import jass.render.*;
import jass.generators.*;
import jass.utils.*;
import java.awt.*;
import javax.swing.*;
public class VTNTDemo implements Runnable {
static final String aboutStr = "This demo uses a numerical solution of the linearized 1D Navier-Stokes PDE as well as a lip model. Select various vowels by clicking the buttons in the control panel. This will generate a particular vocal tract shape matching the vowel and synthesize the sound of exciting such a vocal tract shape with a Rosenberg type glottal excitation. The airway model is morphed in order to fit this tube model. Start the timeline in order to see the airway change. You can also tweak reflection coefficients at the lip and glottis, attenuation (damping) and the 4 glottal parameters for the excitation. The formants window plots the spectrum of the sound. After you move the sliders you need to click the formants button to see the update.\n The particular vowels implemented here are the six Russian vowels as described in \"Acoustics Theory of Speech Production\", Chapter 2.3, Gunnar Fant, 1970. Nasal tract is controlled by parameters Velum (0 nasal tract is closed, 1 vocal tract is closed) and M-N balance which determines the mix out the nose and mouth sound sources. Finally the geometry can be specified with the sliders.";
int nTubeSections;
double[] tract;// = new double[nTubeSections]; // for presets
//static final double tubeLength=-1;
String[] args;// = {".17","44100",".10","6","5",".5"};
SourcePlayer player;
Controller a_controlPanel; // VT
Controller a_controlPanelNasal; // nasal tract
Controller a_controlPanelRosenberg; // Rosenberg glottal model
Controller a_controlPanelTwoMass; // Ishizak-Flanagan model
//Airway airway=null;
FormantsPlotter formantsPlotter;
boolean useTwoMassModel = true; // or if false use Rosenberg model
float srate;
boolean slideStarted = false;
public String getAbout() {
return aboutStr;
}
private boolean haltMe=false;
public void detach() {
halt();
System.out.println("halt!!");
}
public void halt() {
haltMe=true;
player.stopPlaying();
a_controlPanel.dispose();
a_controlPanelRosenberg.dispose();
a_controlPanelTwoMass.dispose();
a_controlPanelNasal.dispose();
if(formantsPlotter != null) {
formantsPlotter.close();
}
}
public VTNTDemo(String[] args) {
super();
this.args=args;
Thread thread = new Thread(this);
thread.setPriority(Thread.MAX_PRIORITY);
thread.start();
/*
while(airway==null) {
try {
Thread.sleep(50);
} catch(Exception e){}
}
addModel(airway);
*/
}
public static void main(String[] args) {
new VTNTDemo(args);
}
public void run() {
int bufferSize = 256;//512;
int bufferSizeJavaSound = 1024*8;
// int nchannels = 1;
int nTubeSectionsNasal;
/*
try {
airway = new Airway(ArtisynthPath.getHomeRelativePath("src/artisynth/models/tubesounds/airway_t.obj","."),
ArtisynthPath.getHomeRelativePath("src/artisynth/models/tubesounds/fissured-tongue.jpg","."));
} catch(Exception e) {
System.out.println("File not found"+e);
}
*/
if(args.length != 6) {
System.out.println("Usage: java VTNTDemo .17 srate nasalLen nNasalSections nTubeSections cflNumber");
return;
}
double tubeLength = Double.parseDouble(args[0]);
double tubeLengthNasal = Double.parseDouble(args[2]);
nTubeSectionsNasal = Integer.parseInt(args[3]); // only for control
nTubeSections = Integer.parseInt(args[4]); // only for control
tract = new double[nTubeSections];
srate = (float) Double.parseDouble(args[1]);
double cflNumber = Double.parseDouble(args[5]);
// TubeModel will decide how many segments are needed and interpolate
final TubeModel tm = new TubeModel(nTubeSections);
final TubeModel tmNasal = new TubeModel(nTubeSectionsNasal);
tm.setLength(tubeLength);
tmNasal.setLength(tubeLengthNasal);
player = new SourcePlayer(bufferSize,bufferSizeJavaSound,srate);
double c= 350; // vel. of sound
double minLen = .15;
double minLenNasal = tubeLengthNasal;
final RightLoadedWebsterTube filter = new RightLoadedWebsterTube(srate,tm,minLen,tmNasal,minLenNasal,cflNumber);
filter.useLipModel = !filter.useLipModel; // set to false
final RightLoadedWebsterTube filterCopy = new RightLoadedWebsterTube(srate,tm,minLen,tmNasal,minLenNasal,cflNumber);
filterCopy.setOutputVelocity(true); // to display formants correctly
