// WaveBox.java (c) 2001 by Paul Falstad, www.falstad.com.
// Rendering algorithm in this applet is based on the description of
// the algorithm used in Atom in a Box by Dean Dauger (www.dauger.com).
// We raytrace through a 3-d dataset, sampling a number of points and
// integrating over them using Simpson's rule.
import java.io.InputStream;
import java.awt.*;
import java.awt.image.ImageProducer;
import java.applet.Applet;
import java.applet.AudioClip;
import java.util.Vector;
import java.util.Hashtable;
import java.util.Enumeration;
import java.io.File;
import java.net.URL;
import java.util.Random;
import java.util.Arrays;
import java.awt.image.MemoryImageSource;
import java.lang.Math;
import java.lang.reflect.Constructor;
import java.lang.reflect.Method;
import java.awt.event.*;
class WaveBoxCanvas extends Canvas {
WaveBoxFrame pg;
WaveBoxCanvas(WaveBoxFrame p) {
pg = p;
}
public Dimension getPreferredSize() {
return new Dimension(300,400);
}
public void update(Graphics g) {
pg.updateWaveBox(g);
}
public void paint(Graphics g) {
pg.updateWaveBox(g);
}
};
class WaveBoxLayout implements LayoutManager {
public WaveBoxLayout() {}
public void addLayoutComponent(String name, Component c) {}
public void removeLayoutComponent(Component c) {}
public Dimension preferredLayoutSize(Container target) {
return new Dimension(500, 500);
}
public Dimension minimumLayoutSize(Container target) {
return new Dimension(100,100);
}
public void layoutContainer(Container target) {
int barwidth = 0;
int i;
for (i = 1; i < target.getComponentCount(); i++) {
Component m = target.getComponent(i);
if (m.isVisible()) {
Dimension d = m.getPreferredSize();
if (d.width > barwidth)
barwidth = d.width;
}
}
Insets insets = target.insets();
int targetw = target.size().width - insets.left - insets.right;
int cw = targetw-barwidth;
int targeth = target.size().height - (insets.top+insets.bottom);
target.getComponent(0).move(insets.left, insets.top);
target.getComponent(0).resize(cw, targeth);
cw += insets.left;
int h = insets.top;
for (i = 1; i < target.getComponentCount(); i++) {
Component m = target.getComponent(i);
if (m.isVisible()) {
Dimension d = m.getPreferredSize();
if (m instanceof Scrollbar)
d.width = barwidth;
if (m instanceof Label) {
h += d.height/5;
d.width = barwidth;
}
m.move(cw, h);
m.resize(d.width, d.height);
h += d.height;
}
}
}
};
public class WaveBox extends Applet implements ComponentListener {
static WaveBoxFrame ogf;
void destroyFrame() {
if (ogf != null)
ogf.dispose();
ogf = null;
repaint();
}
boolean started = false;
public void init() {
addComponentListener(this);
}
public static void main(String args[]) {
ogf = new WaveBoxFrame(null);
ogf.init();
}
void showFrame() {
if (ogf == null) {
started = true;
ogf = new WaveBoxFrame(this);
ogf.init();
repaint();
}
}
public void paint(Graphics g) {
String s = "Applet is open in a separate window.";
if (!started)
s = "Applet is starting.";
else if (ogf == null)
s = "Applet is finished.";
else
ogf.show();
g.drawString(s, 10, 30);
}
public void componentHidden(ComponentEvent e){}
public void componentMoved(ComponentEvent e){}
public void componentShown(ComponentEvent e) { showFrame(); }
public void componentResized(ComponentEvent e) {}
public void destroy() {
if (ogf != null)
ogf.dispose();
ogf = null;
repaint();
}
};
class WaveBoxFrame extends Frame
implements ComponentListener, ActionListener, AdjustmentListener,
MouseMotionListener, MouseListener, ItemListener {
Thread engine = null;
Dimension winSize;
Image dbimage, memimage;
MemoryImageSource imageSource;
Random random;
int gridSizeX = 200;
int gridSizeY = 200;
public String getAppletInfo() {
return "WaveBox by Paul Falstad";
}
Checkbox stoppedCheck;
Checkbox intensityCheck;
Checkbox sidesCheck;
Choice modeChooser;
Choice sliceChooser;
static final int SLICE_NONE = 0;
static final int SLICE_X = 1;
static final int SLICE_Y = 2;
static final int SLICE_Z = 3;
Scrollbar speedBar;
Scrollbar resolutionBar;
Scrollbar brightnessBar;
Scrollbar freqBar;
Scrollbar aux1Bar;
Scrollbar aux2Bar;
Scrollbar aux3Bar;
Scrollbar sampleBar;
class AuxBar {
Scrollbar bar;
Label label;
AuxBar(Label l, Scrollbar b) { label = l; bar = b; }
};
AuxBar auxBars[];
Choice setupChooser;
Vector setupList;
Setup setup;
double dragZoomStart;
double zoom = 7.5;
double rotmatrix[];
Rectangle view3d;
double colorMult;
static final double pi = 3.14159265358979323846;
static final double pi2 = pi*2;
int xpoints[];
int ypoints[];
int spectrum[];
static final int spectrumSpacing = 50;
double func[][][];
double boxwidth = 2;
double boxheight = 2;
double resadj;
boolean dragging = false;
int pixels[];
int maxTerms = 16;
static int maxModes = 10;
static int maxDispCoefs = 8;
static int viewDistance = 12;
int pause;
WaveBox applet;
int selection = -1;
static final int SEL_NONE = 0;
static final int SEL_3D = 1;
static final int SEL_MAG = 2;
static final int SEL_SPECTRUM = 3;
static final int MODE_ANGLE = 0;
static final int MODE_ZOOM = 1;
static final int MODE_SLICE = 2;
int slicerPoints[][];
double sliceFaces[][];
double sliceFace[];
int sliceFaceCount;
double sliceval = 0;
int sampleCount = 15;
int sampleMult[];
boolean selectedSlice;
boolean needsPrecompute;
double magDragStart;
double cost1, cost2, sint1, sint2;
int dragX, dragY, oldDragX, oldDragY, dragStartX, dragStartY;
double t = 0;
public static final double epsilon = .00001;
public static final double epsilon2 = .003;
int getrand(int x) {
int q = random.nextInt();
if (q < 0) q = -q;
return q % x;
}
WaveBoxCanvas cv;
WaveBoxFrame(WaveBox a) {
super("3D Wave Applet v1.5a");
applet = a;
}
boolean useBufferedImage = false;
public void init() {
setupList = new Vector();
Setup s = new SingleSourceSetup();
while (s != null) {
setupList.addElement(s);
s = s.createNext();
}
String jv = System.getProperty("java.class.version");
double jvf = new Double(jv).doubleValue();
if (jvf >= 48)
useBufferedImage = true;
setLayout(new WaveBoxLayout());
cv = new WaveBoxCanvas(this);
cv.addComponentListener(this);
cv.addMouseMotionListener(this);
cv.addMouseListener(this);
add(cv);
add(new Label("Setup:", Label.CENTER));
setupChooser = new Choice();
int i;
for (i = 0; i != setupList.size(); i++)
