[Proj] Ortho Projection Question

[Noel Zinn (cc)]

Brian,

If ESRI's PROJECTION["Local"] is also known as ESRI's "Local Cartesian", 
then you'll need an ellipsoidal version of the orthographic projection to 
match it.  I suspect that Proj.4's +proj=ortho is a spherical version of the 
orthographic.

You make it difficult to test this by tossing in a transformation from NAD27 
to WGS84 (+proj=longlat +datum=WGS84 +no_defs no_defs) with parameters 
unknown to me.  Is this NADCON?  How about one problem at a time?  Can you 
provide ESRI and Proj.4 lat/lon outputs in NAD27?

You can find the equations for the ellipsoidal orthographic here:
http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf

The inverse given in the link is iterative.  Charles Karney has provided a 
closed inverse that has not yet been included in the linked paper.

Noel

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)

-----Original Message----- 
From: Brian Krzys
Sent: Thursday, November 03, 2011 8:37 PM
To: Proj at lists.maptools.org
Subject: [Proj] Ortho Projection Question

I am trying to duplicate an ESRI "local" projection with Proj.4
parameters and can't quite get it worked out.  The ESRI custom
projection file has:

PROJCS["Twin_Creeks_Mine_Grid (Local)",
GEOGCS["GCS_North_American_1927",
DATUM["D_North_American_1927",SPHEROID["Clarke_1866",6378206.4,294.9786982]],
PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],
PROJECTION["Local"],
PARAMETER["False_Easting",14225.0],
PARAMETER["False_Northing",36603.0],
PARAMETER["Scale_Factor",1.0],
PARAMETER["Azimuth",0.0],
PARAMETER["Longitude_Of_Center",-117.183175],
PARAMETER["Latitude_Of_Center",41.217358],
UNIT["Foot_US",0.3048006096012192]]

The equivalent Proj.4 parameters I've setup are:

+proj=ortho +datum=NAD27 +lat_0=41.217358 +lon_0=-117.183175
+x_0=14225.0 +y_0=36603.0 +units=us-ft no_defs

I want to convert to lat-long WGS84 so I am going to this:

+proj=longlat +datum=WGS84 +no_defs no_defs

My input test point is:

x = 15768.1900000000 y = 65384.1600000000

In ESRI land I get back (lat-long): 41.160175 -117.177571

With Proj.4 I am getting: 41.0674232619472 -117.296349865729

I've also tried this with a couple of specific +to_wgs transformations
on the ESRI and Proj.4 side and still cannot get the conversions to
match.

This is all with Proj.4 Rel. 4.7.1, 23 September 2009.

What I'm wondering about is the ortho "projection" and if there is
maybe a better option to use?  I've searched around the web a bit and
read about concerns with ortho so also not sure if there is a proj
update beyond 4.7.1 that might help?  I know this whole kind of
direct-Cartesian conversion isn't the best thing, but generally stuck
just trying to match what Arc is doing.

Thanks for the help, Brian.
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