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Topic: Lissajous curve

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	Lissajous Lab (Site not responding. Last check: 2007-10-16)
		Lissajous' setup was similar to the apparatus which is used today to project laser light shows.
		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.
		Lissajous figures often appeared as props in science fiction movies made during the 1950's.
	www.math.com /students/wonders/lissajous/lissajous.html (347 words)

	NationMaster - Encyclopedia: Harmonograph (Site not responding. Last check: 2007-10-16)
		The drawings created typically are Lissajous curves, or related drawings of greater complexity.
		The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890's, cannot be conclusively attributed to a single person, although Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor.
		Lissajous figure on an Oscilloscope Lissajous figure in three dimensions In mathematics, a Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations which describes complex harmonic motion.
	www.nationmaster.com /encyclopedia/Harmonograph (687 words)

	Lissajous curve Summary
		The visual form of these curves is often suggestive of a three-dimensional knot, and indeed the many kinds of knots, including those known as Lissajous knots, project to the plane as Lissajous figures.
		Lissajous figures are sometimes used in graphic design as logos.
		Lissajous curves can be traced mechanically by means of a harmonograph.
	www.bookrags.com /Lissajous_curve (843 words)

	Lissajous figuren
		Lissajous was a french mathematician, who lived 1822 to 1880.
		Lissajous curves are made by so called "parametric functions".
		Lissajous curves, like common functions, will be smooth, without sharp angles.
	home.hccnet.nl /david.dirkse/math/lissa.html (457 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		It is a trumpet-shaped curve that is the locus of points P such that the square of distance of P from the origin is inversely proportional to the angle theta that p makes with the horizontal axis.
		The curve t->epitrochoid3d[a,b,h,0][t] is a (planar) epitrochoid and the curve epitrochoid3d[a,b,h,Pi][t] is a (planar) hypotrochoid.
		viviani[a][t] is a Viviani curve on a sphere of radius 2*a.
	www.maths.man.ac.uk /~kd/mmaprogs/CURVES.m (5260 words)

	Lissajous (Site not responding. Last check: 2007-10-16)
		The magenta locus is a lissajous curve, the path of a point each of whose coordinates is under harmonic motion.
		The cyan segment (at the bottom of the sketch) determines the length of the curve.
		The curve could thus be represented analytically as [sin(bt+k0), sin(gt+k1)] t e {0..c} where k0 and k1 are constants, and b, g, and c the lengths of the blue, green, and cyan segments respectively.
	mathforum.org /dynamic/java_gsp/lissa.html (136 words)

	Reference.com/Encyclopedia/Lissajous curve
		Prior to modern computer graphics, Lissajous curves were typically generated using an oscilloscope (as illustrated).
		Lissajous curves can also be traced mechanically by means of a harmonograph.
		Even though they look similar, Spirographs are different as they are generally enclosed by a circular boundary where a Lissajous curve is bounded by a square (±1, ±1).
	www.reference.com /browse/wiki/Lissajous (418 words)

	An Introduction to Lissajous Patterns
		A Lissajous pattern is a graph of one frequency plotted on the y axis combined with a second frequency plotted on the x axis.
		The Lissajous pattern changes to a line when the X and Y frequencies are in phase by either 180 or 0 degrees.
		It is possible to create lissajous patterns by using one wave form function generator, an oscilloscope, a tuning fork and a microphone.
	www.egr.msu.edu /classes/ece482/Teams/99spr/design2/web/resources/lissajous/lissajous.htm (792 words)

	WUGNET - Lissajous 3D - Windows XP/2000/NT Screensavers
		A Lissajous curve is a curve traced out by the motion of an oscillating point.
		The original Lissajous curves were inspired by sound, and were made by attaching mirrors to a tuning fork and using those to reflect light to make the patterns.
		Lissajous 3D draws figures in 3D as a ribbon, or a tube, with varying cross section, and uses a point oscillating in three dimensions instead of the original two.
	www.wugnet.com /screensavers/ssow.asp?ID=35 (249 words)

	Lissajous Figures
		Lissajous Figures were first described in 1815 by Nathaniel Bowditch (1773-1838), who is best known today for his book, "The New American Practical Navigator", still available today.
		Another device that relies on Lissajous Figures is the Tune Analyzer made by Newton and Co. of London.
		The Lissajous figure demonstration device at the left was made by the firm of Ferdinand Ernicke of Berlin.
	physics.kenyon.edu /EarlyApparatus/Oscillations_and_Waves/Lissajous_Figures/Lissajous_Figures.html (954 words)