setupChooser.add(((Setup) setupList.elementAt(i)).getName());
add(setupChooser);
setupChooser.addItemListener(this);
setup = (Setup) setupList.elementAt(2);
setupChooser.select(2);
stoppedCheck = new Checkbox("Stopped");
stoppedCheck.addItemListener(this);
add(stoppedCheck);
intensityCheck = new Checkbox("Show Intensity");
intensityCheck.addItemListener(this);
add(intensityCheck);
sidesCheck = new Checkbox("Show Sides");
sidesCheck.addItemListener(this);
add(sidesCheck);
modeChooser = new Choice();
modeChooser.add("Mouse = Adjust Angle");
modeChooser.add("Mouse = Adjust Zoom");
modeChooser.addItemListener(this);
add(modeChooser);
sliceChooser = new Choice();
sliceChooser.add("No Slicing");
sliceChooser.add("Show X Slice");
sliceChooser.add("Show Y Slice");
sliceChooser.add("Show Z Slice");
sliceChooser.addItemListener(this);
add(sliceChooser);
add(new Label("Simulation Speed", Label.CENTER));
add(speedBar = new Scrollbar(Scrollbar.HORIZONTAL, 15, 1, 1, 200));
speedBar.addAdjustmentListener(this);
add(new Label("Brightness", Label.CENTER));
add(brightnessBar = new Scrollbar(Scrollbar.HORIZONTAL, 240,
1, 1, 2000));
brightnessBar.addAdjustmentListener(this);
add(new Label("Image Resolution", Label.CENTER));
add(resolutionBar =
new Scrollbar(Scrollbar.HORIZONTAL, 100, 2, 20, 240));
resolutionBar.addAdjustmentListener(this);
add(new Label("Frequency", Label.CENTER));
add(freqBar = new Scrollbar(Scrollbar.HORIZONTAL, 24, 1, 5, 60));
freqBar.addAdjustmentListener(this);
Label lb;
auxBars = new AuxBar[3];
add(lb = new Label("Aux 1", Label.CENTER));
add(aux1Bar = new Scrollbar(Scrollbar.HORIZONTAL, 10, 1, 0, 100));
aux1Bar.addAdjustmentListener(this);
auxBars[0] = new AuxBar(lb, aux1Bar);
add(lb = new Label("Aux 2", Label.CENTER));
add(aux2Bar = new Scrollbar(Scrollbar.HORIZONTAL, 0, 1, 0, 100));
aux2Bar.addAdjustmentListener(this);
auxBars[1] = new AuxBar(lb, aux2Bar);
add(lb = new Label("Aux 3", Label.CENTER));
add(aux3Bar = new Scrollbar(Scrollbar.HORIZONTAL, 0, 1, 0, 100));
aux3Bar.addAdjustmentListener(this);
auxBars[2] = new AuxBar(lb, aux3Bar);
hideBars();
/*add(new Label("Samples", Label.CENTER));
add(sampleBar = new Scrollbar(Scrollbar.HORIZONTAL, 10, 1, 0, 20));
sampleBar.addAdjustmentListener(this);*/
add(new Label("", Label.CENTER));
try {
String param = applet.getParameter("PAUSE");
if (param != null)
pause = Integer.parseInt(param);
} catch (Exception e) { }
slicerPoints = new int[2][5*2];
sliceFaces = new double[4][3];
rotmatrix = new double[9];
rotmatrix[0] = rotmatrix[4] = rotmatrix[8] = 1;
xpoints = new int[4];
ypoints = new int[4];
setupSimpson();
setup.select();
random = new Random();
reinit();
cv.setBackground(Color.black);
cv.setForeground(Color.white);
resize(650,550);
handleResize();
Dimension x = getSize();
Dimension screen = getToolkit().getScreenSize();
setLocation((screen.width - x.width)/2,
(screen.height - x.height)/2);
show();
}
void setupSimpson() {
sampleCount = 23; // 15
/*sampleCount = sampleBar.getValue()*2+1;
System.out.println("samples = " + sampleCount);*/
// generate table of sample multipliers for efficient Simpson's rule
sampleMult = new int[sampleCount];
int i;
for (i = 1; i < sampleCount; i += 2) {
sampleMult[i ] = 4;
sampleMult[i+1] = 2;
}
sampleMult[0] = sampleMult[sampleCount-1] = 1;
}
void handleResize() {
reinit();
}
void reinit() {
setMaxTerms();
Dimension d = winSize = cv.getSize();
if (winSize.width == 0)
return;
dbimage = createImage(d.width, d.height);
setupDisplay();
pixels = null;
if (useBufferedImage) {
try {
/* simulate the following code using reflection:
dbimage = new BufferedImage(d.width, d.height,
BufferedImage.TYPE_INT_RGB);
DataBuffer db = (DataBuffer)(((BufferedImage)memimage).
getRaster().getDataBuffer());
DataBufferInt dbi = (DataBufferInt) db;
pixels = dbi.getData();
*/
Class biclass = Class.forName("java.awt.image.BufferedImage");
Class dbiclass = Class.forName("java.awt.image.DataBufferInt");
Class rasclass = Class.forName("java.awt.image.Raster");
Constructor cstr = biclass.getConstructor(
new Class[] { int.class, int.class, int.class });
memimage = (Image) cstr.newInstance(new Object[] {
new Integer(view3d.width), new Integer(view3d.height),
new Integer(1)}); // BufferedImage.TYPE_INT_RGB)});
Method m = biclass.getMethod("getRaster", null);
Object ras = m.invoke(memimage, null);
Object db = rasclass.getMethod("getDataBuffer", null).
invoke(ras, null);
pixels = (int[])
dbiclass.getMethod("getData", null).invoke(db, null);
} catch (Exception ee) {
// ee.printStackTrace();
System.out.println("BufferedImage failed");
}
}
if (pixels == null) {
pixels = new int[view3d.width*view3d.height];
int i;
for (i = 0; i != view3d.width*view3d.height; i++)
pixels[i] = 0xFF000000;
imageSource = new MemoryImageSource(view3d.width, view3d.height,
pixels, 0, view3d.width);
imageSource.setAnimated(true);
imageSource.setFullBufferUpdates(true);
memimage = cv.createImage(imageSource);
}
}
int getTermWidth() {
return 8;
}
// multiply rotation matrix by rotations through angle1 and angle2
void rotate(double angle1, double angle2) {
double r1cos = java.lang.Math.cos(angle1);
double r1sin = java.lang.Math.sin(angle1);
double r2cos = java.lang.Math.cos(angle2);
double r2sin = java.lang.Math.sin(angle2);
double rotm2[] = new double[9];
// angle1 is angle about y axis, angle2 is angle about x axis
rotm2[0] = r1cos;
rotm2[1] = -r1sin*r2sin;
rotm2[2] = r2cos*r1sin;
rotm2[3] = 0;
rotm2[4] = r2cos;
rotm2[5] = r2sin;
rotm2[6] = -r1sin;
rotm2[7] = -r1cos*r2sin;
rotm2[8] = r1cos*r2cos;
double rotm1[] = rotmatrix;
rotmatrix = new double[9];
int i, j, k;
for (j = 0; j != 3; j++)
for (i = 0; i != 3; i++) {
double v = 0;
for (k = 0; k != 3; k++)
v += rotm1[k+j*3]*rotm2[i+k*3];
rotmatrix[i+j*3] = v;
}
}
double max(double a, double b) { return a > b ? a : b; }
double min(double a, double b) { return a < b ? a : b; }
void setMaxTerms() {
gridSizeX = gridSizeY = (resolutionBar.getValue() & ~1);
maxTerms = gridSizeX;
/*if (maxTerms > 100)
maxTerms = 100;*/
resadj = 50./maxTerms;
needsPrecompute = true;
}
void setupBar(int n, String text, int val) {
auxBars[n].label.setText(text);
auxBars[n].label.show();
auxBars[n].bar.setValue(val);
auxBars[n].bar.show();
}
// set view rectangles for the various subwindows
