Rovaniemi University of Applied Sciences / School of Technology
Technical Computing and Programming 2007 (3 ects)
DPIT & International Students
Veikko Keränen

A possible assignment for the second exercise work:

Study the (12.5 MB) notebook O:\Opettajat\Veikko Keränen\_IAS2005\Veikko_MMAnotebooks\Chains.nb (created for IAS, Murmansk, May 2005) and use it to create your own graphics based possibly on other strings like DNA (found e.g. in O:\Opettajat\Veikko Keränen\VeikkoKeranen1999-2006\IMS_presentation.nb (2003)). One example of the graphics constructed in   Chains.nb  is the following string over four letters:


In creating this image we have been using constructs like this:

tangentVector = ∂_tmyCurve[t] ;

normalVector = ∂_ttangentVector ;

binormalVector = tangentVector  normalVector ; 

unitTangentVector = tangentVector/Norm[tangentVector] ;

unitNormalVector = normalVector/Norm[normalVector] ;

unitBinormalVector = binormalVector/Norm[binormalVector] ;

In addition, utilising the results of Linear Algebra we may align parts of the chain by changing the coordinate basis. This in turn can be accomplished simply by using the following kind of rotation matrix:  

Clear[rotMatrix] ;

rotMatrix[t_] := Transpose[{unitTangentVector, unitNormalVector, unitBinormalVector}]//Evaluate ;

You might also enjoy studying O:\Opettajat\Veikko Keränen\VeikkoKeranen1999-2006\___6_85_Chain  (18.5 MB).

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