filterCopy.useLipModel = !filterCopy.useLipModel; // set to false (will be reset later on)
final FilterContainer filterContainer = new FilterContainer(srate,bufferSize,filter);
final GlottalWave source = new GlottalWave(srate,bufferSize);
final TwoMassModel twoMassSource = new TwoMassModel(bufferSize,srate);
final RandOut randOut= new RandOut(bufferSize);
final Silence silence= new Silence(bufferSize);
filterCopy.setFlowNoiseLevel(0); // no noise for spectrum
try {
if(useTwoMassModel) {
filter.setTwoMassModel(twoMassSource);
filterContainer.addSource(source); // add Rosenberg source also
//filterContainer.addSource(randOut); // add Rand source
} else {
filterContainer.addSource(source);
}
player.addSource(filterContainer);
//player.addSource(twoMassSource);
} catch(Exception e) {}
preset("a");
for(int i=0;i<nTubeSections;i++) {
tm.setRadius(i,tract[i]);
}
//airway.init(tm);
filter.changeTubeModel();
filterCopy.changeTubeModel();
// set up control panels
// Vocal tract control panel:
int nbuttons = 4 + 7 + 2;
final int nAuxSliders = 5;
final int nSliders = nTubeSections+nAuxSliders;
String[] names = new String[nSliders];
double[] val = new double[nSliders];
double[] min = new double[nSliders];
double[] max = new double[nSliders];
final int tubelengthSliderIndex = nAuxSliders-1;
//names[0] = "f1 ";
//val[0] = 250; min[0] = 10; max[0] = 800;
//names[1] = "f2 ";
//val[1] = 2000; min[1] = 801; max[1] = 10000;
names[0] = "u_xx mult";
val[0] = 1; min[0] = 0.0; max[0] = 20;
names[1] = "u mult";
val[1] = 1; min[1] = 0.0; max[1] = 20;
names[2] = "wall coeff ";
val[2] = 1; min[2] = 0; max[2] = 5;
names[3] = "lipCf ";
val[3] = 1; min[3] = .05; max[3] = 30;
names[4] = "length ";
val[4] = tubeLength; min[4] = .15; max[4] = tubeLength*4;
double minA = 0;
double maxA = 20;
for(int k=nAuxSliders;k<nSliders;k++) {
names[k] = "A("+new Integer(k-nAuxSliders).toString() + ") ";
val[k] = 1;
min[k] = minA;
max[k] = maxA;
double r=Math.sqrt(val[k]/Math.PI);
tm.setRadius(k-nAuxSliders,r/100); // in meters
//tmAirway.setRadius(k-nAuxSliders,r); // in cm!
}
a_controlPanel = new Controller(new java.awt.Frame ("Vocal Tract"),
false,val.length,nbuttons) {
private static final long serialVersionUID = 1L;
boolean muted=false;
private void handleReset() {
filter.reset();
twoMassSource.reset();
player.resetAGC();
muted = !muted;
player.setMute(muted);
player.resetAGC();
try {
Thread.sleep(100);
} catch(Exception e){};
muted = !muted;
player.setMute(muted);
player.resetAGC();
}
public void onButton(int k) {
switch(k) {
case 0:
handleReset();
slideStarted = !slideStarted;
break;
case 1: {
FileDialog fd = new FileDialog(new Frame(),"Save");
fd.setMode(FileDialog.SAVE);
fd.setVisible(true);
saveToFile(fd.getFile());
}
break;
case 2: {
FileDialog fd = new FileDialog(new Frame(),"Load");
fd.setMode(FileDialog.LOAD);
fd.setVisible(true);
loadFromFile(fd.getFile());
handleReset();
}
break;
case 3: {
muted = !muted;
player.setMute(muted);
player.resetAGC();
}
break;
case 4: {
preset("a");
double tubeLen = .17;
handlePresetChange(tubeLen);
}
break;
case 5: {
preset("o");
double tubeLen = .185;
handlePresetChange(tubeLen);
}
break;
case 6: {
preset("u");
double tubeLen = .195;
handlePresetChange(tubeLen);
}
break;
case 7: {
preset("i_");
double tubeLen = .19;
handlePresetChange(tubeLen);
}
break;
case 8: {
preset("i");
double tubeLen = .165;
handlePresetChange(tubeLen);
}
break;
case 9: {
preset("e");
double tubeLen = .165;
handlePresetChange(tubeLen);
}
break;
case 10: {
preset("-");
double tubeLen = .17;
handlePresetChange(tubeLen);
}
break;
case 11: { //plot formants
updateFormantsPlot();
}
break;
case 12: { //toggle lipmodel
filter.useLipModel = !filter.useLipModel;
filterCopy.useLipModel = filter.useLipModel;
if(filter.useLipModel) {
a_controlPanel.setButtonName("ToggleLipModel (is on)",12);
} else {
a_controlPanel.setButtonName("ToggleLipModel (is off)",12);
}
handleReset();
}
break;
}
}
private void handlePresetChange(double tubeLen) {
tm.setLength(tubeLen);
val[tubelengthSliderIndex] = tubeLen;
//min[tubelengthSliderIndex] = tubeLen;
for(int k=nAuxSliders;k<nSliders;k++) {
val[k] = 100*tract[k-nAuxSliders]; // in cm!
