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Plotting

Plotting. Read/write files in processing Refine a sampled curve Plot curves Exaggerate the discrepancy between two curves Use keys to control view parameters Produce pulsating animation Form teams for Project 1 Investigate how to visualize plot discrepancies. Write to a file.

fredericka-mclaughlin
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Plotting

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  1. Plotting • Read/write files in processing • Refine a sampled curve • Plot curves • Exaggerate the discrepancy between two curves • Use keys to control view parameters • Produce pulsating animation • Form teams for Project 1 • Investigate how to visualize plot discrepancies

  2. Write to a file float [] F = {200,240,250,210.1,160,150,170,200,209,240,250,220,200,150,110,100}; // array of values int n=F.length; // number of entries in F String [] SF = new String [n]; // allocate table of strings that will contain strings representing F[0], F[1]...F[n-1] for (int i=0; i<n; i++) SF[i]=str(F[i]); // store string forms of F values in SF saveStrings("F.val",SF); // writes content of SF to a file named F.val created in the sketch folder

  3. Read a file String [] SF = loadStrings("F.val"); // reads array of strings from a file named F.val in the sketch folder int n=SF.length; // sets the number of values in the array float [] F = new float [n]; // table of values that will be extracted from the strings for (int i=0; i<n; i++) F[i] = float(SF[i]); // recovers float values from strings and stores in F for (int i=0; i<n; i++) println(F[i]); // prints read values in the bottom pane of the Processing window // does not work in applets

  4. Interpolate Write the expression for C in terms of A and B d d A C= B d sd A C= B

  5. C(0) C(1) C(-1) M B D C(-3) A C(3) E M’ Insert new sample • Insert a new sample along each edge: M=(B+D)/2 • Displace it (bulge-out). By how much? • Fit a cubit C=C(t) through A, B, D, and E C(t)=at3+bt2+ct+d, and thus C(0)=d Set 4 constraints and solve for d: B=C(–1)= –a+b–c+d D=C( 1)= a+b+c+d A=C(–3)= –27a+9b–3c+d E=C( 3)= 27a+9b M=(B+D)/2=b+d M’–9M=–8d M’=(A+E)/2=9b+d C(0)=d=M+(M–M’)/8 bulge = M’M/8

  6. C(0) C(1) C(-1) M B D C(-3) A C(3) If A is unknown, estimate it as E+3(B–D) E M’ Boundary conditions • The bulge of an edge is computed from 2 neighbors on each side • What if you have only one neighbor on one side? • Add a dummy (missing) sample estimated from neighbors

  7. Refine a sampling String [] SF = loadStrings("F.val"); // reads array from F.val int n=SF.length; // sets the number of values in the array float [] F = new float [n]; // table of values for (int i=0; i<n; i++) F[i]=float(SF[i]); // recover F values from strings int r = 2*n-1; // number of values in refined array float [] R = new float [r]; // refined array for (int i=0; i<n; i++) R[2*i]=F[i]; // copies F values into even entries of R for (int i=3; i<r-3; i=i+2) R[i]=((-R[i-3]+9*R[i-1]+9*R[i+1]-R[i+3])/16); // computes intermediate odd values through cubit interpolation R[1]=(3*R[0]+6*R[2]-R[4])/8; R[r-2]=(3*R[r-1]+6*R[r-3]-R[r-5])/8; // computes first and last odd value using estimated dummy String [] SR = new String [r]; // allocate table of strings for (int i=0; i<r; i++) SR[i]=str(R[i]); // store string forms of R values in SR saveStrings("F.val",SR); // overwrite F.val with refeined values

  8. Exaggerate discrepancy Write the expression for C in terms of A and B d d A B C = d sd A B C =

  9. Exaggerate discrepancy of two plots void exaggerate (float s) { for (int i = 0; i<n; i++) { EF[i]=(s+1.)*F[i]-s*G[i]; EG[i]=(s+1.)*G[i]-s*F[i]; }; } What happens when s=0? What happens when s=1?

  10. Plot: Global variables color red; …. // declare colors but do not assign values yet // because we want to use the HSB color mode int n=1000; // cap on the number of values float [] F = new float [n]; // table F float [] G = new float [n]; // table G float [] EF = new float [n]; // table of exaggerated F float [] EG = new float [n]; // table of exaggerated G float s=1.0; // exaggeration factor boolean showExaggerated=false; // toggle normal/exaggerate mode boolean pulsing=false; // toggle pulsing mode

  11. Plot: setup (initialization code) void setup() { size(500, 400); // open graphic window (size in pixels) smooth(); strokeJoin(ROUND); strokeCap(ROUND); // want nice polylines colorMode(HSB,121); // color mode: Hue, Saturation, Brightness in [0..120] red = color(0, 120, 120); // …saturated, bright red String [] SF = loadStrings("F.val"); // reads array of strings from F.val n=SF.length; // sets the number of values in array for (int i=0; i<n; i++) F[i]=float(SF[i]); // store string forms of F values String [] SG = loadStrings("G.val"); // reads array of strings from G.val for (int i=0; i<n; i++) G[i]=float(SG[i]); // store string forms of G values exaggerate(s); // computes EF and EG exaggerating differences by factor s }

  12. Draw (redisplay loop) void draw() { background(50); // erase window using gray color strokeWeight(2); // set line width to 2 noFill(); // do not fill the interior of shapes if (pulsing) exaggerate(s*(2-cos(millis()/100.))); // if pulsing, exaggerate by a factor in [ 0 , 2s ] // computed using the current time in hundredths of milliseconds if (showExaggerated) {stroke(red); plot(EF); stroke(green); plot(EG);} else {stroke(orange); plot(F); stroke(cyan); plot(G); }; } void plot (float [] F) { // plot through n samples with values in F beginShape(); for (int i = 0; i<n; i++) vertex(i,height-F[i]); endShape(); } // y axis goes down, so we use height-F[i]

  13. User Interface (keyboard) void keyPressed() { // executed when a key is pressed if (key==' ') showExaggerated=!showExaggerated; // toggle normal/exagerated display mode if (key=='/') {pulsing=!pulsing;}; // toggle pulsing if (key=='.') s*=2; if (key==',') s/=2; // double / half the exaggeration factor if (key=='1') s=1; // resets s to 1 (mild exaggeration) exaggerate(s); // re-computes the exaggerated values };

  14. Results s=16 s=1

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