

*(a)2+(b-j)2=r22*

So we solve for the only unknown which is (j), now with the center of our secondary curve we have all we need to determine the point where the secondary curve and the tertiary curve meet, which we will call {c,d}, and we know that we know that our x coordinate for our point (c) is equal to the width of our secondary curve plus 1/2 our OZ diam or (a), so our equation boils down to:

*c = secondary curve width + 1/2 OZ diam = secondary curve width + (a)*

*c2+(d-j)=r22*

we know our x axis (c), we know our centers y axis (j) from the previous step, and we know our secondary curve radius (r2) so then we would only need to solve for the y axis of our point (d). Now that we know our point {c,d}, we are almost there hang with me, we need to determine our point where the tertiary curve meets the edge of our lens, which I will call {e,f} and we will call our tertiary curve (r3), so now we need to determine the center of our tertiary curve which we will call {l,m}, since e know that point {c,d} falls on this curve and we know the tertiary curve radius wich we will determine (r3) our equation comes down to:

*(c-l)2+(d-m)2=r32*

Now just like our previous examples we know that our x axis (l) is directly on the y axis so it's equal to 0, and we know what our point {c,d} is, and we know what our tertiary curve is (r3), our equation boils down to: 

*c2+(d-m)2=r32*

So now we can solve for point {l,m} and once we have that point we are almost home, we will use the center of the tertiary curve {l,m} and our tertiary radius (r3) and determine our edge point {e,f}, so our equation boils down to:

*e2+(f-m)2=r32*

Again we know that our x axis coordinate (e) is 1/2 the diameter and the center y coordinate (m) from the previous step, and our tertiary radius (r3), so we will solve for (f)

Now that we have our point {e,f} we know where the edge of our lens lies in 2 demensional space so to find the edge lift we would need to find the coordinate for our cornea directly below our edge point, which we will call {g,n} which we will do with our "K" reading which if fit on "K" will be the same as our base curve so the center would be the {h,k} which we set at {0,0} to simplify, and we know the x axis coordinate (g) would be the same as our edges (e) if we want to find the distance directly below it, so our equation is:

*g2+n2="K"2**

so we know our x axis coordinate (g) and our "K" reading which is equal to (r) so we only have to determine the y axis coordinate (n), so our edge lift is:

*Edge Lift = f - n*

_*if the base curve is not fit on "K" then subtract difference from the base curve radius and use that as the center coordinate for your last equation._ 

Whew, if you followed that all the way through :cheers: I will draw up a diagram and post it when I get the chance so that it can be visualized as well, it was more of an exercise for my mind than anything else, but thanks chip for the noograms, I will use them in a program version I will be writing as a default or recommended guide, if I ever et around to it.

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## Fezz

See what a little cigar smoke and rum will do to a guy!


Good job!! Whew we! That made my head hurt just trying to read it!

Thanks Harry!

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## HarryChiling

Here is the diagram of the whole thing along with some of my chicken scratch.

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## Dave Nelson

BTW, I tell people designing RGPs using nomograms is like a blind man driving a car, while his sighted passenger yells intructions. It can work, but is the driver really in control?

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## HarryChiling

> BTW, I tell people designing RGPs using nomograms is like a blind man driving a car, while his sighted passenger yells intructions. It can work, but is the driver really in control?


True it may not be the most accurate, but nomograms are created by people who have found that these curves are tried and true.  I would use a nomogram as well, but I want to know how to design one as well (doing the math) so that I can build ituition into what will and will not work.  The great fitters on this board, I have no doubt; can design one from scratch using nothing but formulas, but over the years they have honed their ability to guestimate a good fit and it usually works, and when it doesn't they have the skillset to modify them.

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## chip anderson

I have found that using a "factory nomogram" often means one if fitting lenses like the founder of whatever company did 20 years ago.   I can remember when PCL had a group of nomograms, most of thier customers were O.D.'s who fit flat.   Nomograms from other companies would be for low K, mean K, or steep depending on who thier customer/owner bases were.  I found Soper's thicknesses to fit well but be far too delicate for the average patient.
Read your history, read everything you can find and base *your fitting* on your observations and ideas.  Often the "consultant" on the phone had two weeks course which 10 days consisted of how to psychologicly handle customers during sales.
Read the information and books available from CLSA, but never swallow anyone whole.  
You will find that most Doctors try to treat every problem, including those of contact lenses with drugs "you got de dry eye, use restatis and if that doesn't work we'll have to use puctum plugs."  Opticians who are primarily contact lens fitters try to modify lenses for every situation mechanicly.  The truth often lies somewhere inbetween.