void setupDisplay() {
view3d = new Rectangle(0, 0, winSize.width, winSize.height);
}
// compute func[][][] array (2-d view) by raytracing through a
// 3-d dataset (data[][][])
void computeFunction() {
int i, j;
double q = 3.14159265/maxTerms;
cost1 = java.lang.Math.cos(t);
sint1 = java.lang.Math.sin(t);
cost2 = java.lang.Math.cos(t+setup.getPhaseShift());
sint2 = java.lang.Math.sin(t+setup.getPhaseShift());
double shiftcos = java.lang.Math.cos(setup.getPhaseShift());
double shiftsin = java.lang.Math.sin(setup.getPhaseShift());
double izoom = 1/zoom;
double rotm[] = rotmatrix;
double boxhalfwidth = boxwidth/2;
double boxhalfheight = boxheight/2;
double aratio = view3d.width/(double) view3d.height;
double xmult = maxTerms/boxwidth;
double ymult = maxTerms/boxheight;
double zmult = maxTerms/2.;
boolean intensity = intensityCheck.getState();
double aratiox = izoom, aratioy = izoom;
// preserve aspect ratio no matter what window dimensions
if (aratio < 1)
aratioy /= aratio;
else
aratiox *= aratio;
int slice = sliceChooser.getSelectedIndex();
if (sidesCheck.getState())
slice = SLICE_NONE;
double bmult = (intensity) ? 20 : 1;
for (i = 0; i != gridSizeX; i++)
for (j = 0; j != gridSizeY; j++) {
// calculate camera direction
double camvx0 = (2*i/(double) gridSizeX - 1)*aratiox;
double camvy0 = (2*j/(double) gridSizeY - 1)*aratioy;
// rotate camera with rotation matrix
double camx = rotm[2]*viewDistance;
double camy = rotm[5]*viewDistance;
double camz = rotm[8]*viewDistance;
double camvx = rotm[0]*camvx0+rotm[1]*camvy0-rotm[2];
double camvy = rotm[3]*camvx0+rotm[4]*camvy0-rotm[5];
double camvz = rotm[6]*camvx0+rotm[7]*camvy0-rotm[8];
double camnorm =
java.lang.Math.sqrt(camvx0*camvx0+camvy0*camvy0+1);
int n;
double simpr = 0;
double simpg = 0;
// calculate intersections with planes containing box edges
double tx1 = (-boxhalfwidth-camx)/camvx;
double tx2 = ( boxhalfwidth-camx)/camvx;
double ty1 = (-boxhalfheight-camy)/camvy;
double ty2 = ( boxhalfheight-camy)/camvy;
double tz1 = (-1-camz)/camvz;
double tz2 = ( 1-camz)/camvz;
// calculate portion of line that intersects box
double mint =
max(min(tx1, tx2),
max(min(ty1, ty2), min(tz1, tz2)))+.001;
double maxt =
min(max(tx1, tx2),
min(max(ty1, ty2), max(tz1, tz2)))-.001;
if (maxt < mint) {
// doesn't hit box
fillSquare(i, j, 0, 0, 0);
continue;
}
if (slice != SLICE_NONE) {
double t = -100;
switch (slice) {
case SLICE_X: t = (sliceval-camx)/camvx; break;
case SLICE_Y: t = (sliceval-camy)/camvy; break;
case SLICE_Z: t = (sliceval-camz)/camvz; break;
}
if (t < mint || t > maxt) {
fillSquare(i, j, 0, 0, 0);
continue;
}
mint = maxt = t;
}
// sample evenly along intersecting portion
double tstep = (maxt-mint)/(sampleCount-1);
double pathlen = (maxt-mint)*camnorm;
int maxn = sampleCount;
if (sidesCheck.getState()) {
maxn = 1;
pathlen = 5;
} else if (slice != SLICE_NONE) {
maxn = 1;
pathlen = 2;
}
double xx = (camx + camvx * mint + boxhalfwidth) * xmult;
double yy = (camy + camvy * mint + boxhalfheight) * ymult;
double zz = (camz + camvz * mint + 1) * zmult;
camvx *= tstep*xmult;
camvy *= tstep*ymult;
camvz *= tstep*zmult;
for (n = 0; n < maxn; n++) {
// find grid element that contains sampled point
int xxi = (int) xx;
int yyi = (int) yy;
int zzi = (int) zz;
double f = 0;
if (intensity) {
// this is pretty inefficient but the speed
// requirements are much less for intensity
cost1 = 1; sint1 = 0;
cost2 = shiftcos; sint2 = shiftsin;
double a = setup.computePoint(xxi, yyi, zzi);
cost1 = 0; sint1 = 1;
cost2 = -shiftsin; sint2 = shiftcos;
double b = setup.computePoint(xxi, yyi, zzi);
f = a*a+b*b;
} else
f = setup.computePoint(xxi, yyi, zzi);
if (f < 0) {
simpr -= sampleMult[n] * f;
} else
simpg += sampleMult[n] * f;
xx += camvx;
yy += camvy;
zz += camvz;
}
simpr *= pathlen/n;
simpg *= pathlen/n;
fillSquare(i, j, simpr*bmult, simpg*bmult, 0);
}
}
int sign(double x) {
return x < 0 ? -1 : 1;
}
public void paint(Graphics g) {
cv.repaint();
}
long lastTime;
public void updateWaveBox(Graphics realg) {
Graphics g = null;
if (winSize == null || winSize.width == 0)
return;
g = dbimage.getGraphics();
g.setColor(cv.getBackground());
g.fillRect(0, 0, winSize.width, winSize.height);
g.setColor(cv.getForeground());
boolean allQuiet = false;
if (!stoppedCheck.getState()) {
long sysTime = System.currentTimeMillis();
double tadd = 0;
if (lastTime != 0) {
int val = speedBar.getValue();
tadd = val*(sysTime-lastTime)*.0003;
t += tadd;
}
lastTime = sysTime;
} else {
lastTime = 0;
allQuiet = true;
}
if (intensityCheck.getState())
allQuiet = true;
colorMult = brightnessBar.getValue() * 5;
if (needsPrecompute) {
setup.precompute();
needsPrecompute = false;
}
computeFunction();
int i, j, k;
boolean sliced = sliceChooser.getSelectedIndex() != SLICE_NONE;
if (imageSource != null)
imageSource.newPixels();
g.drawImage(memimage, view3d.x, view3d.y, null);
g.setColor(Color.white);
drawCube(g, false);
realg.drawImage(dbimage, 0, 0, this);
if (!allQuiet)
cv.repaint(pause);
}
// see if the face containing (nx, ny, nz) is visible.
boolean visibleFace(int nx, int ny, int nz) {
double viewx = viewDistance*rotmatrix[2];
double viewy = viewDistance*rotmatrix[5];
double viewz = viewDistance*rotmatrix[8];
return (nx-viewx)*nx+(ny-viewy)*ny+(nz-viewz)*nz < 0;
}
void fillSquare(int i, int j, double cr, double cg, double cb) {
int winw = view3d.width;
int winh = view3d.height;
int x = i*winw/gridSizeX;
int y = j*winh/gridSizeY;
int x2 = (i+1)*winw/gridSizeX;
int y2 = (j+1)*winh/gridSizeY;
cr *= colorMult;
cg *= colorMult;
cb *= colorMult;
int k, l;
if (cr == 0 && cg == 0 && cb == 0) {
int y2l = y2*view3d.width;
for (k = x; k < x2; k++)
for (l = y*view3d.width; l < y2l; l += view3d.width)
pixels[k+l] = 0xFF000000;
return;
}
double fm = max(cr, max(cg, cb));
if (fm > 255) {
fm /= 255;
cr /= fm;
cg /= fm;
cb /= fm;
}
int colval = 0xFF000000 +
(((int) cr) << 16) |
(((int) cg) << 8) |
(((int) cb));
int y2l = y2*view3d.width;
for (k = x; k < x2; k++)
for (l = y*view3d.width; l < y2l; l += view3d.width)
pixels[k+l] = colval;
}
// draw the cube containing the particles. if drawAll is false then
// we just draw faces that are facing the camera. This routine draws
// each edge twice which is unnecessary, but easier.
