Solve & RotationMatrix
- To: mathgroup at smc.vnet.net
- Subject: [mg75836] Solve & RotationMatrix
- From: gentilemathieu at gmail.com
- Date: Fri, 11 May 2007 06:20:04 -0400 (EDT)
Hello, Can somebody please help me understand how to make this works? \[Alpha] =.; \[Beta] =.; \[Gamma] =.; VectX = {1, 0, 0}; VectY = {0, 1, 0}; VectZ = {0, 0, 1}; RotX = RotationMatrix[\[Alpha], VectX]; RotY = RotationMatrix[\[Beta], VectY]; RotZ = RotationMatrix[\[Gamma], VectZ]; Rotation = RotX.RotY.RotZ; PtO = {0, 0, 0}; PtA = {1, 0, 0}; PtB = {0, 1, 1}; VectN = Normalize[Cross[PtA - PtO, PtB - PtO]]; Solve[VectN == Rotation.VectY, {\[Alpha], \[Beta], \[Gamma]}] I have a crystal with a face on which I can measure the XYZ coordinates of 3 points PtO, PtA, PtB. >From these I compute the vector normal to the surface. I would then like to compute the Alpha, Beta, Gamma rotation angles about the x, y and z axis respectively as compared to the ideal position for which the crystal face would lie in the XZ plane, i.e. its normal vector being the y axis. Thank you, Best regards, Mathieu