	Lambdoma
		The original Lissajous curves were inspired by sound - as they were made by attaching mirrors to a tuning fork and using those to reflect light to make the patterns.
		Sometimes it says that the curve continues - in that case, that means that the calculation went on for a fair while and the curve hadn't met up yet at the point that the calculation stopped - it probably continued a fair way beyond the part that actually gets drawn.
		The standard setting in FTS is that you see the curve change as you release the notes of a chord of three or more notes, until you reach a two note chord.
	tunesmithy.netfirms.com /fts_help/lambdoma.htm (4515 words)

	Lissajous Curve (Site not responding. Last check: 2007-10-16)
		Lissajous curves are composed from two sine waves (with a 90° relative phase shift), applied to the X and Y coordinates, respectively.
		It is interesting to note that sometimes the curve will not become closed in a straightforward way, such is the case with (2.0, 5.0).
		This curve appears to have two open ends at the left-hand side (but is in fact closed).
	javasite.bme.hu /~vi/math_curveplot_lissajous (316 words)

	Lissajous curve
		When the constant a is rational, the curve is algebraic and closed.
		The curves are constructed as a combination of two perpendicular harmonic oscillations.
		besace: its parameter a is equal to the tangent of the Lissajous curve's parameter b.
	www.2dcurves.com /higher/higherli.html (330 words)

	Lissajous curves (Bowditch curves) - physics explanation (Site not responding. Last check: 2007-10-16)
		The Lissajous curves, also known as Bodwitch curves, have applications in Physics, Astronomy and other sciences.
		The circle is therefore one of the Lissajous curves.
		Lissajous curves are equally important in Physics and Mathematics.
	www.staff.amu.edu.pl /~romangoc/M2-4-lissajous-bowditch-curves.html (274 words)

	boostworthyisryantaylor » Art
		I was experimenting in Flash with some Lissajous curves and decided to use one as the foundation for a new design.
		The foundation for that piece was created using a script in Flash which generated a Lissajous curve.
		By definition, a Lissajous curve is the graph of the system of parametric equations which describes complex harmonic motion.
	www.boostworthy.com /blog/?cat=3 (485 words)

	Professional plugins for Final Cut Pro and Final Cut Express by chv-electronics
		Lissajous Text Pro V4.0 creates the first ever Lissajous effect with text running along the created line for Final Cut Pro and Final Cut Express.
		Lissajous Text Pro V4.0 is also equipped with the highly sophisticated outline feature of CHV.
		A Lissajous curve is a figure created by overlaying two frequencies.
	www.chv-plugins.com /lissajous.html (1245 words)

	Synthesis
		Cycloid curves, sometimes called trochoids, are created by a circle rotating inside or outside of another circle.
		Cycloid curves were made popular by Hasbro's game Spirograph which consisted of various disks with gear teeth on the edges.
		A pen was used to trace the curve of the cycloid through holes in the disks.
	www.csounds.com /ezine/spring1999/synthesis/index.html (466 words)

	Lissajous figures, a 3D java applet
		The Lissajous figures in some books may look different to those generated here.
		Count the number of the intersection points of the vertical line and the curve.
		As well, count the number of the intersection points of the horizontal line and the curve.
	www.ngsir.netfirms.com /englishhtm/Lissajous.htm (273 words)

	Lissajous or Bowditch Curves - National Curve Bank (Site not responding. Last check: 2007-10-16)
		Also, these curves are easily entered and modified on a graphing calculator.
		Moreover, he was the first to investigate a family of curves now usually named for the French physicist, Jules-Antoine Lissajous.
		Lissajous (1822 - 1880) is thought to have encountered these curves when he collected data for his optical method of studying vibrations.
	curvebank.calstatela.edu /lissajous/lissajous.htm (397 words)

	Lissajous
		Lissajous curves or Lissajous figures are sometimes called Bowditch curves after Nathaniel Bowditch who considered them in 1815.
		They were studied in more detail (independently) by Jules-Antoine Lissajous in 1857.
		Lissajous curves have applications in physics, astronomy and other sciences.
	www-groups.dcs.st-and.ac.uk /~history/Curves/Lissajous.html (110 words)

	Mediamacros Inc. - Curve Sprite - Move a sprite along a curved path. (Site not responding. Last check: 2007-10-16)
		Curve Sprite - Move a sprite along a curved path.
		Based on a Lissajous curve algorithm, this behavior is extremely versatile, and can produce an amazing variety of results.
		A lower number produces a smoother curve, but is slower to draw.
	www.mediamacros.com /item/item-1006687017 (332 words)

