get y value at x,z ?

hope this is not too off-topic but atleast it's about 3D.

I guess a picture sez more than a thousand words so here goes...

http://mabuk.virtualave.net/3d.jpg

with the information known how do i get the y value at
any x,z point ???

any formulas would be greatly appretiated...

John
ArachnidAsked:
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lordxerothCommented:
Hi John,

I asume that you expect something in the 'plain' created by p0 through p4? So for a certain x and z point you expect one 'valid' y value?
Now in that case, things get quite complicated. In a normal plain (described by 3 points) you can just use some basic maths, but here you've got a 4th point.
In this case you have to define a 4th parameter to handle the curve (or bending of the plain) created by that 4th point. Look at it like it is a part of the surface a sphere. The problem here is that you don't know if it is a sphere and you certainly don't know the radius of the sphere.
So with the given information it is impossible to get a y value, unless you use a 4th paramater to define curve (which can be anything from a nice spherisch thing to more complex things like sinuses, etc...).

Jan
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jonninCommented:
Its a shallow saddle surface.
You will have to create an equation that describes the surface y = f(x,z);

or use interpolation to approximate a value (or treat as a plane and correct with an error term). It would really help to have the point in the center of the thing; then your equation to describe it could be very close! Without that, we don't know the depth of that point, so we don't know how curved it is...



 
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ArachnidAuthor Commented:
i'll pass the points to you Jan, since your answer got me going in the right direction.


John
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