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Parametric Curves from 2-D Data using Discrete Fourier Transforms

This application will generate parametric equations for a set of 2-D points. When plotted, the parametric equations resemble the shape of the points. Turn X-Y points like this......into two parametric equations......which look like this when 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NiI= This application has an interactive plot that lets you draw a curve. Maple will generate discrete points on this curve as it is drawn. Maple will thencompute the discrete Fourier transforms (DFT) of the X and Y coordinates.generate two parametric equations that consist of a sum of sines. The frequency and amplitude of each sine term are extracted from the DFT.assign the equations to two variables.The equations can be now be plotted or manipulated.The core calculations are exposed at the bottom of the worksheet.INSTRUCTIONSClick the reset button (this removes the old points from the plot)Click and drag a curve on the large plot (you could draw any curve, including "handwritten" words, as long as it is one continuous curve). Maple will generate points on this curve as it is drawn.Release the left-mouse button when you're finished with the curve.. Maple will now generate the parametric equations, plot them in a preview, and assign the equations to two variables.You can remove every nth point from the input data using the data filter slider (a value of 2 seems to generate a good result).

Click and drag a curve on the plot belowThe parametric equations are plotted 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filterApplicationActions:-changeFilterValue():ApplicationActions:-Reset(); LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

The parametric equations are assigned to Actions:-x and Actions:-y evalf(ApplicationActions:-x, 2); evalf(ApplicationActions:-y, 2)

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plot([ApplicationActions:-x, ApplicationActions:-y, t = 0..ApplicationActions:-t_max], scaling = constrained, axes = boxed)

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rot := Matrix([[cos(theta), -sin(theta)], [sin(theta), cos(theta)]]). < x, y>

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rot_ang := Pi / 4: eq_vec := eval(subs({x = ApplicationActions:-x, y = ApplicationActions:-y}, rot), theta = rot_ang): plot([eq_vec[1], eq_vec[2], t = 0..ApplicationActions:-t_max], scaling = constrained, axesfont = [Arial])

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shear_x := Matrix([[1, lambda], [0, 1]]). < x, y>

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shear_value := 1: eq_vec := eval(subs({x = ApplicationActions:-x, y = ApplicationActions:-y}, shear_x), lambda = shear_value): plot([eq_vec[1], eq_vec[2], t = 0..ApplicationActions:-t_max], scaling = constrained)

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shear_y := Matrix([[1, 0], [lambda, 1]]). <x, y>

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shear_value := 1: eq_vec := eval(subs({x = ApplicationActions:-x, y = ApplicationActions:-y}, shear_y), lambda = shear_value): plot([eq_vec[1], eq_vec[2], t = 0..ApplicationActions:-t_max], scaling = constrained)

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rot_shear := Matrix([[cos(theta), -sin(theta)],[sin(theta), cos(theta)]]) . Matrix([[1, lambda],[0, 1]]) . < x, y>

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f := proc(rot_ang, shear_value) local eq_vec: eq_vec := eval(subs({x = ApplicationActions:-x, y = ApplicationActions:-y}, rot_shear), [lambda =shear_value, theta = rot_ang]): return plot([eq_vec[1], eq_vec[2], t = 0..ApplicationActions:-t_max], scaling = constrained) end proc: Explore(f(rot_val, shear_val), parameters=[rot_val = 0..2.*Pi, shear_val = 0..5.0]) 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# The following code is autogenerated by the Explore command. Do not edit. # Explore:-Runtime:-Update( f(rot_val,shear_val), ':-Plot0', [':-rot_val', ':-shear_val'], ':-sliders'=["Sliderrot_val", "Slidershear_val"], ':-labels'=["Labelrot_val", "Labelshear_val"],':-isplot'=true, ':-handlers'=[rot_val=handlertab[rot_val],shear_val=handlertab[shear_val]]); # # End of autogenerated code. # SSpzaGVhcl92YWxHNiI=# # The following code is autogenerated by the Explore command. Do not edit. # Explore:-Runtime:-Update( f(rot_val,shear_val), ':-Plot0', [':-rot_val', ':-shear_val'], ':-sliders'=["Sliderrot_val", "Slidershear_val"], ':-labels'=["Labelrot_val", "Labelshear_val"],':-isplot'=true, ':-handlers'=[rot_val=handlertab[rot_val],shear_val=handlertab[shear_val]]); # # End of autogenerated code. #

The code for the application is in the startup code region editor (Edit > Startup Code). The core calculations are exposed here. Consider these points X := Array([558, 533, 512, 509, 519, 538, 527, 501, 485, 493, 499, 499, 465, 406, 413, 441, 430, 406, 397, 393, 392, 397, 403, 406, 397, 365, 356, 354, 326, 311, 336, 355, 315, 278, 278, 249, 242, 232, 204, 208, 209, 204, 206, 242, 242, 263, 274, 287, 334, 361, 320, 314, 344, 355, 360, 379, 406, 407, 399, 393, 391, 394, 404, 415, 439, 431, 402, 438, 487, 503, 497, 486, 488, 514, 538, 537, 511, 508, 518, 546]): Y := Array([420, 412, 431, 480, 522, 505, 444, 431, 480, 591, 605, 548, 444, 416, 426, 478, 516, 533, 488, 395, 305, 356, 463, 525, 418, 414, 488, 465, 416, 458, 497, 495, 463, 409, 488, 514, 458, 512, 441, 441, 485, 412, 508, 493, 463, 516, 437, 403, 503, 482, 495, 429, 416, 499, 439, 407, 490, 533, 392, 309, 333, 452, 520, 529, 499, 452, 418, 416, 492, 593, 606, 544, 448, 429, 482, 518, 508, 450, 424, 414]): plot(X, Y, style = point)

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DFT of X and Y points dft_X := Vector(SignalProcessing:-FFT(X)): dft_Y := Vector(SignalProcessing:-FFT(Y)): Phase and amplitude of sines n := numelems(X): P_X := Re(argument~(dft_X[2..ceil(n / 2)])): A_X := abs(dft_X[2..ceil(n / 2)]): P_Y := Re(argument~(dft_Y[2..ceil(n / 2)])): A_Y := abs(dft_Y[2..ceil(n / 2)]): Parametric curves curve_X := evalf[3](add(seq(A_X[i] * sin(Pi / 2 - 2 * Pi / n * i * t + P_X[i]), i = 1..ceil(n / 2) - 1))); curve_Y := evalf[3](add(seq(A_Y[i] * sin(Pi / 2 - 2 * Pi / n * i * t + P_Y[i]), i = 1..ceil(n / 2) - 1)));

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

Plot the parametric curves plot([curve_X, curve_Y, t = 0 .. n / 2])

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