Mapping lat/lon coordinate pairs to a given EPSG:4326 projected cartesian coordinate system

Question

I want to find out the timezone a GPX track is in by looking up the first coordinate pair. I took the shapefile from Timezone Boundary Builder and created a PNG image via qgis from it (using the default projection, "WGS 84 – EPSG:4326"), with one color per defined timezone. I also have a color-timezone mapping.

I know the width and the height of the image (which represents all possible coordinates on earth), and I have a lat/lon pair. Now I "only" need to map the coordinate pair to the respective pixel (x/y) to get it's color, which then maps to the timezone I need.

But how do I calculate the mapping? I know how to do it using the Mercator projection (I wrote a function doing that some time ago: mercatorProjection, but I'm struggling to find respective code for EPSG:4326 (or WGS84).

Answer 1

EPSG:4326 is not a projected coordinate system, but ellipsoidal coordinate system, using degrees for longitude and latitude coordinates. In your case these [lng, lat] values are simply used on a flat surface as cartesian coordinates.

This then means you have simple linear cartesian math. Upper side of image has y=90, bottom has y=-90, left side has x=-180, right side has x=180. Conversion to image pixels is then just linear function, taking into account image size in pixels.

Answer 2

Just to also leave the code here: This is how I map coordinates to the image (m_timezoneMap is a QImage created from the said PNG file):

const double width = m_timezoneMap.size().width();
const double height = m_timezoneMap.size().height();

// Scale the coordinates to the image size, relative to the image center
int mappedLon = std::round(lastCoordinates.lon() / 180.0 * (width / 2.0));
int mappedLat = std::round(lastCoordinates.lat() / 90.0 * (height / 2.0));

// Move the mapped coordinates to the left lower edge
mappedLon = width / 2 + mappedLon;
mappedLat = height - (height / 2 + mappedLat);

// Get the respective pixel's color
const auto timezoneColor = m_timezoneMap.pixelColor(mappedLon, mappedLat).name();