	Lissajous
		Other well-known curves are Lissajous curves as well.
		This discussion about the parameter is important if in the definition of parametric curve the condition of being locally injective is included [1] [4].
		The implicit equation of a Lissajous curve is obtained by eliminating the parameter
	boj.pntic.mec.es /~jcastine/Lissajous2.htm (320 words)

	Lissajous 3D Download Page
		If you want to purchase Lissajous directly from within the application, you can get the other version which uses the eSellerate system.
		To join it, send an e-mail to support@tunesmithy.co.uk to say you want to be on the Lissajous 3D list and / or the new 3D programs announcement list.
		Home users are free to use Lissajous 3D on any of their machines - you don't need to buy a site license for home use.
	www.robertinventor.com /Lissajous_3D/index.htm (1652 words)

	Hell Labs » Lissajous load display (Site not responding. Last check: 2007-10-16)
		Geeks with Engineering or Mathematics background are familiar with the family of curves described by the parametric equations
		It generates, for instance, a circle, when the amplitudes and angular speeds are equal, and the difference of phase is π/2.
		This Lissajous load display seems to work surprisingly well (if you know how to interpret it) — and also looks like something you’d find in a cheesy 60s B-movie computer.
	helllabs.org /blog/20050815/lissajous-load-display (355 words)

	Lissajous Figures
		Jules Antoine Lissajous (1822-1880) was a French physicist who was interested in waves, and around 1855 developed a method for displaying them optically by reflecting a light beam from a mirror attached to a vibrating object such as a tuning fork.
		A Lissajous figure is produced by taking two sine waves and displaying them at right angles to each other.
		Before there were frequency counters and phase locked loops, Lissajous Figures were used to compare two frequencies (such as a reference signal to an unknown signal) that were within a few integer multiples apart.
	www.jmargolin.com /mtest/LJfigs.htm (1692 words)

	Lissajous.htm
		Type I curves are "smooth", while Type II curves have sharp "ends".
		A Type II curve is drawn from one "end" to the other.
		varies, then the particle is always moving in the same direction for the smooth or Type I curves, while there has to be a reversal of direction at the "ends" in the Type II curves.
	www.math.neu.edu /~bridger/u170/lissajous/lissajous.htm (648 words)

	Portfolio \| Physics and Mathematics. (Site not responding. Last check: 2007-10-16)
		Lissajous curves are parametrically defined as a function of time:
		I constructed a pair of optical modulators by cementing a mirror and some support hardware to the drivers of a pair of speakers.
		I was able to produce these and many other Lissajous curves with my apparatus.
	www.cs.swarthmore.edu /~bsetlow/Portfolio/physicsmathematics (282 words)

	Debian -- qliss3d
		Qliss3d is a tool that generates various Lissajous figures.
		Also changing the frequency and replay of the sinus sounds by the same frequency rate are implemented.
		In mathematics, a Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations which describes complex harmonic motion.
	packages.debian.org /unstable/graphics/qliss3d (191 words)

	funny 3D screensaver tool - Lissajous 3D 1.2 download
		Lissajous 3D -- Make animated swirly curves which change shape.
		Lissajous 3D draws these figures in 3D as a ribbon, or a tube, with varying cross section, and uses a point oscillating in three dimensions instead of the original two.
		Radar Screensaver - A modern and outstanding screensaver which is able to turn your video display into a screen of a fabulous radar watching the skies, seas, and near-Earth space.
	www.tomdownload.com /desktop_enhancements/screensavers/lissajous_3d.htm (568 words)

	Lissajous Lab
		Lissajous (pronounced LEE-suh-zhoo) figures were discovered by the French physicist Jules Antoine Lissajous.
		One of the best examples can be found in the opening sequence of The Outer Limits TV series.
		The Lissajous Lab and description were created by Ed Hobbs.
	www.mathcats.com /explore/lissajous/lissajous.html (418 words)

	Dynamic Color Gradient Generator
		The blue wave uses a 5-term expansion, the green curve uses a 4-term expansion, the red curve uses a 3-term expansion, and the yellow curve a 2-term expansion.
		The problem is: Just plotting such a curve would be easy to compute, but useless for the purpose of this programme, because it needs to calculate the distance(shortest distance that is) from every pixel to the curve.
		so that all points of the curve where the tangent is perpendicular to the line from the curve to the point take part in the illumination.
	www.allegro.cc /forums/print-thread/536928 (2120 words)

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