I'm sure I've done this before, so here is some minimal code to generate a HSV colour swatch (in Processing as an example).

minimal hsv to rgb

void setup() {
  size(256,256);
  
  colorMode(RGB,1.0);
  for(int x=0;x<width;x++) {
    
    float h = (float)x/width;
    float v = 1;
    
    for(int y=0;y<width;y++) {    
      
      float s = (float)y/height;
      
      float r = (max(0,min(1,abs(h*2%2-1)*3-1))*s+(1-s))*v;
      float g = (max(0,min(1,abs(((1-h)+1/3.0)*2%2-1)*3-1))*s+(1-s))*v;
      float b = (max(0,min(1,abs((h+1/3.0)*2%2-1)*3-1))*s+(1-s))*v;
        
      set(x,y,color(r,g,b));
    }
  }
}