Hi Bill,
did you came up with an other solution finally ?

Thanks for any help.

Ben.

Bill Brehm wrote:
>Mike, thanks for all your help. Unfortunately, if I can't figure out how to
>solve the the symmetry problem, I won't be able to use povray to simulate
>lens distortion for high accuracy tests. But I did learn a lot. Thanks,
>again. Bill
>
>
>"Mike Williams" <mik### [at] nospamplease> wrote in message
>news:emU### [at] econymdemoncouk...
>> Wasn't it Bill Brehm who wrote:
>> >Mike,
>> >
>> >1. I cannot use square images, but was able to modify the function to
>give
>> >symmetrical results. I'm curious how you found the Z value
>experimentally,
>> >if you wouldn't mind explaining. I might have to confirm if it ever
>changes
>> >for different camera parameters.
>>
>> I tried these two functions
>>
>> #declare lens_dist = function(x, y, z, a, b) {
>>    select (z-0.017, 1, 1/x) }
>>
>> #declare lens_dist = function(x, y, z, a, b) {
>>    select (z-0.016, 1, 1/x) }
>>
>> Note: "select()" is like an "#if" that works inside a function{}. It's
>> the same as saying
>>         if ((z-0.016)<0) then 1 else 1/x
>>
>> With z-0.017 (or any higher numbers) I get the undistorted picture which
>> indicates that "1" was selected. With z-0.016 (or any lower numbers) I
>> get a very distorted picture because "1/x" is being selected. Therefore
>> the z value being tested during the camera normal is somewhere between
>> 0.016 and 0.017.
>>
>> I used the same trick (with select x+-K and select z+-K) to determine
>> that the edges of the image are at +-0.5 in the x any y directions.
>>
>>
>> >I think the normal does some kind of approximate calculation. Try
>rendering
>> >the code below and you'll see that the rendered image is not symmetrical,
>> >even though everything in the code is symmetrical.
>> >
>> >#declare lens_dist = function(x, y, a, b) {
>> >   (x + a * x * sqrt(x*x + y*y) + b * x^3 * sqrt(x*x + y*y) ) ^ 2 + (y +
>a *
>> >y * sqrt(x*x + y*y) + b * y^3 * sqrt(x*x + y*y) ) ^ 2
>> >}
>> >
>> >#declare a_factor = 0.69;
>> >#declare b_factor = 0.1;
>> >
>> >camera {
>> >
>> >  location <0, 0, -100>
>> >  look_at <0, 0, 0>
>> >  right <4/4, 0, 0>
>> >
>> >  normal{function {lens_dist(x, y, a_factor, b_factor)} }
>> >}
>> >
>> >light_source { <0, 0, -100> color rgb <1, 1, 1> }
>> >
>> >plane{-z, -10 pigment{color rgb <0, 0, 1>}}
>> >
>> >box{<-25, -25, 0>, <25, 25, 0> pigment {color rgb <1, 0, 0>}}
>>
>> Now that is weird.
>>
>> --
>> Mike Williams
>> Gentleman of Leisure
>

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