[Proj] Robinson projection

[Mikael Rittri]

Bernie wrote:

> PROJ.4 places the 40 degree latitude at 0.4968, whereas Robinson places it at 0.4958.
> [ --- ]
> Is this a simple mistyping,

Yes, it must be. Well spotted. 

I don't have the Robinson article, but the tables can be 
found on http://en.wikipedia.org/wiki/Robinson_projection ,
where the PDFE value for latitude 40 is 0.4958 as you say. 

Out of curiosity, I computed the first, second and third 
differences of the PDFE column from Wikipedia. I give them 
here (multiplied by 10000):

First	Second  Third differences
620
	   0
620		  0
	   0
620		  0
	   0
620		  0
	   0
620		  0
	   0
620		  0
	   0
620		 -2
	  -2
618		 -3
	  -5
613		 -3
	  -8
605		 -4
	 -12
593		 -4
	 -16
577		 -4
	 -20
557		 -5
	 -25
532		 -6	
	 -31
501		-12
	 -43
458		-48
	 -91
367		-37
	-128
239

Even though the PDFE column is not specified by a formula, it seems
to define a nice and smooth function, since the third differences 
decrease smoothly (except the final one, from the highest latitudes).

If one replaces the latitude 40 value by 0.4968, as the Proj.4 code
has done, the hiccup is clearly seen in the differences:

First	Second  Third differences
620
	   0
620		  0
	   0
620		  0
	   0
620		  0
	   0
620		  0
	   0
620		  0
	   0
620		 +8
	  +8
628		-33
	 -25
603		+27
	  +2
605		-14
	 -12
593		 -4
	 -16
577		 -4
	 -20
557		 -5
	 -25
532		 -6	
	 -31
501		-12
	 -43
458		-48
	 -91
367		-37
	-128
239

By the way, the Robinson projection is analysed in this article:

Cengizhan Ipbuker:
Numerical Evaluation of the Robinson Projection.
Cartography and Geographic Information Science, 
Volume 31, Number 2, April 2004, pages 79-88.
http://www.ingentaconnect.com/content/acsm/cagis/2004/00000031/00000002/art00002

Regards,

Mikael Rittri
Carmenta
Sweden
http://www.carmenta.com

-----Original Message-----
From: proj-bounces at lists.maptools.org [mailto:proj-bounces at lists.maptools.org] On Behalf Of Bernhard Jenny
Sent: den 6 juni 2011 12:12
To: proj at lists.maptools.org
Subject: [Proj] Robinson projection

I think I found an inconsistency in the PROJ.4 implementation of the Robinson projection. Robinson specifies the vertical distribution and length of parallels in his 1974 text for every 5 degrees of increasing latitude.  PROJ.4 places the 40 degree latitude at 0.4968, whereas Robinson places it at 0.4958. This corresponds to a vertical shift of about 9 km at 40 degrees north and south. Is this a simple mistyping, or are there any reasons to change Robinson's definition?

Reference:
Robinson, A. (1974). A New Map Projection: Its Development and Characteristics. International Yearbook of Cartography, p. 145-155.

Thanks,
Bernie
 
Bernhard Jenny
Institute of Cartography and Geoinformation ETH Zurich jenny at karto.baug.ethz.ch http://jenny.cartography.ch


_______________________________________________
Proj mailing list
Proj at lists.maptools.org
http://lists.maptools.org/mailman/listinfo/proj