// title: Animation of Simple Harmonic Motion // author: eli.fieldsteel // description: // A GUI for animating summation of partials as simple harmonic motion, depicted as circular rotation correlated with a graph of amplitude vs. time. // code: ( //Created by Eli Fieldsteel 2022 Feb 26 var shm, spectrum; //frequency-scaling factor: closer to zero -> slow motion var freq_scale = 0.5; //amplitude-scaling factor: pixel radius when amplitude = 1 var amp_scale = 80; //spectrum is provided as an array containing one or more events //each event represents a sine wave with keys for 'freq', 'amp', and 'phs' //uncomment for examples /*sine (the default)*/ spectrum = [ (freq:1, amp:1, phs:0) ]; // /*harmonics 1 & 2 */ spectrum = [ (freq:1, amp:1, phs:0), (freq:2, amp:1/2, phs:0) ]; // /*harmonics 1 thru 4 */ spectrum = ((1..4).collect({ |n| (freq:n, amp:1/n, phs:0) })); // /*sawtooth*/ spectrum = ((1..12).collect({ |n| (freq:n, amp:1/n, phs:0) })); // /*square*/ spectrum = ((1,3..11).collect({ |n| (freq:n, amp:1/n, phs:0) })); // /*triangle*/ spectrum = ((1,3..11).collect({ |n| (freq:n, amp:1/(n**2), phs:n.odd.asInteger*pi+(pi/2)) })); // /*impulse (i.e. "Blip")*/ spectrum = ((1..12).collect({ |n| (freq:n, amp:1/4, phs:pi/2) })); Window.closeAll; shm = { arg input = [(freq:1, amp:1, phs:0)], freqscl=0.5, ampscl=75, datasize=200, framerate=40; var win, cview, wview, phs; var t = 0; //time/phase counter var wavedata = Array.newClear(datasize); //waveform y-coordinate values win = Window( "Simple Harmonic Motion Animation — (spacebar to pause/unpause)", Rect(100, 100, 1020, 520) ).background_(Color.gray(0.2)).front; win.view.decorator_(FlowLayout(win.view.bounds, 10@10, 10@10)); cview = UserView(win.view, 1000@500).background_(Color.gray(0.25)); cview.drawFunc_({ |v| var center, newcenter, x, y; //dividing line between circles/waveform Pen.width_(2); Pen.strokeColor_(Color.gray(0.5)); Pen.line(600@0, 600@520); Pen.stroke; //draw circles Pen.capStyle_(1); Pen.width_(2); input.do({ |sine, i| if (center == nil) { center = 300@250} { center = newcenter }; x = cos(( (((t * freqscl) + (sine.phs / sine.freq ))) * sine.freq ) % 2pi) * sine.amp; y = sin(( (((t * freqscl) + (sine.phs / sine.freq ))) * sine.freq ) % 2pi) * sine.amp; newcenter = (x@y) * ampscl * Point(1,-1); newcenter = newcenter.translate(center); Pen.strokeColor_(Color.gray(i.linlin(0, input.size, 0.7, 0.5), 0.8)); Pen.addArc(center, sine.amp * ampscl, 0, 2pi); }); Pen.stroke; //draw radii center = nil; Pen.width_(4); input.do({ |sine, i| if (center == nil) { center = 300@250} { center = newcenter }; x = cos(( (((t * freqscl) + (sine.phs / sine.freq ))) * sine.freq ) % 2pi) * sine.amp; y = sin(( (((t * freqscl) + (sine.phs / sine.freq ))) * sine.freq ) % 2pi) * sine.amp; newcenter = (x@y) * ampscl * Point(1,-1); newcenter = newcenter.translate(center); Pen.strokeColor_(Color(0.25, i.linlin(0, input.size-1, 0.55, 0.85), 0.95, 0.9)); Pen.line(center, newcenter); Pen.stroke; }); //draw horizontal line connecting radii to waveform Pen.width_(2); Pen.strokeColor_(Color.gray(1,0.3)); Pen.line(600@(newcenter.y), newcenter); Pen.stroke; //store y-coordinate wavedata = wavedata.rotate(1); wavedata.put(0, newcenter.y); //draw waveform with connecting lines between adjacent wavedata values Pen.width_(3); Pen.strokeColor_(Color(1, 0.75, 0, 0.6)); wavedata.drop(-1).do({ |y,i| if (y.notNil && wavedata.wrapAt(i+1).notNil) {Pen.line(Point(600 + (i*2), y), Point(600 + (i*2+2), wavedata.wrapAt(i+1)))}; }); Pen.stroke; //advance time (t = t + (2pi/framerate))%2pi; }); cview.frameRate_(framerate); cview.animate_(true); //spacebar to pause cview.keyDownAction_({ |v, char| if (char == \$ ) { cview.animate_(cview.animate.not) }; }); }; shm.(spectrum, freq_scale, amp_scale); //run )