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Old 10-07-2013, 06:37 PM   #1
captainentropy
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Perl Math::Bezier returns Math::Bizarre output


I'm using Math::Bezier to create a smooth curve from a set of three x,y coordinates. I'm not having problems with accomplishing that per se, my program does, essentially, what I need it to. The thing is that 1) to get the interpolated curve to go through the correct maximum y-value (which was fed into the module as one of the three control sets) I have to multiply the resulting y-values by 2. And 2) the shape of the curve is wrong. It comes out as a simple, symmetric parabola (p<0). When I graph the same points in Excel using the "XY Scatter With Smooth Lines" function (which uses Bezier interpolation) it comes out perfect, exactly as it should. So, anyone have an idea what's happening?

Here's an example of what I'm seeing https://www.dropbox.com/s/vtwwzkvo1l...er_example.pdf

Let me explain the curves in the linked file. "Control points Alpha" is just the control set I'm using to evaluate my output. In this case the three XY coordinates are (0,0; 208,67.07; 690,0). "(Excel)" means, duh, graphed in Excel. Math::Bezier Alpha corrected y-max is the resulting curve if I multiply all the y-values of Math::Bezier Alpha original by 2. Control points Beta is adding two more control points (104,33.54; 312,33.54), graphed in Excel. And Math::Bezier Beta is the output of Math::Bezier with the two extra control points. The first curve - "control points Alpha (Excel)" - is exactly what I want to see from my perl script. Hopefully, someone has some experience using Math::Bezier and can tell me what I'm doing wrong. I emailed the author but have not received a reply.

Here's my code, though it works, I'm not sure if it's the Math::Bezier that's at fault, or me. It's probably me but I can't find anyone discussing Math::Bezier anywhere.

Code:
#!/usr/bin/perl
use warnings;
use Getopt::Long;
use Getopt::ArgvFile;
use Math::Bezier;
use Math::Round;

@peaks = $ARGV[0];
open ( IN, "@peaks" ) or die "Can't open file: $!";

while (<IN>)	{
	next if /#/;		# remove the header
	next if /start/;	# including column descriptor
	chomp;
	my @fields = split ("\t",$_);
	print "fixedStep chrom=$fields[0] start=$fields[1] step=1\n"; 
	my $bezier = Math::Bezier->new(0,0,$fields[4],$fields[6],$fields[3],0); # this feeds my control points into the bezier module
	my @points = $bezier->curve($fields[3]);
	while (@points) {
		my ($x,$y) = splice(@points,0,2);
		my $ynew = nearest(0.01,($y*2));
		print "$ynew\n";
			}
		}
close IN;
Thanks!

Last edited by captainentropy; 10-15-2013 at 04:40 PM. Reason: clarity
 
Old 10-08-2013, 12:48 PM   #2
smallpond
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I think that Excel is trying to fit a curve that passes through a set of points. Math::Bezier is trying to create a curve based on a set of control points as described here. You might want to look at Math::Spline.

Also I really like the idea of a Math::Bizarre module on CPAN.

Last edited by smallpond; 10-08-2013 at 03:18 PM.
 
Old 10-08-2013, 05:33 PM   #3
captainentropy
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Quote:
Originally Posted by smallpond View Post
I think that Excel is trying to fit a curve that passes through a set of points. Math::Bezier is trying to create a curve based on a set of control points as described here. You might want to look at Math::Spline.

Also I really like the idea of a Math::Bizarre module on CPAN.
Thanks smallpond, I'll try out Math::Spline and report back
 
Old 10-09-2013, 09:00 PM   #4
captainentropy
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OK, I modified the program as follows (main part in bold):
Code:
#!/usr/bin/perl
use warnings;
use Getopt::Long;
use Getopt::ArgvFile;
use Math::Spline;
use Math::Derivative;
use Math::Round;

@peaks = $ARGV[0];
open ( IN, "@peaks" ) or die "Can't open file: $!";

while (<IN>)	{
	next if /#/;		# remove the header
	next if /start/;	# including column descriptor
	chomp;
	my @fields = split ("\t",$_);
	print "fixedStep chrom=$fields[0] start=$fields[1] step=1\n";
	require Math::Spline;
	my @x=(0,$fields[4],$fields[3]); # control X-values for spline
	my @y=(0,$fields[6],0);          # control Y-values for spline
	$spline = Math::Spline->new(\@x,\@y);
	my $iter=0;
	
	while ($iter <= $fields[3])	{
		my @ynew = $spline->evaluate($iter);
		my @yRound = nearest(0.01,@ynew);
		print "@yRound\n";
		$iter ++;
					}
		}
close IN;
The output is not any better than with Math::Bezier. In fact, the y-max for the curve is greater than the y-max I used in the control (one of the three points used as controls) that I fed into the module. And adding more control points makes the curve even worse looking. Here's a graph of the output (orange curve). The one main feature that I would really like to have is the curves go through the maximum x,y point (x:208 y:67.07 in this example).

https://www.dropbox.com/s/pl9jt8fk0w...r_example2.pdf

Perhaps I'm using Math::Spline incorrectly. Any ideas?

Update:10.15.2013. I experimented with adding more control points, which I have to interpolate on my own, and I found a couple more points in certain places along the hypothetical curve get me a lot closer to the Excel ideal. It's probably close enough, but I'll leave this "unsolved" until I complete a few more runs.

Last edited by captainentropy; 10-15-2013 at 05:17 PM. Reason: update
 
  


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