Finding values in scattered 3D data
in [Matlab]
|
From: Blaine on 26 May 2010 13:45 So here's the situatio: I have a set of 3d data, lets call it 'd', that is evenly distributed across each axis (in this case 0:.1:6), but i need to find a subset s.t. d=.75. And because i know the nature of the solution, i know the shape of the solution curve is a balloon-shaped surface. My code currently looks like this: for x=0:0.1:6 for y=-:0.1:6 for z=0:0.1:0.6 d = function(x,y,z) if d = .75 d_true = [d_true d]; x_true = [x_true x]; y_true = [y_true y]; z_true = [z_true z]; end end end end tri = elaunay(x_true,y_true); trisurf(tri,x_true,y,true,z,true); But this method is EXTREMELY slow. I believe there is an interpolative method to find the solution surface, but I have tried for a couple hours now to no avail. Note: the function used to calculate d cannot process vectors. To clarify you cannot use x = y = z = 0:0.1:6 d = function(x,y,z) and get values at each point Thanks!
From: us on 26 May 2010 14:07 "Blaine " <EvilDonut0(a)gmail.com> wrote in message <htjmnh$dv0$1(a)fred.mathworks.com>... > So here's the situatio: > > I have a set of 3d data, lets call it 'd', that is evenly distributed across each axis (in this case 0:.1:6), but i need to find a subset s.t. d=.75. And because i know the nature of the solution, i know the shape of the solution curve is a balloon-shaped surface. > > My code currently looks like this: > > for x=0:0.1:6 > for y=-:0.1:6 > for z=0:0.1:0.6 > d = function(x,y,z) > if d = .75 > d_true = [d_true d]; > x_true = [x_true x]; > y_true = [y_true y]; > z_true = [z_true z]; > end > end > end > end > > tri = elaunay(x_true,y_true); > trisurf(tri,x_true,y,true,z,true); > > But this method is EXTREMELY slow. I believe there is an interpolative method to find the solution surface, but I have tried for a couple hours now to no avail. > > Note: the function used to calculate d cannot process vectors. To clarify you cannot use > x = y = z = 0:0.1:6 > d = function(x,y,z) > and get values at each point > > Thanks! well... how can CSSMers possibly be of any help without the most crucial information: what does MYFUNCTION() do(?!)... us
From: Walter Roberson on 26 May 2010 14:21 Blaine wrote: > I have a set of 3d data, lets call it 'd', that is evenly distributed > across each axis (in this case 0:.1:6), but i need to find a subset s.t. > d=.75. And because i know the nature of the solution, i know the shape > of the solution curve is a balloon-shaped surface. > My code currently looks like this: > > for x=0:0.1:6 > for y=-:0.1:6 > for z=0:0.1:0.6 > d = function(x,y,z) > if d = .75 Just to be sure: I take it that the actual check in your code is for d to be within a tolerance of 0.75? 0.75 _is_ exactly representable in binary floating point, but chances are that your function has some inherent round-off error. > d_true = [d_true d]; > x_true = [x_true x]; > y_true = [y_true y]; > z_true = [z_true z]; > end > end > end > end > But this method is EXTREMELY slow. I believe there is an interpolative > method to find the solution surface, but I have tried for a couple hours > now to no avail. If you already have the complete set of function values, you could use isosurface, or you could extract the coordinates from the complete surface list. If you do not already have the complete set of values, then what _do_ you have available that would be suitable for interpolating? Is the function relatively smooth? Is it symmetric (which would allow you to cut down the search according to the number of axes of symmetry) ? > Note: the function used to calculate d cannot process vectors. To > clarify you cannot use > x = y = z = 0:0.1:6 > d = function(x,y,z) > and get values at each point It is not able to process vectors now, but is it plausible that we might be able to assist you in vectorizing it?
From: dpb on 26 May 2010 14:29 Walter Roberson wrote: > Blaine wrote: > >> I have a set of 3d data, lets call it 'd', that is evenly distributed >> across each axis (in this case 0:.1:6), but i need to find a subset >> s.t. d=.75. And because i know the nature of the solution, i know the >> shape of the solution curve is a balloon-shaped surface. >> My code currently looks like this: >> >> for x=0:0.1:6 >> for y=-:0.1:6 >> for z=0:0.1:0.6 >> d = function(x,y,z) >> if d = .75 > .... >> But this method is EXTREMELY slow. I believe there is an interpolative >> method to find the solution surface, but I have tried for a couple >> hours now to no avail. > > If you already have the complete set of function values, you could use > isosurface, or you could extract the coordinates from the complete > surface list. .... If the surface is relatively smooth, one way to proceed might be to use response surface to fit the function at a set of design points and use it instead. Then, the number of function evaluations is reduced significantly at the cost of, perhaps, some increase in error in the estimate. Surely, as Walter says, the function value won't be identically 0.75 (or any other specific value, either) at the set of points in the 3D mesh you're now using. RH Myers, Response Surface Methodology (2nd Ed was Wiley, I think???) is one of my favorites (altho that worked w/ Ray years ago strongly influences that... :) ) --
From: Blaine on 26 May 2010 14:37
It has to do with fire control. The function basically calculates a hit percentage based on azimuth bias (x), elevation bias (y), and scatter(z), using cumulative normal distributions. The cumulative normal distribution is calculated as: NORMDIST(x,mean,std_dev) = (1/2)*(erf((v-mean)/(sqrt(2)*std_dev))-erf(((-inf)-mean)/(sqrt(2)*std-dev)) v = the value for which you want the distribution mean = arithmetic mean of the distribution std_dev = standard deviation of the distribution You can derive this by integrating he normal distribution found in statistics textbooks from -infinity to x I cannot divulge the complete computation, but az bais and el bias are used as mean, scatter as std_dev, and x is always one of two constants based on the size of the target. For the purposes of my question lets just say my function, as stated in my code above, is: NORMDIST(2,az_bias,scatter) - NORMDIST(3,el_bais,scatter) and i want this computation performed on every point specified by az_bias = 0:0.1:2 (x) el_bias = 0:0.1:3 (y) scatter = 0:0.1:6 (z) |