void drawCube(Graphics g, boolean drawAll) {
int i;
int slice = sliceChooser.getSelectedIndex();
int sp = 0;
for (i = 0; i != 6; i++) {
// calculate normal of ith face
int nx = (i == 0) ? -1 : (i == 1) ? 1 : 0;
int ny = (i == 2) ? -1 : (i == 3) ? 1 : 0;
int nz = (i == 4) ? -1 : (i == 5) ? 1 : 0;
// if face is not facing camera, don't draw it
if (!drawAll && !visibleFace(nx, ny, nz))
continue;
double pts[];
pts = new double[3];
int n;
for (n = 0; n != 4; n++) {
computeFace(i, n, pts);
map3d(pts[0], pts[1], pts[2], xpoints, ypoints, n);
}
g.setColor(Color.gray);
g.drawPolygon(xpoints, ypoints, 4);
if (slice != SLICE_NONE && i/2 != slice-SLICE_X) {
if (selectedSlice)
g.setColor(Color.yellow);
int coord1 = (slice == SLICE_X) ? 1 : 0;
int coord2 = (slice == SLICE_Z) ? 1 : 2;
computeFace(i, 0, pts);
pts[slice-SLICE_X] = sliceval;
map3d(pts[0], pts[1], pts[2],
slicerPoints[0], slicerPoints[1], sp);
computeFace(i, 2, pts);
pts[slice-SLICE_X] = sliceval;
map3d(pts[0], pts[1], pts[2],
slicerPoints[0], slicerPoints[1], sp+1);
g.drawLine(slicerPoints[0][sp ], slicerPoints[1][sp],
slicerPoints[0][sp+1], slicerPoints[1][sp+1]);
sliceFaces[sp/2][0] = nx;
sliceFaces[sp/2][1] = ny;
sliceFaces[sp/2][2] = nz;
sp += 2;
}
}
sliceFaceCount = sp;
}
// generate the nth vertex of the bth cube face
void computeFace(int b, int n, double pts[]) {
// One of the 3 coordinates (determined by a) is constant.
// When b=0, x=-1; b=1, x=+1; b=2, y=-1; b=3, y=+1; etc
int a = b >> 1;
pts[a] = ((b & 1) == 0) ? -1 : 1;
// fill in the other 2 coordinates with one of the following
// (depending on n): -1,-1; +1,-1; +1,+1; -1,+1
int i;
for (i = 0; i != 3; i++) {
if (i == a) continue;
pts[i] = (((n>>1)^(n&1)) == 0) ? -1 : 1;
n >>= 1;
}
}
// map 3-d point (x,y,z) to screen, storing coordinates
// in xpoints[pt],ypoints[pt]
void map3d(double x, double y, double z,
int xpoints[], int ypoints[], int pt) {
x *= boxwidth/2;
y *= boxheight/2;
double rotm[] = rotmatrix;
double realx = x*rotm[0] + y*rotm[3] + z*rotm[6];
double realy = x*rotm[1] + y*rotm[4] + z*rotm[7];
double realz = viewDistance-(x*rotm[2] + y*rotm[5] + z*rotm[8]);
double scalex = view3d.width*zoom/2;
double scaley = view3d.height*zoom/2;
double aratio = view3d.width/(double) view3d.height;
// preserve aspect ratio regardless of window dimensions
if (aratio < 1)
scaley *= aratio;
else
scalex /= aratio;
xpoints[pt] = view3d.width /2 + (int) (scalex*realx/realz);
ypoints[pt] = view3d.height/2 + (int) (scaley*realy/realz);
}
// map point on screen to 3-d coordinates assuming it lies on a given plane
void unmap3d(double x3[], int x, int y, double pn[], double pp[]) {
// first, find all points which map to (x,y) on the screen.
// this is a line.
double scalex = view3d.width*zoom/2;
double scaley = view3d.height*zoom/2;
double aratio = view3d.width/(double) view3d.height;
// preserve aspect ratio regardless of window dimensions
if (aratio < 1)
scaley *= aratio;
else
scalex /= aratio;
double vx = (x-(view3d.width/2))/scalex;
double vy = (y-(view3d.height/2))/scaley;
// vz = -1
// map the line vector to object space
double rotm[] = rotmatrix;
double mx = viewDistance*rotm[2];
double my = viewDistance*rotm[5];
double mz = viewDistance*rotm[8];
double mvx = (vx*rotm[0] + vy*rotm[1] - rotm[2]);
double mvy = (vx*rotm[3] + vy*rotm[4] - rotm[5]);
double mvz = (vx*rotm[6] + vy*rotm[7] - rotm[8]);
// calculate the intersection between the line and the given plane
double t = ((pp[0]-mx)*pn[0] +
(pp[1]-my)*pn[1] +
(pp[2]-mz)*pn[2]) /
(pn[0]*mvx+pn[1]*mvy+pn[2]*mvz);
x3[0] = mx+mvx*t;
x3[1] = my+mvy*t;
x3[2] = mz+mvz*t;
}
double logep2 = 0;
int logcoef(double x) {
double ep2 = epsilon2;
int sign = (x < 0) ? -1 : 1;
x *= sign;
if (x < ep2)
return 0;
if (logep2 == 0)
logep2 = -java.lang.Math.log(2*ep2);
return (int) (255 * sign * (java.lang.Math.log(x+ep2)+logep2)/logep2);
}
int getColorValue(int i, int j, int k) {
int val = (int) (func[i][j][k] * colorMult);
if (val > 255)
val = 255;
return val;
}
public void componentHidden(ComponentEvent e){}
public void componentMoved(ComponentEvent e){}
public void componentShown(ComponentEvent e) {
cv.repaint();
}
public void componentResized(ComponentEvent e) {
handleResize();
cv.repaint(pause);
}
public void actionPerformed(ActionEvent e) {
}
int resBarValue;
public void adjustmentValueChanged(AdjustmentEvent e) {
System.out.print(((Scrollbar) e.getSource()).getValue() + "\n");
if (e.getSource() == freqBar || e.getSource() == aux1Bar ||
e.getSource() == aux2Bar || e.getSource() == aux3Bar)
needsPrecompute = true;
if (e.getSource() == resolutionBar &&
resolutionBar.getValue() != resBarValue) {
setMaxTerms();
resBarValue = resolutionBar.getValue();
}
setupSimpson();
cv.repaint(pause);
}
public void mouseDragged(MouseEvent e) {
dragging = true;
oldDragX = dragX;
oldDragY = dragY;
dragX = e.getX(); dragY = e.getY();
edit(e);
}
boolean csInRange(int x, int xa, int xb) {
if (xa < xb)
return x >= xa-5 && x <= xb+5;
return x >= xb-5 && x <= xa+5;
}
void checkSlice(int x, int y) {
if (sliceChooser.getSelectedIndex() == SLICE_NONE) {
selectedSlice = false;
return;
}
int n;
selectedSlice = false;
for (n = 0; n != sliceFaceCount; n += 2) {
int xa = slicerPoints[0][n];
int xb = slicerPoints[0][n+1];
int ya = slicerPoints[1][n];
int yb = slicerPoints[1][n+1];
if (!csInRange(x, xa, xb) || !csInRange(y, ya, yb))
continue;
double d;
if (xa == xb)
d = java.lang.Math.abs(x-xa);
else {
// write line as y=a+bx
double b = (yb-ya)/(double) (xb-xa);
double a = ya-b*xa;
// solve for distance
double d1 = y-(a+b*x);
if (d1 < 0)
d1 = -d1;
d = d1/java.lang.Math.sqrt(1+b*b);
}
if (d < 6) {
selectedSlice = true;
sliceFace = sliceFaces[n/2];
break;
}
}
}
public void mouseMoved(MouseEvent e) {
checkSlice(e.getX(), e.getY());
if ((e.getModifiers() & MouseEvent.BUTTON1_MASK) != 0) {
if (selection != -1) {
dragging = true;
}
return;
}
}
public void mouseClicked(MouseEvent e) {
}
public void mouseEntered(MouseEvent e) {
}
public void mouseExited(MouseEvent e) {
}
public void mousePressed(MouseEvent e) {
if ((e.getModifiers() & MouseEvent.BUTTON1_MASK) == 0)
return;
oldDragX = dragStartX = e.getX();
oldDragY = dragStartY = e.getY();
dragZoomStart = zoom;
dragging = true;
edit(e);
}
public void mouseReleased(MouseEvent e) {
if (dragging)
cv.repaint();
dragging = false;
}
public void itemStateChanged(ItemEvent e) {
if (e.getItemSelectable() == setupChooser) {
sliceChooser.select(0);
setup.deselect();
setup = (Setup)
setupList.elementAt(setupChooser.getSelectedIndex());
hideBars();
setup.select();
setup.precompute();
validate();
}
cv.repaint(pause);
}
void hideBars() {
int i;
for (i = 0; i != 3; i++) {
auxBars[i].label.hide();
auxBars[i].bar.hide();
}
}
public boolean handleEvent(Event ev) {
if (ev.id == Event.WINDOW_DESTROY) {
applet.destroyFrame();
return true;
}
return super.handleEvent(ev);
}
void edit(MouseEvent e) {
if (selection == SEL_NONE)
return;
int x = e.getX();
int y = e.getY();
edit3d(x, y);
}
void edit3d(int x, int y) {
int mode = modeChooser.getSelectedIndex();
if (selectedSlice)
mode = MODE_SLICE;
if (mode == MODE_ANGLE) {
int xo = oldDragX-x;
int yo = oldDragY-y;
rotate(xo/40., yo/40.);
cv.repaint(pause);
} else if (mode == MODE_ZOOM) {
int xo = x-dragStartX;
zoom = dragZoomStart + xo/20.;
if (zoom < .1)
zoom = .1;
cv.repaint(pause);
} else if (mode == MODE_SLICE) {
double x3[] = new double[3];
unmap3d(x3, x, y, sliceFace, sliceFace);
switch (sliceChooser.getSelectedIndex()) {
case SLICE_X: sliceval = x3[0]; break;
case SLICE_Y: sliceval = x3[1]; break;
case SLICE_Z: sliceval = x3[2]; break;
}
// Avoid -1 because it causes particles to drift out of the
// cube too easily. Avoid +1 because of that and because it is
// not included in any density group.
