Cartesian co-ordinate rotation around an Axis

[fraizerangus]

Hi Monks I'm writing a Perl program to rotate some Cartesian co-ordinates around an axis (acting as a pivot) but the new cartesian co-ordinates are way out, (* is dot product and x cross product). Its broken down into 2 subroutines, can anyone give any pointers or tell me where I'm going wrong please?! many thanks in advance x

sub Axis {

#2 sets of cartesian XYZ co-ordinates on the axis
($Xl1, $Yl1, $Zl1, $Xl2, $Yl2, $Zl2) = @_;

$Axx = $Xl1 - $Xl2; 
$Axy = $Yl1 - $Yl2;
$Axz = $Zl1 - $Zl2;

$Vform = V($Axx,$Axy,$Axz);

$eq = sqrt($Axx**2 + $Axy**2 + $Axz**2);

$Unitvector = 1/$eq * $Vform;

return($Vform, $Unitvector);

}

sub rotator {

(*xcord, *ycord, *zcord, *TotalnumberofCoords, $lineUnitvector, $Xline
+coord, $Ylinecoord, $Zlinecoord) = @_;

$angle = 9.4;
$translation = 0.4;

$coefl1 = 1-cos($angle);
$coefl2 = sin($angle);

($LUVx, $LUVy, $LUVz) = &VectorBreakdown($lineUnitvector);

for (my $i = 0; $i < @TotalnumberofCoords; $i++) {

$Xco[$i] = $xcord[$i] - $Xlinecoord;
$Yco[$i] = $ycord[$i] - $Ylinecoord;
$Zco[$i] = $zcord[$i] - $Zlinecoord;

$Vector[$i] = V($Xco[$i], $Yco[$i], $Zco[$i]);

$scal[$i] = $lineUnitvector * $Vector[$i];

$f[$i] = $scal[$i] * ($lineUnitvector - $Vector[$i]);

$f[$i] = $coefl1 * $f[$i];

$s[$i] = $lineUnitvector x $Vector[$i];

$s[$i] = $coefl2 * $s[$i];

($fx[$i], $fy[$i], $fz[$i]) = &VectorBreakdown($f[$i]);

($sx[$i], $sy[$i], $sz[$i]) = &VectorBreakdown($s[$i]);

$xo[$i] = $xcord[$i] + $fx[$i] + $sx[$i] + ($transl * $LUVx);

$yo[$i] = $ycord[$i] + $fy[$i] + $sy[$i] + ($transl * $LUVy);

$zo[$i] = $zcord[$i] + $fz[$i] + $sz[$i] + ($transl * $LUVz);

$xo[$i] = sprintf("%.3f", $xo[$i]);

$yo[$i] = sprintf("%.3f", $yo[$i]);

$zo[$i] = sprintf("%.3f", $zo[$i]);

}

return(\@xo, \@yo, \@zo);

}

[FunkyMonk]

$angle = 9.4;
$translation = 0.4;

$coefl1 = 1-cos($angle);
$coefl2 = sin($angle);

$angle looks to be measured in degrees, whereas, cos, sin etc use radians.

</guess>

[zentara]

You might find some clues by looking at a pure trig solution to the problem in Rotate a 3D vector. Maybe try to compare outputs for similar inputs, and see where your logic/math error is? One big error to watch out for is degree/rad mixups.

[moritz]

Start by posting a self-contained example that we can actually run, including the output and expected output.

You're using a lot of functions that you never declare, and neither tells us what they do, nor if you're certain that they do what you think they do (are they tested?).

[fraizerangus]

Hi Sorry I was trying to simplify the code, here's the working example:

#XYZ Coordinates of point 1 on the axis
$Xl1 =   -3.902;
$Yl1 =    9.353;
$Zl1 =   -1.556;

#XYZ Coordinates of point 2 on the axis
$Xl2 =  -47.470;
$Yl2 =   -2.908;
$Zl2 =  -17.596;

#XYZ Coordinates of a midpoint on the axis
$XlM =  -20.284;
$YlM =    4.548;
$ZlM =   -7.261;

