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German: Bahnkreuzung

English translation: intersection of the Lissajous curve







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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
German term or phrase:Bahnkreuzung
English translation:intersection of the Lissajous curve
Entered by:Meturgan
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5:00am Dec 6, 2004Login or register (free) for more options.
German to English translations [PRO]
Medical - Medical: Dentistry / CO2 Laser Ablation
German term or phrase: Bahnkreuzung
Bei gleicher Zeitdauer (1 s) kann dagegen das entsprechende Areal im cw-Betrieb immer noch 10-mal bestrahlt werden.2 Zudem beschreibt der Scanner eine sog. Lissajousche Bahnfigur, bei der es zu ***Bahnkreuzungen*** kommt. An Stellen der ***Bahnkreuzungen*** besteht eine höhere Wahrscheinlichkeit für eine mehrfache Applikation von Laserpulsen, während in benachbarten Arealen bisweilen keine Pulse auftreffen.7 Damit ist erklärbar, dass Zonen dysplastischer Zellen an der Oberfläche nicht vom Laserstrahl erfasst werden und somit überleben."

From a text about CO2 laser ablation. What exactly is a Bahnkreuzung here? Path crossing? Path intersection? Maybe just intersection on its own? TIA for your help.
Rowan Morrell
New Zealand
Clarification request(s) and response
Rowan Morrell (asker): 5:31am Dec 6, 2004: Thank you - But WHY do you think it's "path crossing" in this particular context? Some explanations or references would help a great deal. Just proposing an answer without backing it up with some arguments or references doesn't really help at all.
Rowan Morrell (asker): 7:35am Dec 6, 2004: Thanks Meturgan - I don't mind guesses if they're backed up by an explanation and/or references, which you've done, so thanks for that. I do tend to think that "intersection" is more likely than "path crossing", but the "Bahn" bit makes me a bit uncertain.
Rowan Morrell (asker): 8:38am Dec 6, 2004: Pretty convincing added note - I'm beginning to think I should have asked this under Mathematics, though. :-) But thanks again. Protradit, take note of Meturgan's answering style and try to emulate it in the future. Make a case for your answer, even if you're not sure.
Rowan Morrell (asker): 9:28am Dec 6, 2004: Whole phrase - Come to think of it, how would you translate the whole phrase, "bei der es zu Bahnkreuzungen kommt"? The meaning isn't too clear to me at all.

intersection(s) of the Lissajous curves / Lissajous figures
Explanation:
I found something that might help you. It's just a guess.



http://www.math.com/students/wonders/lissajous/lissajous.htm...

Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.


http://www-gap.dcs.st-and.ac.uk/~history/Curves/Lissajous.ht...

Pedal curve : Given a curve C then the pedal curve of C with respect to a fixed point O (called the pedal point) is the locus of the point P of intersection of the perpendicular from O to a tangent to C.


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Note added at 3 hrs 9 mins (2004-12-06 08:09:34 GMT)
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Lissajous figure, also called Bowditch Curve, is a pattern produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other. First studied by the American mathematician Nathaniel Bowditch in 1815, the curves were investigated independently by the French mathematician Jules-Antoine Lissajous in 1857–58. www.britannica.com/eb/article?tocId=9048492


Lissajousche Bahnfigur = Lissajous figure = Lissajous curve

Bahnkreuzungen = intersections of the Lissajous figure / Lissajous curve

[0034] If one associates each intersection of the Lissajous figure with an image point, i.e. a point on the image field at which a light point 35 with desired brightness is to be created by modulation of the light beam 18, in order to result in the image to be projected together with other image points, and counts each reversal point as half an intersection, the following applies for the number N of the image points defined in this way:
http://www.freshpatents.com/Photofinishers-dt20041104ptan200...


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Note added at 4 hrs 53 mins (2004-12-06 09:54:06 GMT)
--------------------------------------------------

Still guessing:

.... a so called Lissajous figure with intersections in it
Selected response from:

Meturgan
Hungary
Note from asker to answerer
Thank you for this impressive and well-referenced answer. Thanks also to Kenneth for an extremely helpful comment. Appreciate the assistance from you both.
4 KudoZ points were awarded for this answer



Summary of answers provided
3path crossingProtradit
1 +1intersection(s) of the Lissajous curves / Lissajous figuresMeturgan


  

Answers

9 mins   confidence: Answerer confidence 3/5Answerer confidence 3/5
path crossing

Explanation:
.

Protradit
United States
Native speaker of: Native in EnglishEnglish
Note from asker to answerer
If you're not prepared to explain your answer, then I'm sorry, but I'm not prepared to accept it.
Login to enter a peer comment (or grade)
The asker has declined this answer
Comment: If you're not prepared to explain your answer, then I'm sorry, but I'm not prepared to accept it.


2 hrs   confidence: Answerer confidence 1/5Answerer confidence 1/5 peer agreement (net): +1
intersection(s) of the Lissajous curves / Lissajous figures

Explanation:
I found something that might help you. It's just a guess.



http://www.math.com/students/wonders/lissajous/lissajous.htm...

Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.


http://www-gap.dcs.st-and.ac.uk/~history/Curves/Lissajous.ht...

Pedal curve : Given a curve C then the pedal curve of C with respect to a fixed point O (called the pedal point) is the locus of the point P of intersection of the perpendicular from O to a tangent to C.


--------------------------------------------------
Note added at 3 hrs 9 mins (2004-12-06 08:09:34 GMT)
--------------------------------------------------

Lissajous figure, also called Bowditch Curve, is a pattern produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other. First studied by the American mathematician Nathaniel Bowditch in 1815, the curves were investigated independently by the French mathematician Jules-Antoine Lissajous in 1857–58. www.britannica.com/eb/article?tocId=9048492


Lissajousche Bahnfigur = Lissajous figure = Lissajous curve

Bahnkreuzungen = intersections of the Lissajous figure / Lissajous curve

[0034] If one associates each intersection of the Lissajous figure with an image point, i.e. a point on the image field at which a light point 35 with desired brightness is to be created by modulation of the light beam 18, in order to result in the image to be projected together with other image points, and counts each reversal point as half an intersection, the following applies for the number N of the image points defined in this way:
http://www.freshpatents.com/Photofinishers-dt20041104ptan200...


--------------------------------------------------
Note added at 4 hrs 53 mins (2004-12-06 09:54:06 GMT)
--------------------------------------------------

Still guessing:

.... a so called Lissajous figure with intersections in it

Meturgan
Hungary
PRO pts in category: 4
Note from asker to answerer
Thank you for this impressive and well-referenced answer. Thanks also to Kenneth for an extremely helpful comment. Appreciate the assistance from you both.

Peer comments on this answer (and responses from the answerer)
agree Ken Cox: With 'intersection(s) of the Lissajous figure'. A Lissajous figure is is a closed curve with one or more intersections, and if the laser beam follows the path of such a curve, the only points to be exposed to the light will be those lying on the curve.
2 hrs
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