if (sliceval < -.99)
sliceval = -.99;
if (sliceval > .99)
sliceval = .99;
cv.repaint(pause);
}
}
abstract class Setup {
abstract String getName();
void select() {}
void precompute() {}
void deselect() {}
double getPhaseShift() { return 0; }
abstract double computePoint(int x, int y, int z);
abstract Setup createNext();
Setup() { }
};
class SingleSourceSetup extends Setup {
int dataxy[][];
double datadzr[][], datadzi[][];
int mxhalf;
int mxlast;
String getName() { return "point source"; }
void select() { }
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
int maxdist = 0;
double mult = freqBar.getValue() / 50.;
dataxy = new int[maxTerms][maxTerms];
int distmult = 4;
for (x = 0; x != maxTerms; x++)
for (y = 0; y != maxTerms; y++) {
double xi = x-mxhalf;
int yi = y-mxhalf;
dataxy[x][y] = (int)
(distmult*java.lang.Math.sqrt(xi*xi+yi*yi)+.5);
if (dataxy[x][y] > maxdist)
maxdist = dataxy[x][y];
}
datadzr = new double[maxdist+1][maxTerms];
datadzi = new double[maxdist+1][maxTerms];
for (x = 0; x != maxTerms; x++)
for (y = 0; y <= maxdist; y++) {
int xi = x-mxhalf;
double r = java.lang.Math.sqrt(y*y/(distmult*distmult)+
xi*xi)*resadj+.00000001;
datadzr[y][x] = java.lang.Math.cos(r*mult)/r;
datadzi[y][x] = -java.lang.Math.sin(r*mult)/r;
}
}
void deselect() {
dataxy = null;
datadzr = datadzi = null;
}
double computePoint(int x, int y, int z) {
int d = dataxy[x][y];
return datadzr[d][z]*cost1 - datadzi[d][z]*sint1;
}
Setup createNext() { return new PinholeSetup(); }
};
class PinholeSetup extends Setup {
int dataxy[][];
double datadzr[][], datadzi[][];
int mxhalf;
int mxlast;
String getName() { return "pinhole"; }
void select() { }
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
int maxdist = 0;
double mult = freqBar.getValue() / 50.;
dataxy = new int[maxTerms][maxTerms];
int distmult = 4;
for (x = 0; x != maxTerms; x++)
for (y = 0; y != maxTerms; y++) {
double xi = x-mxhalf;
int yi = y-mxhalf;
dataxy[x][y] = (int)
(distmult*java.lang.Math.sqrt(xi*xi+yi*yi)+.5);
if (dataxy[x][y] > maxdist)
maxdist = dataxy[x][y];
}
datadzr = new double[maxdist+1][maxTerms];
datadzi = new double[maxdist+1][maxTerms];
for (x = 0; x != maxTerms; x++)
for (y = 0; y <= maxdist; y++) {
double r = java.lang.Math.sqrt(y*y/(distmult*distmult)+
x*x)*resadj+.00000001;
datadzr[y][x] = java.lang.Math.cos(r*mult)/r;
datadzi[y][x] = -java.lang.Math.sin(r*mult)/r;
}
}
void deselect() {
dataxy = null;
datadzr = datadzi = null;
}
double computePoint(int x, int y, int z) {
int d = dataxy[x][y];
return datadzr[d][z]*cost1 - datadzi[d][z]*sint1;
}
Setup createNext() { return new TwoSourcesSetup(); }
};
class TwoSourcesSetup extends Setup {
int dataxy[][];
double datadzr[][], datadzi[][], w1mult, w2mult;
int mxhalf;
int mxlast;
boolean dipole;
String getName() { return "2 point sources"; }
void select() {
setupBar(0, "Source Separation", 30);
setupBar(1, "Phase Difference", 0);
setupBar(2, "Balance", 50);
dipole = false;
}
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
dataxy = new int[maxTerms][maxTerms];
double mult = freqBar.getValue() / 50.;
int distmult = 4;
double sep = aux1Bar.getValue()/3./resadj;
int maxdist = 0;
for (x = 0; x != maxTerms; x++) {
double xi = x-mxhalf+sep+.001;
for (y = 0; y != maxTerms; y++) {
double yi = y-mxhalf+.001;
dataxy[x][y] = (int)
(distmult*java.lang.Math.sqrt(xi*xi+yi*yi)+.5);
if (dataxy[x][y] > maxdist)
maxdist = dataxy[x][y];
}
}
datadzr = new double[maxdist+1][maxTerms];
datadzi = new double[maxdist+1][maxTerms];
for (z = 0; z != maxTerms; z++)
for (y = 0; y <= maxdist; y++) {
int zi = z-mxhalf;
double r =
java.lang.Math.sqrt(y*y/(distmult*distmult)+zi*zi)*resadj
+ .0000001;
datadzr[y][z] = java.lang.Math.cos(r*mult)/r;
datadzi[y][z] = -java.lang.Math.sin(r*mult)/r;
}
w1mult = (dipole) ? .5 : aux3Bar.getValue() / 100.;
w2mult = 1-w1mult;
}
double getPhaseShift() {
return (dipole) ? pi : aux2Bar.getValue()*pi/50.;
}
void deselect() {
dataxy = null;
datadzr = datadzi = null;
}
double computePoint(int x, int y, int z) {
int d1 = dataxy[x][y];
int d2 = dataxy[maxTerms-1-x][y];
return w1mult*(datadzr[d1][z]*cost1 - datadzi[d1][z]*sint1) +
w2mult*(datadzr[d2][z]*cost2 - datadzi[d2][z]*sint2);
}
Setup createNext() { return new DipoleSourceSetup(); }
};
class DipoleSourceSetup extends TwoSourcesSetup {
String getName() { return "dipole source"; }
void select() {
setupBar(0, "Source Separation", 8);
dipole = true;
}
Setup createNext() { return new LateralQuadrupoleSetup(); }
};
class LateralQuadrupoleSetup extends Setup {
int dataxy[][];
double datadzr[][], datadzi[][], w1mult;
int mxhalf;
int mxlast;
String getName() { return "lateral quadrupole"; }
void select() {
setupBar(0, "Source Separation", 20);
}
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
dataxy = new int[maxTerms][maxTerms];
double mult = freqBar.getValue() / 50.;
int distmult = 4;
double sep = aux1Bar.getValue()/3./resadj;
int maxdist = 0;
for (x = 0; x != maxTerms; x++) {
double xi = x-mxhalf+sep+.001;
for (y = 0; y != maxTerms; y++) {
double yi = y-mxhalf+.001;
dataxy[x][y] = (int)
(distmult*java.lang.Math.sqrt(xi*xi+yi*yi)+.5);
if (dataxy[x][y] > maxdist)
maxdist = dataxy[x][y];
}
}
datadzr = new double[maxdist+1][maxTerms];
datadzi = new double[maxdist+1][maxTerms];
for (z = 0; z != maxTerms; z++)
for (y = 0; y <= maxdist; y++) {
int zi = z-mxhalf;
double r =
java.lang.Math.sqrt(y*y/(distmult*distmult)+zi*zi)*resadj
+ .0000001;
datadzr[y][z] = .25*java.lang.Math.cos(r*mult)/r;
datadzi[y][z] = -.25*java.lang.Math.sin(r*mult)/r;
}
}
void deselect() {
dataxy = null;
datadzr = datadzi = null;
}
double computePoint(int x, int y, int z) {
int d1 = dataxy[x][y];
int d2 = dataxy[maxTerms-1-x][y];
int d3 = dataxy[y][x];
int d4 = dataxy[maxTerms-1-y][x];
return (datadzr[d1][z]+datadzr[d2][z]-
datadzr[d3][z]-datadzr[d4][z])*cost1 -
(datadzi[d1][z]+datadzi[d2][z]-
datadzi[d3][z]-datadzi[d4][z])*sint1;
}
Setup createNext() { return new LinearQuadrupoleSetup(); }
};
class LinearQuadrupoleSetup extends Setup {
int dataxy1[][], dataxy2[][];
double datadzr[][], datadzi[][];
int mxhalf;
int mxlast;
String getName() { return "linear quadrupole"; }
void select() {
setupBar(0, "Source Separation", 20);
}
