Elnaz wrote:> It doesn't work, I mean it works somewhere doesn't work somewhere > else. I got straight lines around the boundaries but nothing in the > middle but a sudden jump. > As I mentioned the middle space is empty because |x-x1| never meets > values around K. So no small (x' ,y') > I'm looking for more sufisticated, robust, reliable mappings that can > convert any irregular quadrilateral given that it has a known boundary > to a rectangle. > Any ideas?What did not try to invent the fools who are too stupid to solve the trivial dipole equation. VLV
mapping an irregular 2D shape to represent monitor screen
Started by ●October 10, 2011
Reply by ●October 12, 20112011-10-12
Reply by ●October 12, 20112011-10-12
On 10/12/2011 12:59 AM, Elnaz wrote:>> What you described below seems more complicated than need be (if I >> understand it) but I wouldn't knock it if it works. > > It doesn't work, I mean it works somewhere doesn't work somewhere > else. I got straight lines around the boundaries but nothing in the > middle but a sudden jump. > As I mentioned the middle space is empty because |x-x1| never meets > values around K. So no small (x' ,y') > I'm looking for more sufisticated, robust, reliable mappings that can > convert any irregular quadrilateral given that it has a known boundary > to a rectangle. > Any ideas? >> >> What you described below seems more complicated than need be (if I >> understand it) > > You mean K - |x-x1| is complicated? or finding its respective pairs on > the boundaries? It's only couple of lines of code.I think you'll find that you need to deal with more than just the boundaries. The equations of the hyperbolas in the ideal case are simple enough, but those simple equations assume point sources and sensors. Nearby point dipoles are hard to come by.> p.s. Jerry, I like your signature sentence very much, Wise!Thanks. Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●October 14, 20112011-10-14
On 10/12/2011 06:59 AM, Elnaz wrote:> I'm looking for more sufisticated, robust, reliable mappings that can > convert any irregular quadrilateral given that it has a known boundary > to a rectangle.> Any ideas?Yes, in the computer graphic world this is known as a bilinear coons warp. In short you define four functions for the four irregular sides of your quad and the warp maps this into a rectangle. There is a nice article about that in the book "Graphic Gems IV". It focuses on image manipulation so the article goes into the details on how to solve this probem fast for huge amounts of pixels. However the mathematical principle can be applied to just one coodinate as well. A Google search for "bilinear coons warp" will find the article and the source-code. Cheers, Nils
Reply by ●October 14, 20112011-10-14
On 10/14/2011 1:29 AM, Nils wrote:> On 10/12/2011 06:59 AM, Elnaz wrote: >> I'm looking for more sufisticated, robust, reliable mappings that can >> convert any irregular quadrilateral given that it has a known boundary >> to a rectangle. > >> Any ideas? > > Yes, in the computer graphic world this is known as a bilinear coons warp. > > In short you define four functions for the four irregular sides of your > quad and the warp maps this into a rectangle. > > There is a nice article about that in the book "Graphic Gems IV". It > focuses on image manipulation so the article goes into the details on > how to solve this probem fast for huge amounts of pixels. However the > mathematical principle can be applied to just one coodinate as well. > > A Google search for "bilinear coons warp" will find the article and the > source-code.Suppose that when all is done, some straight lines in the physical world, distorted by the sensing setup, don't emerge from the coons warp as straight lines? As an alternate, you could probably use a Schwartz-Christoffel transformation, but that doesn't guarantee linear-to-linear either. Jerry -- Engineering is the art of making what you want from things you can get.