val[k] *= val[k];
val[k] *= Math.PI;
}
a_controlPanel.setSliders(val,min,max,names);
for(int i=0;i<nTubeSections;i++) {
tm.setRadius(i,tract[i]);
}
filter.changeTubeModel();
handleReset();
//updateFormantsPlot();
}
private void updateFormantsPlot() {
filterCopy.changeTubeModel();
filterCopy.reset();
if(formantsPlotter == null) {
formantsPlotter = new FormantsPlotter();
formantsPlotter.setLocation(300,500);
}
formantsPlotter.plotFormants(filterCopy,srate);
//formantsPlotter.dumpData(filterCopy,srate);
}
public void onSlider(int k) {
switch(k) {
/*
case 0:
filter.setOm1(2*Math.PI*this.val[k]);
filterCopy.setOm1(2*Math.PI*this.val[k]);
filter.changeTubeModel();
break;
case 1:
filter.setOm2(2*Math.PI*this.val[k]);
filterCopy.setOm2(2*Math.PI*this.val[k]);
filter.changeTubeModel();
break;
*/
case 0:
filter.multDSecond = this.val[k];
filterCopy.multDSecond = this.val[k];
filter.changeTubeModel();
break;
case 1:
filter.multDWall = this.val[k];
filterCopy.multDWall = this.val[k];
break;
case 2:
filter.setWallPressureCoupling((double)this.val[k]);
filterCopy.setWallPressureCoupling((double)this.val[k]);
filter.changeTubeModel();
break;
case 3:
filter.lipAreaMultiplier = (double)this.val[k];
filterCopy.lipAreaMultiplier = (double)this.val[k];
filter.changeTubeModel();
break;
case 4:
tm.setLength((double)this.val[k]);
filter.changeTubeModel();
break;
default:
double r=Math.sqrt(val[k]/Math.PI);
tm.setRadius(k-nAuxSliders,r/100);// in meters
//tmAirway.setRadius(k-nAuxSliders,r);// in cm
filter.changeTubeModel();
break;
}
}
};
a_controlPanel.addWindowListener(new java.awt.event.WindowAdapter() {
public void windowClosing(java.awt.event.WindowEvent e) {
System.out.println("Close handler called");
player.stopPlaying();
}
});
a_controlPanel.setSliders(val,min,max,names);
a_controlPanel.setButtonNames (new String[] {"Reset","Save","Load","(Un)mute","[a]","[o]","[u]","[i-]","[i]","[e]","[-]","Formants","ToggleLipModel (is on)"});
a_controlPanel.setVisible(true);
a_controlPanel.onButton(nbuttons-1); // put up formants
// End Vocal tract control panel:
// Nasal tract control panel:
int nbuttonsNasal = 2;
final int nAuxSlidersNasal = 3;
int nSlidersNasal = nTubeSectionsNasal+nAuxSlidersNasal;
String[] namesNasal = new String[nSlidersNasal];
final double[] valNasal = new double[nSlidersNasal];
double[] minNasal = new double[nSlidersNasal];
double[] maxNasal = new double[nSlidersNasal];
namesNasal[0] = "Velum(0noNasal)";
valNasal[0] = 0.0; minNasal[0] = 0; maxNasal[0] = 1;
namesNasal[1] = "M-N Bal";
valNasal[1] = .5; minNasal[1] = 0; maxNasal[1] = 1;
namesNasal[2] = "NasalLen";
valNasal[2] = .11; minNasal[2] = .1; maxNasal[2] = .18;
double minANasal = .01;
double maxANasal = 10;
double[] dangHondaFig6 = {.7,1.5,5,1,.8,.5,.6,.8}; // 8 sliders
int ii=0;
for(int k=nAuxSlidersNasal;k<nSlidersNasal;k++,ii++) {
