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)!.