map uv coordinates to do a background-position: cover in screen space

background-cover.frag

vec2 backgroundCoverUV(vec2 uv, vec2 resolution, vec2 texResolution) {
  vec2 s = resolution;
  vec2 i = texResolution;
  float rs = s.x / s.y;
  float ri = i.x / i.y;
  vec2 new = rs < ri ? vec2(i.x * s.y / i.y, s.y) : vec2(s.x, i.y * s.x / i.x);
  vec2 offset = (rs < ri ? vec2((new.x - s.x) / 2.0, 0.0) : vec2(0.0, (new.y - s.y) / 2.0)) / new;
  return uv * s / new + offset;
}

//
// use like this:
//

uniform vec2 screenReso;
uniform vec2 mapReso;
uniform sampler2D map;

// map fragment screen coordinate to 0,0 / 1,1 space
vec2 st = gl_FragCoord.xy / screenReso.xy;

// get uv applying the background-position: cover logic
vec2 uv = backgroundCoverUV(st, screenReso, mapReso);

// get texture color
gl_FragColor = texture2D(map, uv);