namesNasal[k] = "A("+new Integer(k-nAuxSlidersNasal).toString() + ") ";
valNasal[k] = dangHondaFig6[ii];
minNasal[k] = minANasal;
maxNasal[k] = maxANasal;
double r=Math.sqrt(valNasal[k]/Math.PI);
tmNasal.setRadius(k-nAuxSlidersNasal,r/100); // in meters
}
a_controlPanelNasal = new Controller(new java.awt.Frame ("Nasal Tract"),
false,valNasal.length,nbuttonsNasal) {
private static final long serialVersionUID = 2L;
boolean muted=false;
public void onButton(int k) {
switch(k) {
case 0: {
FileDialog fd = new FileDialog(new Frame(),"Save");
fd.setMode(FileDialog.SAVE);
fd.setVisible(true);
saveToFile(fd.getFile());
}
break;
case 1: {
FileDialog fd = new FileDialog(new Frame(),"Load");
fd.setMode(FileDialog.LOAD);
fd.setVisible(true);
loadFromFile(fd.getFile());
}
break;
}
}
public void onSlider(int k) {
switch(k) {
case 0:
filter.velumNasal = this.val[k];
filterCopy.velumNasal = this.val[k];
break;
case 1:
filter.mouthNoseBalance = this.val[k];
filterCopy.mouthNoseBalance = this.val[k];
break;
case 2:
tmNasal.setLength((double)this.val[k]);
filter.changeTubeModel();
break;
default:
double r=Math.sqrt(this.val[k]/Math.PI);
tmNasal.setRadius(k-nAuxSlidersNasal,r/100);// in meters
filter.changeTubeModel();
break;
}
}
};
a_controlPanelNasal.setSliders(valNasal,minNasal,maxNasal,namesNasal);
a_controlPanelNasal.setButtonNames (new String[] {"Save","Load"});
a_controlPanelNasal.setVisible(true);
// End Nasal tract control panel:
// Rosenberg glottal source control panel:
int nbuttonsRosenberg = 2;
int nSlidersRosenberg = 4;
String[] namesRosenberg = new String[nSlidersRosenberg];
double[] valRosenberg = new double[nSlidersRosenberg];
double[] minRosenberg = new double[nSlidersRosenberg];
double[] maxRosenberg = new double[nSlidersRosenberg];
namesRosenberg[0] = "freq";
valRosenberg[0] = 100; minRosenberg[0] = 20; maxRosenberg[0] = 1000;
namesRosenberg[1] = "openQ";
valRosenberg[1] = .5; minRosenberg[1] = 0.001; maxRosenberg[1] = 1;
namesRosenberg[2] = "slopeQ";
valRosenberg[2] = 4; minRosenberg[2] = .15; maxRosenberg[2] = 10;
namesRosenberg[3] = "gain";
valRosenberg[3] = 0.0; minRosenberg[3] = 0; maxRosenberg[3] = 1;
a_controlPanelRosenberg = new Controller(new java.awt.Frame ("Rosenberg Glottal Model"),
false,valRosenberg.length,nbuttonsRosenberg) {
private static final long serialVersionUID = 1L;
public void onButton(int k) {
switch(k) {
case 0: {
FileDialog fd = new FileDialog(new Frame(),"Save");
fd.setMode(FileDialog.SAVE);
fd.setVisible(true);
saveToFile(fd.getFile());
}
break;
case 1: {
FileDialog fd = new FileDialog(new Frame(),"Load");
fd.setMode(FileDialog.LOAD);
fd.setVisible(true);
loadFromFile(fd.getFile());
}
break;
}
}
public void onSlider(int k) {
switch(k) {
case 0:
source.setFrequency((float)this.val[k]);
break;
case 1:
source.setOpenQuotient((float)this.val[k]);
break;
case 2:
source.setSpeedQuotient((float)this.val[k]);
break;
case 3:
source.setVolume((float)this.val[k]);
break;
default:
break;
}
}
};
a_controlPanelRosenberg.setSliders(valRosenberg,minRosenberg,maxRosenberg,namesRosenberg);
a_controlPanelRosenberg.setButtonNames (new String[] {"Save","Load"});
a_controlPanelRosenberg.setVisible(true);
// end Rosenberg panel
//Ishizak-Flanagan twomass model panel
int nbuttonsTwoMass = 2;
int nSlidersTwoMass = 6;
String[] namesTwoMass = new String[nSlidersTwoMass];
double[] valTwoMass = new double[nSlidersTwoMass];
double[] minTwoMass = new double[nSlidersTwoMass];
double[] maxTwoMass = new double[nSlidersTwoMass];
namesTwoMass[0] = "q(freq)";
valTwoMass[0] = 1; minTwoMass[0] = .05; maxTwoMass[0] = 6;
namesTwoMass[1] = "p-lung";
valTwoMass[1] = 500; minTwoMass[1] = 0; maxTwoMass[1] = 6000;
namesTwoMass[2] = "Ag0(cm^2)";
valTwoMass[2] = -.005; minTwoMass[2] = -.5; maxTwoMass[2] = .5;
namesTwoMass[3] = "noiseLevel";
valTwoMass[3] = .3; minTwoMass[3] = 0; maxTwoMass[3] = 10;
namesTwoMass[4] = "noiseFreq.";
valTwoMass[4] = 1500; minTwoMass[4] = 200; maxTwoMass[4] = 10000;
namesTwoMass[5] = "noiseBW";
valTwoMass[5] = 6000; minTwoMass[5] = 250; maxTwoMass[5] = 10000;
a_controlPanelTwoMass = new Controller(new java.awt.Frame ("TwoMass Glottal Model"),
false,valTwoMass.length,nbuttonsTwoMass) {
private static final long serialVersionUID = 1L;
public void onButton(int k) {
switch(k) {
case 0: {
FileDialog fd = new FileDialog(new Frame(),"Save");
fd.setMode(FileDialog.SAVE);
fd.setVisible(true);
saveToFile(fd.getFile());
}
break;
case 1: {
FileDialog fd = new FileDialog(new Frame(),"Load");
fd.setMode(FileDialog.LOAD);
fd.setVisible(true);
loadFromFile(fd.getFile());
}
break;
}
}
public void onSlider(int k) {
switch(k) {
case 0:
// q factor of two mass model
twoMassSource.getVars().q = this.val[k];
//twoMassSource.getVars().setVars();
break;
case 1:
// lung pressure
twoMassSource.getVars().ps = this.val[k];
//twoMassSource.getVars().setVars();
break;
case 2:
// glottal rest area (displayed in cm^2)
twoMassSource.getVars().Ag0 = 1.e-4 * this.val[k];
//twoMassSource.getVars().setVars();
break;
case 3:
twoMassSource.setFlowNoiseLevel(this.val[k]);
break;
case 4:
twoMassSource.setFlowNoiseFrequency(this.val[k]);
break;
case 5:
twoMassSource.setFlowNoiseBandwidth(this.val[k]);
break;
default:
break;
}
}
};
a_controlPanelTwoMass.setSliders(valTwoMass,minTwoMass,maxTwoMass,namesTwoMass);
a_controlPanelTwoMass.setButtonNames (new String[] {"Save","Load"});
a_controlPanelTwoMass.setVisible(true);
// end Ishizak-Flanagan twomass model panel
// add airflow monitor
final JProgressBar progressBar = new JProgressBar(0, 1000);
progressBar.setValue(0);
progressBar.setStringPainted(true);
a_controlPanelTwoMass.add(progressBar);
a_controlPanelTwoMass.getContentPane ().setLayout (new java.awt.GridLayout (nSlidersTwoMass+(nbuttonsTwoMass+2)/2, 2));
