+/*
+ 0 at threshold, 1 at 0, with 1/x falloff.
+ */
+Real
+peak_around (Real epsilon, Real threshold, Real x)
+{
+ if (x < 0)
+ return 1.0;
+ return max (- epsilon * (x - threshold) / ((x + epsilon) * threshold), 0.0);
+}
+
+/*
+ 0 at 0, 1 at standard_x, and increasing thereafter.
+ */
+Real
+convex_amplifier (Real standard_x, Real increase_factor, Real x)
+{
+ return (exp (increase_factor * x / standard_x) - 1.0) / (exp (increase_factor) - 1.0);
+}
+
+string
+camel_case_to_lisp_identifier (const string &in)
+{
+ vector<char> out;
+
+ /* don't add '-' before first character */
+ out.push_back (char (tolower (in[0])));
+
+ for (size_t inpos = 1; inpos < in.size (); inpos++)
+ {
+ if (isupper (in[inpos]))
+ out.push_back ('-');
+ out.push_back ( char (tolower (in[inpos])));
+ }
+
+ string result (&out[0], out.size ());
+ replace_all (&result, '_', '-');
+
+ return result;
+}
+
+Offset
+get_point_in_y_direction (Offset orig, Real slope, Real dist, Direction dir)
+{
+ if (slope == infinity_f)
+ return orig + Offset (dir * dist, 0.0);
+
+ Real x = slope == 0.0 ? 1.0 * dir : 1.0 * sign (slope) * dir;
+ Real y = slope * x;
+ Real angle = atan2 (y, x);
+
+ complex<Real> orig_c (orig[X_AXIS], orig[Y_AXIS]);
+ complex<Real> to_move = polar (dist, angle);
+ complex<Real> res = orig_c + to_move;
+
+ return Offset (real (res), imag (res));
+}