#XYZ data for all the cartesian co-ordinates to be rotated
@BMxcord = ( -18.731, -19.287, -20.545, -21.421, -19.594, -18.388, -18
+.784, -17.107, -20.681, -21.870, -23.239, -24.201, -21.604, -20.782, 
+-19.827, -29.918, -29.341, -30.384, -31.579, -28.853, -29.953, -27.73
+5, -29.939, -30.878, -31.833, -33.036, -30.088, -29.320, -29.582, -28
+.457, -31.275, -31.996, -31.636, -30.654, -31.599, -30.210, -31.741, 
+-32.428, -32.135, -30.851, -30.080, -33.281, -34.391, -35.291, -33.83
+4, -30.598, -29.385, -28.185, -27.196, -29.374, -28.083, -28.213, -26
+.851, -26.976, -28.281, -27.192, -27.020, -25.897, -27.447, -27.316, 
+-26.408, -28.108, -28.126, -28.039, -27.400, -26.592, -29.432, -29.51
+5, -28.622, -30.990, -27.788, -27.250, -25.745, -25.000, -27.931, -27
+.790, -27.786, -27.688, -25.280, -23.859, -23.145, -22.033, -23.597, 
+-24.127, -23.878, -23.247, -24.368, -23.758, -23.128, -22.938, -21.86
+4, -24.018, -23.448, -22.595, -23.733, -22.035, -23.167, -22.322, -23
+.984, -23.948, -22.987, -22.261, -25.376, -26.289, -25.329, -27.739, 
+-22.959, -22.088, -20.683, -19.718, -22.774, -22.821, -24.225, -20.53
+1, -19.203, -18.510, -17.411, -19.234, -19.923, -19.918, -20.834, -18
+.981);
@BMycord = (  -0.135,  -1.473,  -1.396,  -0.553,  -2.172,  -2.409,  -3
+.016,  -3.128,  -2.300,  -2.245,  -2.337,  -1.730,  -3.351,  -4.304, 
+ -3.453,  -5.632,  -6.925,  -7.735,  -7.459,  -7.732,  -8.003,  -6.95
+8,  -8.747,  -9.551, -10.352, -10.461, -10.510,  -9.797,  -8.595, -10
+.451, -10.936, -11.805, -11.519, -10.802, -13.294, -13.487, -13.642, 
+-12.075, -11.978, -12.716, -12.298, -12.532, -11.563, -12.246, -10.23
+2, -13.835, -14.574, -13.675, -13.667, -15.839, -16.600, -17.957, -18
+.613, -20.031, -12.904, -11.993, -10.918, -10.550, -11.319, -12.286, 
+-13.135, -12.169, -10.396,  -9.393,  -9.998,  -9.339,  -8.849,  -7.90
+9,  -6.677,  -7.549, -11.220, -11.886, -12.043, -11.783, -13.252, -13
+.802, -13.011, -15.033, -12.456, -12.616, -11.284, -11.206, -13.346, 
+-14.755, -15.578, -15.119, -16.813, -10.226,  -8.913,  -8.514,  -8.03
+0,  -7.892,  -6.509,  -6.140,  -5.581,  -4.860,  -4.280,  -3.934,  -8
+.686,  -8.313,  -9.148,  -8.598,  -8.459,  -7.371,  -8.392,  -7.521, 
+-10.461, -11.246, -11.497, -11.631, -12.556, -13.385, -12.310, -11.49
+0, -11.666, -10.387, -10.096, -12.599, -13.930, -14.829, -15.660, -14
+.717);
@BMzcord = ( -11.272, -11.499, -12.335, -12.114, -10.170,  -9.308,  -7
+.671,  -6.966, -13.307, -14.145, -13.447, -13.882, -15.184, -14.461, 
+-13.654, -11.352, -11.736, -12.500, -12.407, -10.500,  -9.622,  -9.75
+5, -13.241, -14.011, -13.136, -13.408, -14.903, -15.991, -16.229, -16
+.622, -12.094, -11.190,  -9.746,  -9.448, -11.440, -11.070, -12.949, 
+ -8.840,  -7.411,  -7.074,  -6.199,  -6.554,  -6.233,  -5.196,  -5.63
+0,  -7.746,  -7.494,  -7.804,  -7.069,  -8.366,  -8.281,  -8.920,  -9
+.055,  -9.478,  -8.884,  -9.228,  -8.147,  -7.798, -10.586, -11.759, 
+-11.716, -12.711,  -7.647,  -6.586,  -5.331,  -4.682,  -6.290,  -5.07
+9,  -5.324,  -4.806,  -4.974,  -3.803,  -3.924,  -2.971,  -3.645,  -2
+.257,  -1.288,  -2.135,  -5.100,  -5.309,  -5.250,  -4.727,  -6.625, 
+ -6.529,  -7.770,  -8.724,  -7.760,  -5.757,  -5.673,  -4.211,  -3.82
+8,  -6.380,  -6.415,  -7.449,  -5.409,  -7.485,  -5.431,  -6.480,  -3
+.405,  -2.000,  -1.168,  -0.347,  -1.390,  -1.967,   0.151,  -1.574, 
+ -1.364,  -0.490,  -1.042,  -0.257,  -0.095,  -1.247,   0.420,  -2.35
+8,  -2.942,  -3.385,  -2.922,  -4.139,  -3.875,  -5.113,  -5.290,  -5
+.920);

