This means that in most cases booth methods will yeild the same result. Default scaled calibration starts with zero and increments by one from point to point. Practically we rarely use scaled calibration in this group. To specify position by scaled calibration incude numbers in round brakets: MyWave(5) or MyWave(5,10).To specify position by point number incude that number in square brackets: MyWave or MyWave.See Calibrations for details on types of calibrations used below.Ī particular point or a range of points within a wave can be addressed by either their position in a sequence or by scaled value: How this is done depends on whether you are reading or writing a value and how do you specify the position(s).Īddressing by position, scaled or calibrated value: In many cases we need to access a particuar point or subrange of points within a wave. If waves are of different size, the smallest size will be copied entirely. Where every point from wave MyData is copied to MyResult if waves have the same size (number of points). See matrices for more details.Įntire array of data in a wave can be addressed and manipulated as one object by using wave name, such as: Matrix can be visualized as a grid of numbers. When several sequences of values are combined together they make a two-dimensional wave, or a matrix. Simple wave above is a one-dimensional wave (linear). Notation MyExperiment means that you need a value at 4th position in wave called MyExperiment. This means that for a wave containing 100 values, index can vary form 0 to 99. Indexing in Igor starts from 0, not from 1 as we normally count. To access specific value you need to indicate the name (nickname) of the wave and which number in the sequence you need. It can be visualized as one column in a spreadsheet. For our convenience waves are given nicknames in human language.Ī simple wave is a single string (or array) of numbers. Wave are collections of number that can be manipulated as a group - all numbers at once. Waves are Igor objects you are most likely to work with. We scaled the wave by /2, so if we do the same for the 2D and 3D wave equation then we get the curve is scaled by /(a 2+b 2) in 2D and /(a 2+b 2)+c 2 in 3D.Īcos(ax(a 2+b 2)/+by(a 2+b 2)/- t(a 2+b 2)/) for 2D.Īnd Acos(ax(a 2+b 2)/+by(a 2+b 2)/+cz(a 2+b 2)/- t(a 2+b 2)/) for 3D.For more details see Waveform model of data, Igor 5 Manual, volume II, p. The wave in 1D is f(x)=Acos(2 x/ -cT2 / ). This is the same as the translation of the 1D wave by cT. The equation of the wave without horizontal scaling is As changes then this changes the translation of the curve. The constant term dt can be written as t, where is the radian frequency. This is an expression of in terms of a,b in 2D and a,b,c in 3D. Since we know that = k in 2D and k in 3D, Using the signed distance (C ''-C ')/(A 2+B 2) 1/2 and (C ''-C ')/(A 2+B 2+C 2) 1/2 from one level to the next ie C '=0 to C ''=2 we get The wavelength is also a multiple of in 2D and in 3D. The wavelength ( ) is perpendicular to the level lines and we can consider this to be the normal to the level lines. This is our affine function, where Acos(ax+by) or Acos(ax+by+cz) is our linear function and the dt part is our translation. Where t=0 and the angle is measured in radians. The wave height is equal to Acos(ax+by+dt)=0 in 2D Amplitude(A) is the distance from the x-axis to the crest while wave height is the distance from the trough to the crest. It is the speed at which a crest travels.Īmplitude and wave height are hard to visualize in 2D and 3D but we can picture it in 1D. Similiarly to the frequency the velocity of a wave in 2D and 3D is similiar to the velocity in 1D. ie how many crest pass the yellow line per second. It is how many crests pass a point per second. The definition for frequency is the same for both 1D, 2D and 3D waves. The wavelength of a 2D and 3D wave is similiar to the wavelength of a 1D wave as shown below. In 1D the crests are the top of cosine wave or the cosine max. The wave in 2D or 3D is very similiar to the waves in 1D. This diagram shows us the crests of the wave, the direction that the wave is travelling, the cosine max(which are the crests) and the wavelength which is one cycle. We can use this to describe the equation of the wave. This actually shows us the level curves of the wave.Īs seen in affine transformation this looks like the many lines of Ax+By=C. If you draw lines following the crests of these waves then we can represent the wave by lines. This diagram represents a part of a wave in 3D. Math 309 - 2d and 3d waves Part 4 - 2D and 3D wavesĪ wave in 3D is very hard to visualize.
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