## Re: [PanoTools-devel] Peirce Quincuncial Projection

 Re: [PanoTools-devel] Peirce Quincuncial Projection From: Daniel M. German - 2007-01-14 08:00:23 ```Hi Michael, Thanks a lot for all the work you have done on this projection! It is not trivial at all (compared to this projection the rest are piece of cake). I tried to use your code but run into a problem. I got a tiny, little image :) Would you mind sending the script you are using to test the projection? Also, how do you compute the mp->distance parameter? it is supposed to be the number of pixels per radiant in the output. b contains the number of radiants in the desired field-of-view, and width is the width of the desired output image. I noticed that in your implementation of the albers it always assumes that the desired field-of-view is 360 degrees (hence it ignores b). -- daniel Michael> Erik Krause wrote: >> I'm pretty sure you and Michael know this already - just in case...: >> http://www.helpfeeds.com/showthread.php?p=1489664 Michael> I read this before. As far as I understand Abramowitz/Stegun 17.3.24 Michael> does not apply here because we have an incomplete elliptic integral and Michael> the 17.3. chapter is about complete elliptic integrals. However the Michael> inverse of the elliptic integral is no problem, as this is the Jacobi Michael> Function and can be easily calculated with the help of Numerical Recipes Michael> (sncndn). Michael> The problems start later when inverting all those equations full of sin Michael> and cos functions. Maple can invert it but the results are full of Michael> square roots so you have multiple results (as far as I understand these Michael> are the quadrants). Michael> In my first trials I did try to use the equations I get from Maple but I Michael> introduced some bugs I couldn't find and I gave up with this approach. Michael> After reading your mail I decided to give it another chance and now it Michael> works: Michael> Because I don't understand what Maple does when solving the equations, I Michael> can't tell which signs are right. So I have to try all combinations of Michael> signs - for each sqrt on time +1.0*sqrt and one time -1.0*sqrt. As there Michael> are 12 sqrts there are 2^12 = 4096 combinations. After I get a Michael> lambda/phi of one combination I put the result into the forward function Michael> and compare the resulting x and y. Michael> This solution is of course much better than the Michael> interpolation/minimization approach I did before. It is also a lot faster: Michael> http://mdgrosse.net/pano/peircequincuncial.c Michael> Michael -- Daniel M. German http://turingmachine.org/ http://silvernegative.com/ dmg (at) uvic (dot) ca replace (at) with @ and (dot) with . ```

 Re: [PanoTools-devel] Peirce Quincuncial Projection From: Michael Gross (adv) - 2007-01-14 01:38:39 ```Erik Krause wrote: > I'm pretty sure you and Michael know this already - just in case...: > http://www.helpfeeds.com/showthread.php?p=1489664 I read this before. As far as I understand Abramowitz/Stegun 17.3.24 does not apply here because we have an incomplete elliptic integral and the 17.3. chapter is about complete elliptic integrals. However the inverse of the elliptic integral is no problem, as this is the Jacobi Function and can be easily calculated with the help of Numerical Recipes (sncndn). The problems start later when inverting all those equations full of sin and cos functions. Maple can invert it but the results are full of square roots so you have multiple results (as far as I understand these are the quadrants). In my first trials I did try to use the equations I get from Maple but I introduced some bugs I couldn't find and I gave up with this approach. After reading your mail I decided to give it another chance and now it works: Because I don't understand what Maple does when solving the equations, I can't tell which signs are right. So I have to try all combinations of signs - for each sqrt on time +1.0*sqrt and one time -1.0*sqrt. As there are 12 sqrts there are 2^12 = 4096 combinations. After I get a lambda/phi of one combination I put the result into the forward function and compare the resulting x and y. This solution is of course much better than the interpolation/minimization approach I did before. It is also a lot faster: http://mdgrosse.net/pano/peircequincuncial.c Michael ```
 Re: [PanoTools-devel] Peirce Quincuncial Projection From: Daniel M. German - 2007-01-14 08:00:23 ```Hi Michael, Thanks a lot for all the work you have done on this projection! It is not trivial at all (compared to this projection the rest are piece of cake). I tried to use your code but run into a problem. I got a tiny, little image :) Would you mind sending the script you are using to test the projection? Also, how do you compute the mp->distance parameter? it is supposed to be the number of pixels per radiant in the output. b contains the number of radiants in the desired field-of-view, and width is the width of the desired output image. I noticed that in your implementation of the albers it always assumes that the desired field-of-view is 360 degrees (hence it ignores b). -- daniel Michael> Erik Krause wrote: >> I'm pretty sure you and Michael know this already - just in case...: >> http://www.helpfeeds.com/showthread.php?p=1489664 Michael> I read this before. As far as I understand Abramowitz/Stegun 17.3.24 Michael> does not apply here because we have an incomplete elliptic integral and Michael> the 17.3. chapter is about complete elliptic integrals. However the Michael> inverse of the elliptic integral is no problem, as this is the Jacobi Michael> Function and can be easily calculated with the help of Numerical Recipes Michael> (sncndn). Michael> The problems start later when inverting all those equations full of sin Michael> and cos functions. Maple can invert it but the results are full of Michael> square roots so you have multiple results (as far as I understand these Michael> are the quadrants). Michael> In my first trials I did try to use the equations I get from Maple but I Michael> introduced some bugs I couldn't find and I gave up with this approach. Michael> After reading your mail I decided to give it another chance and now it Michael> works: Michael> Because I don't understand what Maple does when solving the equations, I Michael> can't tell which signs are right. So I have to try all combinations of Michael> signs - for each sqrt on time +1.0*sqrt and one time -1.0*sqrt. As there Michael> are 12 sqrts there are 2^12 = 4096 combinations. After I get a Michael> lambda/phi of one combination I put the result into the forward function Michael> and compare the resulting x and y. Michael> This solution is of course much better than the Michael> interpolation/minimization approach I did before. It is also a lot faster: Michael> http://mdgrosse.net/pano/peircequincuncial.c Michael> Michael -- Daniel M. German http://turingmachine.org/ http://silvernegative.com/ dmg (at) uvic (dot) ca replace (at) with @ and (dot) with . ```