I said Linear Regression. Actually, the guy is using least squares, since we are trying to fit a quadratic function. The difficult part is that it is a R2->R2 function, that is, (u,v)->(x,y)
But I still want to seek a solution based on the mesh triangles mentioned before, since I believe fitting quadratic curves may be good for one side of the table, but not good for other parts. Thanks! --- In [email protected], "pakachunka" <[EMAIL PROTECTED]> wrote: > > Thomas, > > we have already one guy making the linear regression to fit a > quadractic surface into the points collected. But quadractic is not > always a good solution for a given non-linearty. Unfortunatelly some > of the non-linearities can´t be fitted by quadractic shapes. Because > of that, I believe we start to depend a lot on insights for each > particular tablet, and we need to make thousands. It seems not very > practical, now, but I may be wrong. > > The idea of using triangles is because we are going to use two > vertices of each triangle as the "basis" for the transform. Once we > know in which triangle we are, we can use the "basis transformation > matrix" for each triangle, and all calculations will be linear and > fast. I believe this is a type of interpolation. My concern in this > case is when you move from one triangle domain to another. Straight > lines will suffer a lot in this case. > > But now I am curious if you figured out another way to interpolate. > > Let me know if you are interested on having a tablet yourself. We > can make one for you. > > Thanks, > > Tor > > > --- In [email protected], Thomas Hruska <thruska@> wrote: > > > > pakachunka wrote: > > > Thank you again Thomas! > > > > > > Is there some text referent to "bounding boxes" I can read? Is > there > > > some literature to follow what you are saying? > > > > > > Just to make you understand better what I am doing: I am making a > > > driver for a new type of low cost tablet for linux. Tablets in > general > > > have problems with linearization, so I am creating a way to > convert > > > the (u,v) voltages measured by the tablet, into (x,y) position > in the > > > screen. For that I need a linearization procedure, during which > the > > > user put the tablet stylus over marks in the screen. That is > when the > > > mesh of triangles mentioned before are created. After the mesh is > > > ready and set, I use some Conformal Transform to transform the > (u,v) > > > voltages into (x,y) positions, based on the mesh. For that I > need to > > > determine in which triangle of the mesh the (u,v) voltages are > contained. > > > > > > Everything needs to run in a PIC microcontroller. > > > > > > The tablet aims education and will be freeware. > > > > > > Thanks! > > > > > > Tor > > > > Quick search on Google for "bounding box" turns up: > > > > http://en.wikipedia.org/wiki/Minimum_bounding_rectangle > > > > > > Why a triangle mesh though? If you collected 9 (u,v) data points > from > > the user (corners, midpoints, center), can't you just use linear > > interpolation for the values based on those points? > > > > Or you could figure out a mathematical formula that applies some > sort of > > quadratic curve that better fits the display. Collect a whole > bunch of > > sample (u,v) -> (x,y) values and plug 'em into Excel and stare at > and > > fiddle with the numbers for a while. There are always patterns to > be > > found. If you can avoid the triangle mesh with a few quadratic > curves, > > it would, IMO, be worth the effort and generally perform well. > > > > Collecting data points from the user that form rectangles seems > simpler > > to me than building a big ol' triangle mesh. Simple typically > works > > better (not always the case). But, hey, I'm not an electrical > engineer. > > > > -- > > Thomas Hruska > > CubicleSoft President > > Ph: 517-803-4197 > > > > *NEW* MyTaskFocus 1.1 > > Get on task. Stay on task. > > > > http://www.CubicleSoft.com/MyTaskFocus/ > > >
