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I want to draw a polygon on the world map in different map projections, for example, in mercator proj or stereographic one. They must correspond to ICAO ares G (https://aviationweather.gov/satellite?gis=off). But I got a trouble with geo coordinates. I see that my geo coordinates are differ than they should be. For example, in EPSG:3395 or EPSG:5588 my geocoords coincides in one point on the map, but in EPSG:4326 they are out of bounds of the world map. How can I draw geometry accordingly to geo coordinates? I am using GEOTOOLS. Look at the point (-155.27,67.3623) - it is on the north west of North America, but after reprojection this point appears somewhere in the Pacific Ocean

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The issue is that when you call addLayer and addPoint you pass in the projected coordinate system not the geographic coordinate system, but your points are stored in lon/lat which is geographic so they are in the wrong place. Changing those calls to use geoCRS gives you the following (which is quite close to area G:

enter image description here

though I think it's probably more accurate to use a densified box (polygon = (Polygon) Densifier.densify(polygon, 0.001);) which looks like this, obviously you'll need some more points (or to define the box in your oblique stereo coordinate system) to get an accurate box:

enter image description here

Also to help debug I added the labels to the points style:

Style style = SLD.createSimpleStyle(TYPE, Color.GREEN);
TextSymbolizer textSymb = styleBuilder.createTextSymbolizer(Color.black, styleBuilder.createFont("Arial", 10),
    "fred");
textSymb.setLabel(ff.function("Concatenate", ff.function("getX", ff.property("location")), ff.literal(" "),
    ff.function("getY", ff.property("location"))));
//textSymb.setHalo(styleBuilder.createHalo(Color.white, 1));
style.featureTypeStyles().get(0).rules().get(0).symbolizers().add(textSymb);
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