[GRASS-dev] Re: [GRASS GIS] #929: g.transform: dump coeffs and transform sparse points

[GRASS GIS]

#929: g.transform: dump coeffs and transform sparse points
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  Reporter:  hamish       |       Owner:  grass-dev at lists.osgeo.org
      Type:  enhancement  |      Status:  closed                   
  Priority:  normal       |   Milestone:  7.0.0                    
 Component:  Imagery      |     Version:  svn-trunk                
Resolution:  fixed        |    Keywords:  g.transform              
  Platform:  All          |         Cpu:  All                      
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Comment (by glynn):

 Replying to [comment:4 hamish]:

 > I am wondering if this is useful for us but I am reminded that in stats
 that the simplest model fit that explains the data is usually the best one
 to use. You can use high nth-order polynomials to exactly fit the data,
 but what you are really doing is fitting the noise.

 I would expect that you're typically trying to find a suitable
 approximation to a complex analytic function (i.e. a typical cartographic
 or geometric projection).

 For many projections, a quadratic polynomial will be a poor fit. The main
 reason for using cubic functions for interpolation is that you can specify
 both the value and first derivative at each end (4 degrees of freedom).

 If you consider approximating sin(x) symmetrically about zero: you can get
 a reasonable approximation with a cubic function, but the optimal
 quadratic approximation will actually be linear.

 Note that the most complex case in the above code is the same as
 g.transform with order=3, i.e. generalised cubic (rather than bicubic).

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Ticket URL: <https://trac.osgeo.org/grass/ticket/929#comment:5>
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