Convert Geodetic Cordinates to Lambert Conformal Conic

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I have an FAA sectional map from here. Each package includes a .tif of the chart in question, a .htm file describing the chart, and a .tfw world file. The map projection is a Lambert conformal conic projection.

I'm working on a C# app that needs to be able to convert normal WGS84 (lat/lon) coordinates to (x,y) positions (pixel) on the map.

Things I know about the map:

The Spatial_Reference_Information section from the HTML that came with the map says that it is a Lambert conformal conic projection, and uses WGS83. The Lambert conic parameters are:

Standard_Parallel: 46.666670
Standard_Parallel: 41.333330
Longitude_of_Central_Meridian: -120.995830
Latitude_of_Projection_Origin: 46.750000

And I the world file for the map looks like this:

63.5278030000
0.0000000000
0.0000000000
-63.5278030000
-411036.1271487368
261242.9877766267

What's the simplest way to convert my geodetic coordinates into Cartesian coordinates for my map?

C# code/examples preferred, but C++/Java/others are okay too. It's the algorithm I need, not the code.

Thanks in advance for the help!

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SeyedPooya Soofbaf On BEST ANSWER

There are several libraries for coordinate conversions.

You can see these: GeoUtility, Proj.Net, GeoTools and GeoTools Example And ...