#Array size for for loop
$BMatoms = 122;



($LineVform, $LineUnitvector) = &Haxell($Xl1, $Yl1, $Zl1, $Xl2, $Yl2, 
+$Zl2);

(*xo, *yo, *zo) = &rotator(\@BMxcord, \@BMycord, \@BMzcord, $BMatoms, 
+$LineUnitvector, $XlM, $YlM, $ZlM);

######################
#SUBROUTINES
######################


sub Haxell {

($Xl1, $Yl1, $Zl1, $Xl2, $Yl2, $Zl2) = @_;

$Axx = $Xl1 - $Xl2; 
$Axy = $Yl1 - $Yl2;
$Axz = $Zl1 - $Zl2;

$Vform = V($Axx,$Axy,$Axz);

$vector = sqrt($Axx**2 + $Axy**2 + $Axz**2);

$Unitvector = 1/$vector * $Vform;

return($Vform, $Unitvector);

}

sub rotator {

use Math::Vector::Real;

(*xcord, *ycord, *zcord, $BMatoms, $LineUnitvector, $XlM, $YlM, $ZlM) 
+= @_;

$angrad = 9.4;
$transl = 0.4;

my $coefl1;
my $coefl2;
my @Xco;
my @Yco;
my @Zco;
my @Vector;
my @scal;
my @f;
my @s;
my @fx;
my @fy;
my @fz;
my @sx;
my @sy;
my @sz;
my @xo;
my @yo;
my @zo;

$coefl1 = 1-cos($angrad);
$coefl2 = sin($angrad);

($LUVx, $LUVy, $LUVz) = &VectorBreakdown($LineUnitvector);

for (my $i = 0; $i < $BMatoms; $i++) {

$Xco[$i] = $xcord[$i] - $XlM;
$Yco[$i] = $ycord[$i] - $YlM;
$Zco[$i] = $zcord[$i] - $ZlM;

$Vector[$i] = V($Xco[$i], $Yco[$i], $Zco[$i]);

$scal[$i] = $LineUnitvector * $Vector[$i];

$f[$i] = $scal[$i] * ($LineUnitvector - $Vector[$i]);

$f[$i] = $coefl1 * $f[$i];

$s[$i] = $LineUnitvector x $Vector[$i];

$s[$i] = $coefl2 * $s[$i];

($fx[$i], $fy[$i], $fz[$i]) = &VectorBreakdown($f[$i]);

($sx[$i], $sy[$i], $sz[$i]) = &VectorBreakdown($s[$i]);

$xo[$i] = $xcord[$i] + $fx[$i] + $sx[$i] + ($transl * $LUVx);

$yo[$i] = $ycord[$i] + $fy[$i] + $sy[$i] + ($transl * $LUVy);

$zo[$i] = $zcord[$i] + $fz[$i] + $sz[$i] + ($transl * $LUVz);

$xo[$i] = sprintf("%.3f", $xo[$i]);

$yo[$i] = sprintf("%.3f", $yo[$i]);

$zo[$i] = sprintf("%.3f", $zo[$i]);

}

return(\@xo, \@yo, \@zo);

}



sub VectorBreakdown {

($complete) = @_;

my @personal = ();

@personal = split(/,/, $complete);


$personal[0] = substr($personal[0], 1);

$personal[2] = substr($personal[2], 0, -1);

return ($personal[0], $personal[1], $personal[2]);

}

[dHarry]

I have difficulty understanding your initial post as well as your clarifying post. If you want to rotate you typically need a Rotation matrix R. You represent the point you want to rotate by a vector v and perform the multiplication R.v. This is fairly straightforward. CPAN is your friend: Math::VectorReal contains an example of rotating a vector with a rotation matrix.

HTH

Harry