+ if(refmap)
+ {
+ // refmap: a reference map to define the heights
+ // alpha = weight, color = value
+ // if more than one color value is used, colors are also matched
+
+ // we do linear regression, basically
+ // f'(x, y) = f(x, y) * scale + offset
+ // sum((f(x, y) * scale + offset - ref_y(x, y))^2 * ref_a(x, y)) minimize
+
+ // diff by offset:
+ // sum(-2*ref_y(x,y)*ref_a(x,y) + 2*scale*f(x,y)*ref_a(x,y) + 2*offset*ref_a(x,y)) = 0
+ // diff by scale:
+ // sum(-2*f(x,y)*ref_a(x,y) + 2*scale*f(x,y)^2*ref_a(x,y) + 2*offset*f(x,y)*ref_a(x,y)) = 0
+ // ->
+ // offset = (sfa*sfya - sffa*sya) / (sfa*sfa-sa*sffa)
+ // scale = (sfa*sya - sa*sfya) / (sfa*sfa-sa*sffa)
+
+ double f, a;
+ double o, s;
+ double sa, sfa, sffa, sfva, sva;
+ double mi, ma;
+ sa = sfa = sffa = sfva = sva = 0;
+ mi = 1;
+ ma = -1;
+ for(y = 0; y < h; ++y)
+ for(x = 0; x < w; ++x)
+ {
+ a = (int)refmap[(w*y+x)*4+0];
+ v = (map[(w*y+x)*4+0]*0.114 + map[(w*y+x)*4+1]*0.587 + map[(w*y+x)*4+2]*0.299);
+ v = (v - 128.0) / 127.0; // value 0 is forbidden, 1 -> -1, 255 -> 1
+#ifdef C99
+ f = creal(imgspace1[(w*y+x)]);
+#else
+ f = imgspace1[(w*y+x)][0];
+#endif
+ if(a <= 0)
+ continue;
+ if(y < mi)
+ mi = y;
+ if(y > ma)
+ ma = y;
+ sa += a;
+ sfa += f*a;
+ sffa += f*f*a;
+ sfva += f*v*a;
+ sva += v*a;
+ }
+ sfa /= (w*h);
+ sffa /= (w*h);
+ sffa /= (w*h);
+ sfva /= (w*h);
+ if(mi < ma)
+ {
+ o = (sfa*sfva - sffa*sva) / (sfa*sfa-sa*sffa);
+ s = (sfa*sva - sa*sfva) / (sfa*sfa-sa*sffa);
+ }
+ else // all values of v are equal, so we cannot get scale; we can still get offset
+ {
+ o = ((sva - sfa) / sa);
+ s = 1;
+ }
+ // now apply user-given offset and scale to these values
+ // (x * s + o) * scale + offset
+ // x * s * scale + o * scale + offset
+ offset += o * scale;
+ scale *= s;
+ }
+ else if(scale == 0)