# Converting the Equation of a Line from Symmetric to Parametric Form
# Programmers: Ryan Priest & Alex Mathew
# Math 253 Honors Section 201
# Fall 2012
# Instructor: Philip Yasskin
restart:
with(Maplets[Tools]): with(Maplets[Elements]): with(plots):
StartEngine();

rand1:=rand(-10..10):

NewLine:=proc()
global parx,pary,parz;
local a,b,c,d,e,f,symx,symy,symz;

a:=rand1();
b:=rand1();
c:=rand1();
d:=rand1();
e:=rand1();
f:=rand1();

while b=0 do
   b:=rand1();
end do;
while d=0 do
   d:=rand1();
end do;
while f=0 do
   f:=rand1();
end do;

parx:=a+b*t;
pary:=c+d*t;
parz:=e+f*t;
symx:=(b^(-1))&*(x-a);
symy:=(d^(-1))&*(y-c);
symz:=(f^(-1))&*(z-e);

Set(MMLSymx(value)=symx);
Set(MMLSymy(value)=symy);
Set(MMLSymz(value)=symz);

Set(TFparx="");
Set(replyparx="");
Set(TFpary="");
Set(replypary="");
Set(TFparz="");
Set(replyparz="");
Set(reply="");
end proc:

Checkparx:=proc()
global parx,pary,parz;
local userparx;
userparx:=Get(TFparx::polynom,corrections=true,update=true);
if userparx=parx then
  Set(replyparx="Correct");
  Set(reply="Great job!");
elif userparx=-parx then
  Set(replyparx="Almost");
  Set(reply="Look at the hint and fix the center.");
else
  Set(replyparx="Incorrect");
  Set(reply="Try again.");
end if;
end proc:

Checkpary:=proc()
global parx,pary,parz;
local userpary;
userpary:=Get(TFpary::polynom,corrections=true,update=true);
if userpary=pary then
  Set(replypary="Correct");
  Set(reply="Great job!");
elif userpary=-symy then
  Set(replypary="Almost");
  Set(reply="Look at the hint and fix the center.");
else
  Set(replypary="Incorrect");
  Set(reply="Try again.");
end if;
end proc:

Checkparz:=proc()
global parx,pary,parz;
local userparz;
userparz:=Get(TFparz::polynom,corrections=true,update=true);
if userparz=parz then
  Set(replyparz="Correct");
  Set(reply="Great job!");
elif userparz=-symz then
  Set(replyparz="Almost");
  Set(reply="Look at the hint and fix the center.");
else
  Set(replyparz="Incorrect");
  Set(reply="Try again.");
end if;
end proc:

Showparx:=proc()
global parx,pary,parz;
Set(replyparx="Shown");
Set(reply="Now you know the answer. Next time try yourself.");
Set(TFparx=parx);
end proc:

Showpary:=proc()
global parx,pary,parz;
Set(replypary="Shown");
Set(reply="Now you know the answer. Next time try yourself.");
Set(TFpary=pary);
end proc:

Showparz:=proc()
global parx,pary,parz;
Set(replyparz="Shown");
Set(reply="Now you know the answer. Next time try yourself.");
Set(TFparz=parz);
end proc:

Hint1:=proc()
global parx,pary,parz;
Set(reply="The symmetric equation\n    t = (x-p)/u = (y-q)/v = (z-r)/w\nis equivalent to the parametric equation\n    (x, y, z) = (p+t*u, q+t*v, r+t*w).");
end proc:

LineMaplet2:=Maplet(onstartup = RunWindow(MAIN),
Window[MAIN](title="Converting the Equation of a Line from Symmetric to Parametric Form",
[ valign=none, inset=0, spacing=0,
  [ Button("New Equations", Evaluate(function="NewLine"), background=magenta),
    [ valign=none, inset=0,spacing=0, border=true, 
      caption="Goal: Find the parametric equation of the line equivalent to",
      [ halign=none,
        "the symmetric equations:",
        HorizontalGlue()
      ],
      [ MathMLViewer[MMLSymx](value=(1/b&*(x-a)), width=95, height=50, background=white),
        "=",
        MathMLViewer[MMLSymy](value=(1/d&*(y-c)), width=95, height=50, background=white),
        "=",
        MathMLViewer[MMLSymz](value=(1/f&*(z-e)), width=95, height=50, background=white)
      ]
    ],
    Button("Quit", Shutdown(), background=pink)
  ],
  BoxColumn( valign=none, inset=0, spacing=0, border=true, 
    caption="Step 1: Set each expression equal to t and solve for x, y and z:",
    [ halign=none,
      "x =", 
      TextField[TFparx](width=20, background=turquoise),
      HorizontalGlue(),
      Button("Hint", Evaluate(function="Hint1"), background=Orange),
      Button("Check", Evaluate(function="Checkparx"), background=green),
      TextField[replyparx](width=10, background=white),
      Button("Show",Evaluate(function="Showparx"), background=yellow)
    ],
    [ halign=none,
      "y =", 
      TextField[TFpary](width=20, background=turquoise),
      HorizontalGlue(),
      Button("Hint", Evaluate(function="Hint1"), background=Orange),
      Button("Check", Evaluate(function="Checkpary"), background=green),
      TextField[replypary](width=10, background=white),
      Button("Show",Evaluate(function="Showpary"), background=yellow)
    ],
    [ halign=none,
      "z =", 
      TextField[TFparz](width=20, background=turquoise),
      HorizontalGlue(),
      Button("Hint", Evaluate(function="Hint1"), background=Orange),
      Button("Check", Evaluate(function="Checkparz"), background=green),
      TextField[replyparz](width=10, background=white),
      Button("Show",Evaluate(function="Showparz"), background=yellow)
    ]
  ),
  [ halign=none,
    TextBox[reply](width=40, height=4, editable=false, background=white)
  ],
  [ halign=none,
    "Instructor: Philip Yasskin",
    HorizontalGlue(),
    "Programmers: Alex Mathew and Ryan Priest",
    HorizontalGlue(),
    "Copyright 2012, P. Yasskin"
  ]
]
)
):
Maplets[Display]( LineMaplet2 );