Prism to cut

[rmnrdi]

I'm trying to calculate prism to cut with these formulas but they need a certain sign convention.

P_V=x*Sphere + Cylinder*sin(Φ)*(x*sin(Φ) + y*cos(Φ))
P_H=y*Sphere + Cylinder*cos(Φ)*(x*sin(Φ) + y*cos(Φ))
P_r=sqrt(P_v^2 + P_H^2)
x = horizontal decentration
y = vertical decentration

Can anyone break down the sign convention used. It's a little counter-intuitive to me.

Thanks,
Rob

P.S. This is not homework

[MakeOptics]

I'm trying to calculate prism to cut with these formulas but they need a certain sign convention.

P_V=x*Sphere + Cylinder*sin(Φ)*(x*sin(Φ) + y*cos(Φ))
P_H=y*Sphere + Cylinder*cos(Φ)*(x*sin(Φ) + y*cos(Φ))
P_r=sqrt(P_v^2 + P_H^2)
x = horizontal decentration
y = vertical decentration

Can anyone break down the sign convention used. It's a little counter-intuitive to me.

Thanks,
Rob

P.S. This is not homework

The theta is the axis, the (x,y) are Cartesian coordinates x is horizontal y vertical, + indicates decentration in/up, - indicates decentration out/down.

[rmnrdi]

The only thing is, I'm only getting the correct values if I change horizontal decentration to negative values for inward decentration. It's really driving me bonkers because I can't see what's going on. I've even done the derivation of the formula with points in each quadrant and I'm still missing it.

For example if I want to decenter the OC up and in. x would be negative and y is positive for the formulas to give the correct answers. Likewise if I want to move the OC out and up. x would be positive and y is positive for the correct evaluation.

Thanks for your help,
Rob

[ml43]

If I am reading your formula correctly, pretty sure you are forgetting about OD/OS compensation.

Or you need to rotate your coordinate system about the y-axis 180 degrees.

[rmnrdi]

Yes, for the left eye the axis needs to be rotated to conform with the binasal form. I understand that part. It still requires the horizontal decentration value (x) to have it's sign flipped.

Here's the article from MAFO that outlines the technique. It begins on page 22.
http://en.calameo.com/read/00012606594e0f265a619

I've also seen this formula in "Clinical Optics" page 111 on google books and it has the sign convention a little different. Y is positive in the down direction.

Thanks for the assistance,
Rob

[ml43]

Yes, for the left eye the axis needs to be rotated to conform with the binasal form. I understand that part. It still requires the horizontal decentration value (x) to have it's sign flipped.

Here's the article from MAFO that outlines the technique. It begins on page 22.
http://en.calameo.com/read/00012606594e0f265a619

I've also seen this formula in "Clinical Optics" page 111 on google books and it has the sign convention a little different. Y is positive in the down direction.

Thanks for the assistance,
Rob

just wondering, are you using positive cyl for your calculation?

[rmnrdi]

No I'm using minus cylinder form.

[MakeOptics]

No I'm using minus cylinder form.

Post an example Rx and I am assuming you want it in excel?

[ml43]

Had a few minutes to read the article.

You just need to rotate 180 degrees about the y-axis.

Ophthalmic Rx's are written with the cartisian coordinates/axis from the refractors perspective,
but surfacing is done on the other side(rotated 180 degrees about the y-axis).

Hope that helps.