a_controlPanelTwoMass.pack();
// set locations of panels on screen
a_controlPanel.setLocation(new Point(740,10));
Point p = a_controlPanel.getLocation();
p.translate(430,0);
a_controlPanelNasal.setLocation(p);
p.translate(0,300);
a_controlPanelRosenberg.setLocation(p);
p.translate(0,150);
a_controlPanelTwoMass.setLocation(p);
player.start();
try {
Thread.sleep(1000);
} catch(Exception e){};
filter.reset();
try {
Thread.sleep(100);
} catch(Exception e){};
player.resetAGC();
int sleepms = 100/100;
double maxug = .00000001;
double L0=.17;
double LL = L0;
double L1 = .20;
double dL = .0002;
boolean goUp=true;
while(!haltMe) {
try {
Thread.sleep(sleepms);
if(slideStarted) {
tm.setLength(LL);
if(goUp) {
LL += dL;
} else {
LL -= dL;
}
if(LL<L0) {
goUp=true;
}
if(LL>L1) {
goUp=false;
}
filter.changeTubeModel();
}
/*double ug = twoMassSource.getUg();
ug = Math.abs(ug);
if(ug>maxug) {
maxug=ug;
}
int pval = (int)(1000*ug/maxug);
progressBar.setValue(pval);
progressBar.setString("ug="+String.valueOf(ug));
*/
} catch(Exception e) {}
//airway.scale(tm);
}
}
double[] fantData_a = new double[] {5, 5, 5, 5, 6.5, 8, 8, 8, 8, 8,
8, 8, 8, 6.5, 5, 4, 3.2, 1.6, 2.6, 2.6,
2, 1.6, 1.3, 1, .65, .65, .65, 1, 1.6, 2.6,
4, 1, 1.3, 1.6, 2.6};
double[] fantData_o = new double[] {3.2,3.2,3.2,3.2,6.5, 13,13,16,13,10.5,
10.5,8,8,6.5,6.5, 5,5,4,3.2,2,
1.6,2.6,1.3,.65,.65, 1,1,1.3,1.6,2,
3.2,4,5,5,1.3, 1.3,1.6,2.6};
double[] fantData_u = new double[] {.65,.65,.32,.32,2, 5,10.5,13,13,13,
13,10.5,8,6.5,5, 3.2,2.6,2,2,2,
1.6,1.3,2,1.6,1, 1,1,1.3,1.6,3.2,
5,8,8,10.5,10.5, 10.5,2,2,2.6, 2.6};
double[] fantData_i_ = new double[] {6.5,6.5,2,6.5,8, 8,8,5,3.2,2.6,
2,2,1.6,1.3,1, 1,1.3,1.6,2.6,2,
4,5,6.5,6.5,8, 10.5,10.5,10.5,10.5,10.5,
13,13,10.5,10.5,6, 3.2,3.2,3.2,3.2};
double[] fantData_i = new double[] {4,4,3.2,1.6,1.3, 1,.65,.65,.65,.65,
.65,.65,.65,1.3,2.6, 4,6.5,8,8,10.5,
10.5,10.5,10.5,10.5,10.5, 10.5,10.5,10.5,8,8,
2,2,2.6,3.2};
double[] fantData_e = new double[] {8,8,5,5,4, 2.6,2,2.6,2.6,3.2,
4,4,4,5,5, 6.5,8,6.5,8,10.5,
10.5,10.5,10.5,10.5,8, 8,6.5,6.5,6.5,6.5,
1.3,1.6,2,2.6};
double[] fantData__ = new double[] {5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5};
public void preset(String p) {
double[] f_a=null;
if (p=="a") {
f_a = fantData_a;
}
if (p=="o") {
f_a = fantData_o;
}
if (p=="u") {
f_a = fantData_u;
}
if (p=="i_") {
f_a = fantData_i_;
}
if (p=="i") {
f_a = fantData_i;
}
if (p=="e") {
f_a = fantData_e;
}
if (p=="-") {
f_a = fantData__;
}
// interpolate and invert Fant data
double C = (f_a.length-1.)/(tract.length-1);
for(int i=0;i<tract.length;i++) {
double k = i*C;
int ki = (int)k;
double kfrac = k-ki;
int i1 = ki;
int i2 = i1+1;
if(i2>f_a.length-1) {
i2 = i1;
}
// radii in meters
tract[tract.length-i-1] = Math.sqrt((f_a[i1]*(1-kfrac)+f_a[i2]*kfrac)/Math.PI)/100;
}
}
}