Re:Help with geometry problem required.
- To: mathgroup at smc.vnet.net
- Subject: [mg20851] [mg20851] Re:[mg20801] Help with geometry problem required.
- From: Arnold Seiken <seikena at union.edu>
- Date: Wed, 17 Nov 1999 03:41:14 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Michael, Here is an example which illustrates how to find the matrix of an isometry in R3 given 3 non-collinear points and their images: M={{a11,a12,a13,b1},{a21,a22,a23,b2},{a31,a32,a33,b3},{0,0,0,1}}; Simplify[ Solve[ {M.{1,0,0,1} =={4,4,2,1}, M.{0,1,0,1} == { 3,3,2,1}, M.{0,0,1,1}=={4,3,3,1}, {a11,a12,a13 }.{a21,a22,a23 }==0, {a11,a12,a13 }.{a31,a32,a33 }==0, {a31,a32,a33 }.{a21,a22,a23 }==0, (a11)^2 +(a12)^2 + (a13)^2 == 1, (a21)^2 +(a22)^2 + (a23)^2 == 1, (a31)^2 +(a32)^2 + (a33)^2 == 1, Det[{{a11,a12,a13 },{a21,a22,a23 },{a31,a32,a33 }}]==1}, {a11,a12,a13,a21,a22,a23,a31,a32,a33,b1,b2,b3}] ] You can then take the output of the above and input (M/.%[[1]])//MatrixForm to get the solution in a nice looking form. Arnold Seiken