i came up with a (very bad) hexagon shader. it decomposes the hexagon into 6 triangles, and then uses barycentric weights to determine if a point is inside a valid triangle, it sums all of these and should be about less than 1 + some epsilon.

#version 330

uniform vec2 uResolution;
uniform float uTime;

float circle(vec2 pos, float r) {
  return length(pos) - r;
}

float degrees_to_radians(float degrees) {
  return (2 * 3.14) * degrees / 360;
}

float area_of_triangle(vec2 a, vec2 b, vec2 c) {
  return abs((a.x*(b.y - c.y) + b.x*(c.y - a.y) + c.x*(a.y - b.y)) * 0.5);
}

float triangle(vec2 a, vec2 b, vec2 c, vec2 position) {
  float area = area_of_triangle(a, b, c);
  
  float aa = area_of_triangle(a, b, position);
  float ba = area_of_triangle(b, position, c);
  float ca = area_of_triangle(a, position, c);

  float ab = aa / area;
  float bb = ba / area;
  float cb = ca / area;
  
  float total = ab + bb + cb;
  
  return total <= 1.00199 ? 1 : 0;
}

vec2 rotate(vec2 point, float deg) {
  float x = point.x * cos(degrees_to_radians(deg)) - point.y * sin(degrees_to_radians(deg));
  float y = point.x * sin(degrees_to_radians(deg)) + point.y * cos(degrees_to_radians(deg));
  
  return vec2(x, y);
}

float hexagon(vec2 pos, float r) {
  pos = rotate(pos, uTime * 100);
  
  vec2 a = vec2(0, 0);
  vec2 b = vec2(0, r);
  vec2 c = vec2(cos(degrees_to_radians(30)) * r,
  sin(degrees_to_radians(30)) * r);
  
  float d = 0; 
  
  for (int i = 0; i < 6; ++i) {
          d += triangle(rotate(a, 60 * i), rotate(b, 60 * i), rotate(c, 60 * i), pos);
  }

  return d;
}


out vec4 outColor;

void main()
{
  // -- CURRENT --
  // top-left (0, 1)
  // top-right (1, 1)
  // bottom-left (0, 0)
  // bottom-right (1, 0)
  // middle: (.5, .5)


  // -- DESIRED -- 
  // top-left (-1, 1)
  // top-right (1, 1)
  // bottom-left (-1, -1)
  // bottom-right (1, -1)
  // middle: (0, 0)
  
  vec2 uv = gl_FragCoord.xy / uResolution;
  uv = uv * 2 - 1;
  uv.x *= uResolution.x / uResolution.y;

  vec4 color = vec4(hexagon(uv, .3));

  outColor = color;
}