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
double mult = freqBar.getValue() / 50.;
dataxy1 = new int[maxTerms][maxTerms];
dataxy2 = new int[maxTerms][maxTerms];
int distmult = 4;
double sep = aux1Bar.getValue()/3./resadj;
int maxdist = 0;
for (x = 0; x != maxTerms; x++) {
double xi1 = x-mxhalf+sep+.001;
double xi2 = x-mxhalf+sep/2+.001;
for (y = 0; y != maxTerms; y++) {
double yi = y-mxhalf+.001;
dataxy1[x][y] = (int)
(distmult*java.lang.Math.sqrt(xi1*xi1+yi*yi)+.5);
dataxy2[x][y] = (int)
(distmult*java.lang.Math.sqrt(xi2*xi2+yi*yi)+.5);
if (dataxy1[x][y] > maxdist)
maxdist = dataxy1[x][y];
if (dataxy2[x][y] > maxdist)
maxdist = dataxy2[x][y];
}
}
datadzr = new double[maxdist+1][maxTerms];
datadzi = new double[maxdist+1][maxTerms];
for (z = 0; z != maxTerms; z++)
for (y = 0; y <= maxdist; y++) {
int zi = z-mxhalf;
double r =
java.lang.Math.sqrt(y*y/(distmult*distmult)+zi*zi)*resadj
+ .0000001;
datadzr[y][z] = .25*java.lang.Math.cos(r*mult)/r;
datadzi[y][z] = -.25*java.lang.Math.sin(r*mult)/r;
}
}
void deselect() {
dataxy1 = dataxy2 = null;
datadzr = datadzi = null;
}
double computePoint(int x, int y, int z) {
int d1 = dataxy1[x][y];
int d2 = dataxy2[x][y];
int d3 = dataxy1[maxTerms-1-x][y];
int d4 = dataxy2[maxTerms-1-x][y];
return (datadzr[d1][z]-datadzr[d2][z]+
datadzr[d3][z]-datadzr[d4][z])*cost1 -
(datadzi[d1][z]-datadzi[d2][z]+
datadzi[d3][z]-datadzi[d4][z])*sint1;
}
Setup createNext() { return new TwoPinholesSetup(); }
};
class TwoPinholesSetup extends Setup {
int dataxy[][];
double datadzr[][], datadzi[][], w1mult, w2mult;
int mxhalf;
int mxlast;
String getName() { return "2 pinholes"; }
void select() {
setupBar(0, "Source Separation", 30);
setupBar(1, "Phase Difference", 0);
setupBar(2, "Balance", 50);
}
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
dataxy = new int[maxTerms][maxTerms];
double mult = freqBar.getValue() / 50.;
int distmult = 4;
double sep = aux1Bar.getValue()/3./resadj;
int maxdist = 0;
for (x = 0; x != maxTerms; x++) {
double xi = x-mxhalf+sep+.001;
for (y = 0; y != maxTerms; y++) {
dataxy[x][y] = (int)
(distmult*java.lang.Math.sqrt(xi*xi+y*y)+.5);
if (dataxy[x][y] > maxdist)
maxdist = dataxy[x][y];
}
}
datadzr = new double[maxdist+1][maxTerms];
datadzi = new double[maxdist+1][maxTerms];
for (z = 0; z != maxTerms; z++)
for (y = 0; y <= maxdist; y++) {
int zi = z-mxhalf;
double r =
java.lang.Math.sqrt(y*y/(distmult*distmult)+zi*zi)*resadj
+ .0000001;
datadzr[y][z] = java.lang.Math.cos(r*mult)/r;
datadzi[y][z] = -java.lang.Math.sin(r*mult)/r;
}
w1mult = aux3Bar.getValue() / 100.;
w2mult = 1-w1mult;
}
double getPhaseShift() { return aux2Bar.getValue()*pi/50.; }
void deselect() {
dataxy = null;
datadzr = datadzi = null;
}
double computePoint(int x, int y, int z) {
int d1 = dataxy[x][y];
int d2 = dataxy[maxTerms-1-x][y];
return w1mult*(datadzr[d1][z]*cost1 - datadzi[d1][z]*sint1) +
w2mult*(datadzr[d2][z]*cost2 - datadzi[d2][z]*sint2);
}
Setup createNext() { return new SingleLineSetup(); }
};
class SingleLineSetup extends Setup {
double datar[][];
double datai[][];
int mxhalf;
String getName() { return "single line source"; }
void select() { }
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
datar = new double[maxTerms][maxTerms];
datai = new double[maxTerms][maxTerms];
double mult = freqBar.getValue() / 50.;
for (x = 0; x != maxTerms; x++) {
double xi = x-mxhalf+.001;
for (y = 0; y != maxTerms; y++) {
double yi = y-mxhalf+.001;
double r = java.lang.Math.sqrt(xi*xi+yi*yi)*resadj;
datar[x][y] = .25*bessj0(r*mult);
datai[x][y] = -.25*bessy0(r*mult);
}
}
}
void deselect() {
datar = datai = null;
}
double computePoint(int x, int y, int z) {
return datar[x][y]*cost1-datai[x][y]*sint1;
}
Setup createNext() { return new SingleSlitSetup(); }
};
class SingleSlitSetup extends Setup {
double datar[][];
double datai[][];
int mxhalf;
String getName() { return "single slit"; }
void select() { }
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
datar = new double[maxTerms][maxTerms];
datai = new double[maxTerms][maxTerms];
double mult = freqBar.getValue() / 50.;
for (x = 0; x != maxTerms; x++) {
double xi = x-mxhalf+.001;
for (y = 0; y != maxTerms; y++) {
double r = java.lang.Math.sqrt(xi*xi+y*y)*resadj;
datar[x][y] = .25*bessj0(r*mult);
datai[x][y] = -.25*bessy0(r*mult);
}
}
}
void deselect() {
datar = datai = null;
}
double computePoint(int x, int y, int z) {
return datar[x][y]*cost1-datai[x][y]*sint1;
}
Setup createNext() { return new DoubleLineSetup(); }
};
class DoubleLineSetup extends Setup {
double datar[][];
double datai[][];
int mxhalf;
int mxlast;
double w1mult, w2mult;
String getName() { return "2 line sources"; }
void select() {
setupBar(0, "Source Separation", 30);
setupBar(1, "Phase Difference", 0);
setupBar(2, "Balance", 50);
}
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
mxlast = maxTerms-1;
datar = new double[maxTerms][maxTerms];
datai = new double[maxTerms][maxTerms];
double mult = freqBar.getValue() / 50.;
double sep = aux1Bar.getValue()/3./resadj;
w1mult = aux3Bar.getValue() / 100.;
w2mult = 1-w1mult;
w1mult *= .25;
w2mult *= .25;
for (x = 0; x != maxTerms; x++) {
double xi = x-mxhalf-sep+.001;
for (y = 0; y != maxTerms; y++) {
double yi = y-mxhalf+.001;
double r = java.lang.Math.sqrt(xi*xi+yi*yi)*resadj;
datar[x][y] = bessj0(r*mult);
datai[x][y] = -bessy0(r*mult);
}
}
}
double getPhaseShift() { return aux2Bar.getValue()*pi/50.; }
void deselect() {
datar = datai = null;
}
double computePoint(int x, int y, int z) {
int nx = mxlast - x;
return w1mult*(datar[ x][y]*cost1-datai[ x][y]*sint1) +
w2mult*(datar[nx][y]*cost2-datai[nx][y]*sint2);
}
Setup createNext() { return new DoubleSlitSetup(); }
};
class DoubleSlitSetup extends Setup {
double datar[][];
double datai[][];
int mxhalf;
int mxlast;
double w1mult, w2mult;
String getName() { return "double slit"; }
void select() {
setupBar(0, "Slit Separation", 30);
setupBar(1, "Phase Difference", 0);
setupBar(2, "Balance", 50);
}
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
mxlast = maxTerms-1;
datar = new double[maxTerms][maxTerms];
datai = new double[maxTerms][maxTerms];
double mult = freqBar.getValue() / 50.;
double sep = aux1Bar.getValue()/3./resadj;
