For a stepbystep demonstration of the protocol, please open a dynamic worksheet (link), go to View and then Construction Protocols.
No.  Name  Definition  Value 

1  Number a  a = 0.15  
2  Number c  c = 1.67  
3  Function p_{u}  p_{u}(x) = a x²  p_{u}(x) = 0.15 x² 
4  Function p_{d}  p_{d}(x) = (a) x² + c  p_{d}(x) = (0.15) x² + 1.67 
5  Point P  P = (0.36, 0.22)  
6  Point G  Point on p_{d}  G = (1.19, 1.46) 
7  Line j  Tangent to p_{d} at x = x(G)  j: y = 0.36x + 1.88 
8  Line k  Line through G perpendicular to j  k: x + 0.36y = 0.67 
9  Segment i  Segment [P, G]  i = 1.49 
10  Point P'  P mirrored at k  P' = (1.05, 0.03) 
11  Point G'_{1}  G mirrored at k  G'_{1} = (1.19, 1.46) 
12  Segment i'  Segment [P', G'_{1}]  i' = 1.49 
13  Ray l  Ray through G, P'  l: 1.49x  0.14y = 1.57 
14  Point E  Intersection point of p_{u}, l  E = (1.07, 0.17) 
15  Segment m  Segment [G, E]  m = 1.29 
16  Line n  Tangent to p_{u} at x = x(E)  n: y = 0.32x  0.17 
17  Line p  Line through E perpendicular to n  p: x  0.32y = 1.12 
18  Point G'  G mirrored at p  G' = (0.22, 1.14) 
19  Point E'  E mirrored at p  E' = (1.07, 0.17) 
20  Segment m'  Segment [G', E']  m' = 1.29 
21  Ray q  Ray through E', G'  q: 0.97x  0.85y = 1.19 
22  Point H  Point on p_{d}  H = (1.61, 1.28) 
23  Segment b  MiraReflection[P, H, a, c]  b = 2.24 
23  Segment d  MiraReflection[P, H, a, c]  d = 0.84 
23  Point I  MiraReflection[P, H, a, c]  I = (1.75, 0.46) 
23  Ray e  MiraReflection[P, H, a, c]  e: 0.59x + 0.6y = 1.3 
24  Point J  Intersection point of q, e  J = (0.37, 1.82) 
25  Text text1  text1 = "Drag P to draw a small picture; Right click on P or J to toggle Trace On. Drag c to change vertical alignment of the two parabolas; Drag a to change the curvature of the parabolas." 

26  Point A  A = (2, 3)  
27  Point B  B = (2, 3)  
28  Line f  Line through A parallel to yAxis  f: x = 2 
29  Line g  Line through B parallel to yAxis  g: x = 2 
30  Point C  Intersection point of p_{u}, f  C = (2, 0.6) 
31  Point D  Intersection point of p_{u}, g  D = (2, 0.6) 
32  Line h  Tangent to p_{u} at x = x(C)  h: y = 0.6x  0.6 
33  Line r  Tangent to p_{u} at x = x(D)  r: y = 0.6x  0.6 
34  Line s  Line through C perpendicular to h  s: x + 0.6y = 2.36 
35  Line t  Line through D perpendicular to r  t: x  0.6y = 2.36 
36  Line g'  g mirrored at t  g': 0.47x  0.88y = 1.47 
37  Line f'  f mirrored at s  f': 0.47x + 0.88y = 1.47 
38  Point F  Intersection point of f', g'  F = (0, 1.67) 