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MathGroup Archive 1998

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Beginner question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14078] Beginner question
  • From: bertronj at indra.com (Jean-Denis S Bertron)
  • Date: Tue, 22 Sep 1998 03:25:08 -0400
  • Organization: Indra's Net - Public Internet Access
  • Sender: owner-wri-mathgroup at wolfram.com

Hi all,
I've got this very simple problem, for which I know the solution, but
somehow I can't get mathematica to solve it. The question is : Is it
possible to parameterize a parabolic arc using a bezier curve ?
Here are the basic equations:

The definition of a bezier curve is: eqns = {
X0 == Dx,
Y0 == Dy,
X1 == X0 + Cx /3,
Y1 == Y0 + Cy /3,
X2 == X1 + (Cx+Bx)/3,
Y2 == Y1 + (Cy+By)/3,
X3 == X0 + Cx + Bx + Ax,
Y3 == Y0 + Cy + By + Ay
}
and 
with bezX[t_] == Ax t^3 + Bx t^2 + Cx t + Dx
     bezY[t_] == Ay t^3 + By t^2 + Cy t + Dy with 0 <= t <= 1.
The canonical parabolic arc is defined by: 2 (bezX[t] + bezY[t]) =
(bezX[t] - bezY[t])^2 +1 If there is a solution the boundary conditions
are: bnds = {bezX[0] == 1, bezY[0] == 0, bezX[1] ==0,bezY[1] ==1}

I entered all this stuff in mathematica (eqns,bnds,bezX[t_],bezY[t_])
and each statement returns nice algebraic rules. When I finally give it
the following: SolveAlways[Implies[eqns,2 (bezX[t] + bezY[t]) =
(bezX[t] - bezY[t])^2 +1], t] All it does is reply:
Set::write: Tag Times in 2 (bezX[t] + bezY[t]) is protected.
SolveAlways::elist:
  ---------- Message text not found ---- (....)

What does this mean ? 
J.D.

--
Jean-Denis Bertron	jd.bertron at pobox.com 
http://rainbow.rmi.net/~bertronj  
Disclaimer(message):- Offending(message)!.


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