w1mult = aux3Bar.getValue() / 100.;
w2mult = 1-w1mult;
w1mult *= .25;
w2mult *= .25;
for (x = 0; x != maxTerms; x++) {
double xi = x-mxhalf-sep+.001;
for (y = 0; y != maxTerms; y++) {
double r = java.lang.Math.sqrt(xi*xi+y*y)*resadj;
datar[x][y] = bessj0(r*mult);
datai[x][y] = -bessy0(r*mult);
}
}
}
double getPhaseShift() { return aux2Bar.getValue()*pi/50.; }
void deselect() {
datar = datai = null;
}
double computePoint(int x, int y, int z) {
int nx = mxlast - x;
return w1mult*(datar[ x][y]*cost1-datai[ x][y]*sint1) +
w2mult*(datar[nx][y]*cost2-datai[nx][y]*sint2);
}
Setup createNext() { return new TripleSlitSetup(); }
};
class TripleSlitSetup extends Setup {
double datar[][];
double datai[][];
int mxhalf;
String getName() { return "triple slit"; }
void select() {
setupBar(0, "Slit Separation", 30);
}
void precompute() {
int x, y, z;
mxhalf = maxTerms/2;
datar = new double[maxTerms][maxTerms];
datai = new double[maxTerms][maxTerms];
double mult = freqBar.getValue() / 50.;
double sep = aux1Bar.getValue()/3./resadj;
double m = .25/3;
for (x = 0; x != maxTerms; x++) {
double xi1 = x-mxhalf-sep+.001;
double xi2 = x-mxhalf+sep+.001;
double xi3 = x-mxhalf +.001;
for (y = 0; y != maxTerms; y++) {
double r1 = java.lang.Math.sqrt(xi1*xi1+y*y)*resadj;
double r2 = java.lang.Math.sqrt(xi2*xi2+y*y)*resadj;
double r3 = java.lang.Math.sqrt(xi3*xi3+y*y)*resadj;
datar[x][y] = m*(bessj0(r1*mult)+bessj0(r2*mult)+
bessj0(r3*mult));
datai[x][y] = -m*(bessy0(r1*mult)+bessy0(r2*mult)+
bessy0(r3*mult));
}
}
}
void deselect() {
datar = datai = null;
}
double computePoint(int x, int y, int z) {
return datar[x][y]*cost1-datai[x][y]*sint1;
}
Setup createNext() { return new PlaneWaveSetup(); }
};
class PlaneWaveSetup extends Setup {
String getName() { return "plane wave"; }
void select() { }
double mult;
void precompute() {
int x, y, z;
mult = resadj*freqBar.getValue() / 50.;
}
void deselect() { }
double computePoint(int x, int y, int z) {
return .05*(java.lang.Math.cos(x*mult)*cost1 +
java.lang.Math.sin(x*mult)*sint1);
}
Setup createNext() { return new TwoPlaneWavesSetup(); }
};
class TwoPlaneWavesSetup extends Setup {
double datar[][][];
double datai[][][];
boolean noz;
String getName() { return "2 plane waves"; }
void select() {
setupBar(0, "Source 1 Theta", 25);
setupBar(1, "Source 1 Phi", 0);
setupBar(2, "Balance", 50);
}
double k2x, k2y, k2z, mult, w1mult, w2mult;
void precompute() {
mult = resadj * freqBar.getValue() / 50.;
double ang1 = aux1Bar.getValue() * pi/50;
double ang2 = aux2Bar.getValue() * pi/50;
w1mult = aux3Bar.getValue() / 100.;
w2mult = 1-w1mult;
w1mult *= .05;
w2mult *= .05;
double ang1cos = java.lang.Math.cos(ang1);
double ang1sin = java.lang.Math.sin(ang1);
double ang2cos = java.lang.Math.cos(ang2);
double ang2sin = java.lang.Math.sin(ang2);
k2x = ang2cos * ang1cos * mult;
k2y = -ang2cos * ang1sin * mult;
k2z = -ang2sin * mult;
}
double computePoint(int x, int y, int z) {
double k1 = x*mult;
double k2 = x*k2x + y*k2y + z*k2z;
return w1mult*(java.lang.Math.cos(k1)*cost1 +
java.lang.Math.sin(k1)*sint1) +
w2mult*(java.lang.Math.cos(k2)*cost2 +
java.lang.Math.sin(k2)*sint2);
}
Setup createNext() { return null; }
};
double bessj0(double x) {
double ax = x,z;
double xx,y,ans,ans1,ans2;
if (x < 8.0) {
y=x*x;
ans1=57568490574.0+y*(-13362590354.0+y*(651619640.7
+y*(-11214424.18+y*(77392.33017+y*(-184.9052456)))));
ans2=57568490411.0+y*(1029532985.0+y*(9494680.718
+y*(59272.64853+y*(267.8532712+y*1.0))));
ans=ans1/ans2;
} else {
z=8.0/ax;
y=z*z;
xx=ax-0.785398164;
ans1=1.0+y*(-0.1098628627e-2+y*(0.2734510407e-4
+y*(-0.2073370639e-5+y*0.2093887211e-6)));
ans2 = -0.1562499995e-1+y*(0.1430488765e-3
+y*(-0.6911147651e-5+y*(0.7621095161e-6
-y*0.934935152e-7)));
ans=java.lang.Math.sqrt(0.636619772/ax)*
(java.lang.Math.cos(xx)*
ans1-z*java.lang.Math.sin(xx)*ans2);
}
return ans;
}
double bessy0(double x) {
double z;
double xx,y,ans,ans1,ans2;
if (x < 8.0) {
y=x*x;
ans1 = -2957821389.0+y*(7062834065.0+y*(-512359803.6
+y*(10879881.29+y*(-86327.92757+y*228.4622733))));
ans2=40076544269.0+y*(745249964.8+y*(7189466.438
+y*(47447.26470+y*(226.1030244+y*1.0))));
ans=(ans1/ans2)+0.636619772*bessj0(x)*java.lang.Math.log(x);
} else {
z=8.0/x;
y=z*z;
xx=x-0.785398164;
ans1=1.0+y*(-0.1098628627e-2+y*(0.2734510407e-4
+y*(-0.2073370639e-5+y*0.2093887211e-6)));
ans2 = -0.1562499995e-1+y*(0.1430488765e-3
+y*(-0.6911147651e-5+y*(0.7621095161e-6
+y*(-0.934945152e-7))));
ans=java.lang.Math.sqrt(0.636619772/x)*(java.lang.Math.sin(xx)*ans1+z*java.lang.Math.cos(xx)*ans2);
}
return ans;
}
}
A far higher place must be assigned to Judaism among the competitors for the allegiance of Europe. The cosmopolitan importance at one time assumed by this religion has been considerably obscured, owing to the subsequent devolution of its part to Christianity. It is, however, by no means impossible that, but for the diversion created by the Gospel, and the disastrous consequences of their revolt against Rome, the Jews might have won the world to a purified form of their own monotheism. A few significant circumstances are recorded showing how much influence they had acquired, even in Rome, before the first preaching of Christianity. The first of these is to be found in Cicero¡¯s defence of Flaccus. The latter was accused of appropriating part of the annual contributions sent to the temple at Jerusalem; and, in dealing with this charge, Cicero speaks of the Jews, who were naturally prejudiced against his client, as a powerful faction the hostility of which he is anxious not to provoke.330 Some twenty years later, a great advance has been made. Not only must the material interests of the Jews be respected, but a certain conformity to their religious prescriptions is considered a mark of good breeding, In one of his most amusing satires, Horace tells us how, being anxious to shake off a bore, he appeals for help to his friend Aristius Fuscus, and reminds him of217 some private business which they had to discuss together. Fuscus sees his object, and being mischievously determined to defeat it, answers: ¡®Yes, I remember perfectly, but we must wait for some better opportunity; this is the thirtieth Sabbath, do you wish to insult the circumcised Jews?