Find coordonates of a point relative to a second plane in 3Dby dot_binary Tags: coordonates, plane, point, relative 

#1
Nov1012, 05:30 AM


#2
Nov1012, 08:29 AM

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"Change position", I take it, means to translate the origin. If the new coordinate sytem has center at [itex](x_0, y_0, z_0)[/itex] in the old coordinates then a point that has coordinates (x, y, z) in the old coordinate system will have coordinates [itex](x x_0, y y_0, zz_0)[/itex] in the new coordinate system.
"Rotate on all axis" is harder. A rotation about any axis can be reduced to a series of rotations about the coordinate axes and each of those can be written as a matrix product. Rotation about the zaxis through angle [itex]\theta[/itex] is given by [tex]\begin{bmatrix}cos(\theta) & sin(\theta) & 0 \\ sin(\theta) & cos(\theta) & 0 \\ 0 & 0 & 1\end{bmatrix}[/tex] Rotation about the yaxis through angle [itex]\theta[/itex] is given by [tex]\begin{bmatrix}cos(\theta) & 0 &sin(\theta) \\ 0 & 1 & 0 \\ sin(\theta) & 0 & cos(\theta) \end{bmatrix}[/tex] Rotation about the xaxis through angle [itex]\theta[/itex] is given by [tex]\begin{bmatrix}1 & 0 & 0 \\ 0 & cos(\theta) & sin(\theta)\\ 0 & sin(\theta) & cos(\theta)\end{bmatrix}[/tex] 


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