static double transformBetweenDoubleRanges(double x, DoubleRange src, DoubleRange dest) {
  ret dest.start+dest.length()*doubleRatio(x-src.start, src.length());
}

static DoubleRange transformBetweenDoubleRanges(DoubleRange r, DoubleRange src, DoubleRange dest) {
  ret r == null ?:
    DoubleRange(transformBetweenDoubleRanges(r.start, src, dest),
      transformBetweenDoubleRanges(r.end, src, dest));
}