Hi. My CAD program uses a world cartesian coordinate system, WCS. The User is able to define his own User Coordinate System, UCS which is defined by a new origin and an X-direction vector and a Y- direction Vector. All points are stored in WCS, but I need to convert between the 2. Example: UCS Origin: X=438.8587 Y=180.644 Z=0 X-Direction: X=0.9644 Y=0.2481 Z=0.0913 Y-Direction: X=0.8617 Y=0.5029 Z=0.0679 A point is at X=495.835 Y=203.1717 Z=43.2574 What are it's coordinates in th UCS? Many thanks, Dave Coventry

Adam,

Thanks for the reply.

I've tried as you suggest and have the following results, which don't appear to be correct:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
UCS Origin X Vector X unit Vector Y Vector Y unit Vector Z Vector Z unit Vector
438.86 528.29 0.9644 463.38 0.8459 -8560.4229 -0.1064
180.64 135.89 0.2481 270.45 0.4937 3878.8991 0.0482
0 50 0.0913 36.51 0.0667 79904.8204 0.9932
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Matrix
0.96 0.85 -0.11 438.86
0.25 0.49 0.05 180.64
0.09 0.07 0.99 0
0 0 0 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MatrixTransposed Point NewPoint
0.96 0.25 0.09 -468.06 495.84 64.49
0.85 0.49 0.07 -460.44 203.17 62.2
-0.11 0.05 0.99 37.99 43.26 37.99
0 0 0 1 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The Above is taken from a spreadsheet with the calculation cells as below:
(Copy and paste into your spreadsheet to see my workings)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
UCS Origin X Vector X unit Vector Y Vector Y unit Vector Z Vector Z unit Vector
438.86 528.29 =B2/SQRT($B$2*$B$2+$B$3*$B$3+$B$4*$B$4) 463.38 =D2/SQRT($B$2*$B$2+$B$3*$B$3+$B$4*$B$4) =B3*D4-D3*B4 =F2/SQRT($F$2*$F$2+$F$3*$F$3+$F$4*$F$4)
180.64 135.89 =B3/SQRT($B$2*$B$2+$B$3*$B$3+$B$4*$B$4) 270.45 =D3/SQRT($B$2*$B$2+$B$3*$B$3+$B$4*$B$4) =B4*D2-D4*B2 =F3/SQRT($F$2*$F$2+$F$3*$F$3+$F$4*$F$4)
0 50 =B4/SQRT($B$2*$B$2+$B$3*$B$3+$B$4*$B$4) 36.51 =D4/SQRT($B$2*$B$2+$B$3*$B$3+$B$4*$B$4) =B2*D3-D2*B3 =F4/SQRT($F$2*$F$2+$F$3*$F$3+$F$4*$F$4)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Matrix
=C2 =E2 =G2 =A2
=C3 =E3 =G3 =A3
=C4 =E4 =G4 =A4
0 =E5 =G5 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Matrix Point NewPoint
=A7 =A8 =A9 =-D7*A13+-D8*B13+-D9*C13 495.84 =F13*A13+F14*B13+F15*C13+F16*D13
=B7 =B8 =B9 =-D7*A14+-D8*B14+-D9*C14 203.17 =F13*A14+F14*B14+F15*C14+F16*D14
=C7 =C8 =C9 =-D7*A15+-D8*B15+-D9*C15 43.26 =F13*A15+F14*B15+F15*C15+F16*D15
0 =E11 =G11 1 1 =F13*A16+F14*B16+F15*C16+F16*D16
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I realise that I'm taking huge liberties here and I beg your indulgence.

Many thanks,

Dave Coventry

Sorry about the mangled text. It should still import into Open Office Calc (or Excel) if you set the delimeter as 'space'.