I'm impressed with Harry's formulas but being rather mathmaticly inastute, I do all such design in my head without formulas.   

Chip

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## HarryChiling

> I'm impressed with Harry's formulas but being rather mathmaticly inastute, I do all such design in my head without formulas.


Are you kidding me chip, the reason I do these things is so that I can build the intuition to do the the design in my head.  I have to know how it mechanically works first before I am able to build a solid intuition, I am trying to get where you are.  I said I wanted to take the NCLE - Advanced and I remember you starting a thread related to contact lens facts, but it died off or people stoped adding to it, but I have continued to push forward and am soaking up as much contact lens knowledge as possible.

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## HarryChiling

Chip, you gonna make me beg for them nomograms?  PLEEEEEEEEEEEASE :bbg:

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## tmorse

> If I wanted to create a tricurve lens and I knew the Base Curve, Optic Zone Diameter, Overall Diameter, and the Edge Lift needed, is their a formula out their or research that would help me to determine the best options for the diameter and radius of the secondary and tertiary curves.


Secondary and peripheral curve aren't ordered as a diameter, but rather as a 'width', ordered in mm if you choose to. And diameter is normally selected only after these patient variables... K- readings, interpalbebral fissure size, lid tension, HVID, pupil size, Rx and lid position(s).

Once diameter and base curve are selected, the secondary curve is generally made by the lab 0.75 to 1.50mm flatter, and the tertiary or peripheral cure is 2-3mm flatter this factory secondary curve. The radius of these outside RGP curves is a lab decision because they all follow their own fitting philosophy(ies). Once you get the lab RGP trial set and use it, the RGP lens that you then receive will have the same secondary and peripheral curves as your trial set, so you in effect become 'married' to that lab. Factory nomograms are excellent for first fit choice, and will work first fit 80% of the time. Forget any 20-year anti-nomogram nonsense. 

In fact, don't even consider ordering secondary or tertiary curves on a RGP. K-readings only measure the central 3mm of the cornea, and you (and no-one else) has no idea how much the cornea flattens 4-5mm from centre unless you have decentered the fixation on your keratometer as suggested by CLSA presenters, or have access to a corneal topography unit. Use a good trial set to determine initial lens parameters.:)

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## HarryChiling

> Secondary and peripheral curve aren't ordered as a diameter, but rather as a 'width', ordered in mm if you choose to. And diameter is normally selected only after these patient variables... K- readings, interpalbebral fissure size, lid tension, HVID, pupil size, Rx and lid position(s).
> 
> Once diameter and base curve are selected, the secondary curve is generally made by the lab 0.75 to 1.50mm flatter, and the tertiary or peripheral cure is 2-3mm flatter this factory secondary curve. The radius of these outside RGP curves is a lab decision because they all follow their own fitting philosophy(ies). Once you get the lab RGP trial set and use it, the RGP lens that you then receive will have the same secondary and peripheral curves as your trial set, so you in effect become 'married' to that lab. Factory nomograms are excellent for first fit choice, and will work first fit 80% of the time. Forget any 20-year anti-nomogram nonsense. 
> 
> In fact, don't even consider ordering secondary or tertiary curves on a RGP. K-readings only measure the central 3mm of the cornea, and you (and no-one else) has no idea how much the cornea flattens 4-5mm from centre unless you have decentered the fixation on your keratometer as suggested by CLSA presenters, or have access to a corneal topography unit. Use a good trial set to determine initial lens parameters.:)


Thanks for the info tmorse, I am more interested in how these parameters are determined, I need information on theory.  I have an understanding of the nomograms used for the various curves.  I am also familiar with the flattening of the cornea, and have other such formulas that would work with the previous in factoring that in, and with the corneal topographers become more prevalent in our industry their are more lenses that are taking the eccentricity of the cornea into consideration.  I have an idea for a piece of software and was actually asked by someone for it, so the need is there.  Decentering the keratometer is not used very often and requires a lot of time in front of the keratometer to be of any regular use in an office setting.  I am asking about theory, and theory only.  I will probbly never actually use any of these formulas or even the software in a production enviornment, but they would make a great teaching tool which I suspect is why I am being asked for it.  I appreciate all the information given, I guess I am asking for too much.

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