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Numerisch Partielle Ableitung einer 3D Datenmatrix |
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| NorrinRadd |
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Anmeldedatum: 04.01.16
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Verfasst am: 04.01.2016, 15:50
Titel: Numerisch Partielle Ableitung einer 3D Datenmatrix
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Hallo liebe community, ich bin relativ neu im Umgang mit Matlab und habe ein Problem
das ich alleine nicht in den Griff bekommen. Ich habe die Frage auch schon im Englischen Matlab forum gestellt und poste deshalb hier die englische Frage, ich hoffe das ist in Ordnung?
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I´ll start off with a very general description of what I want to achieve:
I have a few 3D Matrix with the Size of 167x176x2000 Datapoints. The Data is from a physical measurement and unfortunately the datapoints are not evenly spaced in all of these Datasets. In some the are. The Data represents the Potential of a Conservative force. Hence the force can be written as the negative gradient of this potential.
Here is what I need to do:
I want to calculate the partial derivative of this 3D dataset in an arbitrary direction. The Vector would always be parallel to the xy-Plane, albeit not necessarily to the x- or y-Axis. And this is my main problem. In a later step i also want to calculate the Force in (-)-Z-Direction.
Could you point me in the right direction regarding this enterprise? Do i need to make a Spline-Fit in the direction of the derivate before i perform the actual derivation?
I am not sure how to smooth the Data prior to calculating the differentiation of real data. And i fear that, depending on the direction i choose for derivative , the point Density might be to low because i might not intersect enough points of the Data.
Would i need to do a Tricubic Interpolation?Should i project nearby Datapoints onto the "path" of my derivative? Which method is delivering the best result? The derivates needs to be as "good" as possible so i feat a first order central difference might not be good enough.
This is what would be included in my ideal solution: For all these data sets there already exists a closely related Matrix which i´d like to use to "draw" the direction of the actually desired derivate as these additional Matrix shows some topological features wich i want to related to the derivate to be computet. Is this possible? i also need to display cuts through the 3d-Dataset after i calculated the derivative and it would be much more precise to do this by "drawing" the desired direction. Th direction of the cuts and the lenght of the cuts would need to be specified completly seperated from the direction of the derivative tho!
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http://www.mathworks.com/matlabcent.....lyspaced-entrys-in-matlab
Zuletzt bearbeitet von NorrinRadd am 04.01.2016, 16:42, insgesamt einmal bearbeitet
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| laternenjoebla |
Gast
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Verfasst am: 04.01.2016, 16:36
Titel:
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Hallo,
ohne dass ich mir das Problem durchgelesen habe oder Gedanken dazu gemacht habe, wäre es nicht schlecht wenn du einen Link zum Thema machen könntest, dann könnte man sich im Zweifelsfall durchlesen was andere Benutzer bereits dazu gesagt haben und schreibt nicht längst Bekanntes.
mfg
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