MODULE Slider2;

IMPORT Geometry;

FUNC s = SliderVal(a, 
                   b, 
                   c) IS 
      (E y :: 
        b 
      = (s, y) 
    REL (a, c)) 
END;

FUNC b = OnLine(a, 
                c, 
                t) IS 
      b 
    = (t, 0) 
  REL (a, c) 
END;

FUNC p = LinePt(k, 
                l, 
                m, 
                a, 
                b) IS 
      (E t 
       = SliderVal(k, 
                   l, 
                   m) 
   :: p 
    = OnLine(a, 
             b, 
             t)) 
END;

(* "p" is the 
   point at 
   parametric 
   location 
   "t" on the 
   Bezier 
   curve "a", 
   "b", "c", 
   "d". *)

FUNC p = OnCurve(a, 
                 b, 
                 c, 
                 d, 
                 t) IS 
      (E ab
       , bc
       , cd
       , abc
       , bcd 
   :: ab 
    = OnLine(a, 
             b, 
             t) 
  AND bc 
    = OnLine(b, 
             c, 
             t) 
  AND cd 
    = OnLine(c, 
             d, 
             t) 
  AND abc 
    = OnLine(ab, 
             bc, 
             t) 
  AND bcd 
    = OnLine(bc, 
             cd, 
             t) 
  AND p 
    = OnLine(abc, 
             bcd, 
             t)) 
END;

(* The points 
   "k", "l", 
   and "m" 
   compose a 
   slider, the 
   points "a", 
   "b", "c", 
   and "d" are 
   the control 
   points of a 
   Bezier 
   curve, and 
   "pt" is the 
   point at 
   parametric 
   location 
   "t" on the 
   curve, 
   where "t" 
   is the 
   slider 
   value of 
   "k", "l", 
   and "m" 
   (i.e., the 
   ratio 
   "Dist(k,l2)/Dist(k,m)", 
   where "l2" 
   is the 
   projection 
   of "l" onto 
   the segment 
   "km"). *)

FUNC pt = CurvePt(k, 
                  l, 
                  m, 
                  a, 
                  b, 
                  c, 
                  d) IS 
      (E t :: 
        t 
      = SliderVal(k, 
                  l, 
                  m) 
    AND pt 
      = OnCurve(a, 
                b, 
                c, 
                d, 
                t)) 
END;