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distance to quadratic surface

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106922] distance to quadratic surface
  • From: rych <rychphd at gmail.com>
  • Date: Thu, 28 Jan 2010 02:44:59 -0500 (EST)

I'm trying to find a distance from a point {xi,yi,zi} to a quadratic
surface g(x,y,). (With the intent to use the least squares to actually
determine the best quadratic surface later)


dist2[x_, y_, z_] = (x - xi)^2 + (y - yi)^2 + (z - zi)^2;
g[x_, y_] = c0 + c1 x + c2 y + c3 x y + c4 x^2 + c5 y^2;

dx = D[dist2[x, y, g[x, y]], x]
dy = D[dist2[x, y, g[x, y]], y]

Solve[{dx == 0, dy == 0}, {x, y}]


Solve never comes back. Neither would Resolve. It's a system of cubic
equations in x and y, is it not solvable?

Thanks



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