distance to quadratic surface
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From: rych on 28 Jan 2010 02:44 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
From: cire g on 29 Jan 2010 07:47
Hello, I have the similar problem in finding an analytical solutions of a cone intersection a line, two cones intersecting, and three cones intersecting. best regards, eric rych wrote: > 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 > > > > |