¡¯ ¡®I have no scruples on that point,¡® replies the impatient poet. ¡®But I have,¡¯ rejoins Fuscus,¡ª¡®a little weak-minded, one of the many, you know¡ªexcuse me, another time.¡®331 Nor were the Jews content with the countenance thus freely accorded them. The same poet elsewhere intimates that whenever they found themselves in a majority, they took advantage of their superior strength to make proselytes by force.¡¯332 And they pursued the good work to such purpose that a couple of generations later we find Seneca bitterly complaining that the vanquished had given laws to the victors, and that the customs of this abominable race were established over the whole earth.333 Evidence to the same effect is given by Philo Judaeus and Josephus, who inform us that the Jewish laws and customs were admired, imitated, and obeyed over the whole earth.334 Such assertions might be suspected of exaggeration, were they not, to a certain extent, confirmed by the references already quoted, to which others of the same kind may be added from later writers showing that it was a common practice among the Romans to abstain from work on the Sabbath, and even to celebrate it by praying, fasting, and lighting lamps, to visit the synagogues, to study the law of Moses, and to pay the yearly contribution of two drachmas to the temple at Jerusalem.335 Jeff¡¯s hand was quietly coming down. ¡°What happened to you?¡± begged Sandy. ¡°Something new has come up, sir. I was waiting there by my ship a good while back, and I heard another one cruising and spiraling, shooting the field, I guess, because he came in and set down. My crate, just the way you ordered, was down by the grove, not in plain sight in the middle of the course. But Jeff set his ship down, left the engine running, and went off. I stayed hid to see what would happen, but when he didn¡¯t come back, I thought I¡¯d better go and find you¡ªand see if it meant anything to you.¡± She stood alone, with the sticky, wet knife in her hand, catching her breath, coming out of the madness. Then she stooped, and pushing the branches aside felt about for her pistol. It lay at the root of a tree, and[Pg 80] when she had picked it up and put it back in the holster, there occurred to her for the first time the thought that the shot in the dead stillness must have roused the camp. And now she was sincerely frightened. If she were found here, it would be more than disagreeable for Landor. They must not find her. She started at a swift, long-limbed run, making a wide detour, to avoid the sentries, bending low, and flying silently among the bushes and across the shadowy sands. The year 1756 opened with menaces to England of the most serious nature. The imbecility of the Ministry was beginning to tell in the neglect of its colonies and its defences. France threatened to invade us, and a navy of fifty thousand men was suddenly voted, and an army of thirty-four thousand two hundred and sixty-three of native troops; but as these were not ready, it was agreed to bring over eight thousand Hessians and Hanoverians. To pay for all this it was necessary to grant excessive supplies, and lay on new duties and taxes. In presenting the money bills in the month of May, Speaker Onslow could not avoid remarking that there were two circumstances which tended to create alarm¡ªforeign subsidies and foreign troops introduced, and nothing but their confidence in his Majesty could allay their fears, or give them confidence that their burdens would be soon reduced. There was, in fact, no chance for any such reduction, for wars, troubles, and disgraces were gathering around from various quarters. The first reverse came from the Mediterranean. MUCH to their amazement, the boys waked up the next morning in Nashville, and found that they had passed through the "dark and bloody ground" of Kentucky absolutely without adventure. After drawing and dividing the rations and cartridges. Si gave the boys the necessary instruction about having their things ready so that they could get them in the dark the next morning, and ordered them to disregard the bonfires and mirth-making, and lie down to get all the sleep they could, in preparation for the hard work of the next day. Then, like the rest of the experienced men, who saw that the campaign was at length really on, and this would be the last opportunity for an indefinite while to write, he sat down to write short letters to his mother and to Annabel. "Bully for the Wild Wanderers of the Wabash," Shorty joined in. "They're the boss regiment in the army o' the Cumberland, and the Army o' the Cumberland's the boss army on earth. Hooray for US Co. Le's have a speech. Where's Monty Scruggs?" "Bring a light, do¡ªI can't abide this dark." Albert suddenly began to look uneasy. After all he was not really drunk, only a little fuddled. He walked straight, and his roll was natural to him, while though he was exceedingly cheerful, and often burst into song, his words were not jumbled, and he generally seemed to have a fair idea of what he was saying. "But I heard what the doctor said to you." "A purty accident¡ªwud them stacks no more dry than a ditch. 'Twas a clear case of 'bustion¡ªfireman said so to me; as wicked and tedious a bit o' wark as ever I met in my life." Calverley stept from the shadow of the cliff, and beheld a meteor in the sky, brightening and expanding, as the clouds opened, until it assumed the appearance of a brilliant star, of astonishing magnitude, encircled by dazzling rays, which, in a singular manner, were all inclined in one direction, and pointing to that part of the horizon where lay the rival of England¡ªFrance. The foreman's face assumed a deeper hue than usual: he looked fiercely at the galleyman, but there was a determination in the weather-beaten face that made him pause ere he spoke. "Galleyman," he at length said, "you knew the business before you came: if you be so fond of saving old witches' lives, why didn't you say so, that I might not now be in this dilemma?" "No, no, not the boy," replied Merritt, rather impatiently. HoMEÁíÀàС˵ߣɫ
ENTER NUMBET 0017
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