// ModeBox.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.awt.event.*;
class ModeBoxCanvas extends Canvas {
ModeBoxFrame pg;
ModeBoxCanvas(ModeBoxFrame p) {
pg = p;
}
public Dimension getPreferredSize() {
return new Dimension(300,400);
}
public void update(Graphics g) {
pg.updateModeBox(g);
}
public void paint(Graphics g) {
pg.updateModeBox(g);
}
};
class ModeBoxLayout implements LayoutManager {
public ModeBoxLayout() {}
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 ModeBox extends Applet {
static ModeBoxFrame oc;
void destroyFrame() {
if (oc != null)
oc.dispose();
oc = null;
}
public static void main(String args[]) {
oc = new ModeBoxFrame(null);
oc.init();
}
public void init() {
oc = new ModeBoxFrame(this);
oc.init();
}
public void destroy() {
if (oc != null)
oc.dispose();
oc = null;
}
};
class ModeBoxFrame extends Frame
implements ComponentListener, ActionListener, AdjustmentListener,
MouseMotionListener, MouseListener, ItemListener {
Thread engine = null;
Dimension winSize;
Image dbimage;
Random random;
int gridSizeX = 200;
int gridSizeY = 200;
public String getAppletInfo() {
return "ModeBox by Paul Falstad";
}
Button clearButton;
Checkbox memoryImageSourceCheck;
Checkbox stoppedCheck;
Checkbox spectrumCheck;
Choice modeChooser;
Scrollbar speedBar;
Scrollbar resolutionBar;
Scrollbar brightnessBar;
Scrollbar widthBar;
Scrollbar heightBar;
double dragZoomStart;
double zoom = 6.5;
double rotmatrix[];
double selectedMinOmega;
double selectedMaxOmega;
Rectangle view3d;
Rectangle viewSpectrum;
Rectangle viewFreq[];
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 data[][][];
double boxwidth = 2;
double boxheight = 2;
boolean dragging = false;
MemoryImageSource imageSource;
int pixels[];
int maxTerms = 16;
static int maxModes = 10;
static int maxDispCoefs = 8;
static int viewDistance = 12;
Mode modes[];
int modeCount = 0;
int pause;
ModeBox 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;
int selectedCoefX = -1;
int selectedCoefY;
int selectedCoefZ;
static final int sampleCount = 15;
int sampleMult[];
double magDragStart;
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;
}
ModeBoxCanvas cv;
ModeBoxFrame(ModeBox a) {
super("Box Modes Applet");
applet = a;
}
public void init() {
String os = System.getProperty("os.name");
String jv = System.getProperty("java.version");
boolean altRender = true;
int res = 32;
// change settings to speed things up where possible
if (os.indexOf("Windows") == 0) {
res = 48;
if (jv.indexOf("1.1") == 0)
altRender = true;
}
res = 120;
setLayout(new ModeBoxLayout());
cv = new ModeBoxCanvas(this);
cv.addComponentListener(this);
cv.addMouseMotionListener(this);
cv.addMouseListener(this);
add(cv);
add(clearButton = new Button("Clear"));
clearButton.addActionListener(this);
stoppedCheck = new Checkbox("Stopped");
stoppedCheck.addItemListener(this);
add(stoppedCheck);
spectrumCheck = new Checkbox("Show Spectrum");
spectrumCheck.addItemListener(this);
add(spectrumCheck);
memoryImageSourceCheck = new Checkbox("Alternate Rendering",
altRender);
memoryImageSourceCheck.addItemListener(this);
add(memoryImageSourceCheck);
modeChooser = new Choice();
modeChooser.add("Mouse = Adjust Angle");
modeChooser.add("Mouse = Adjust Zoom");
modeChooser.addItemListener(this);
add(modeChooser);
add(new Label("Simulation Speed", Label.CENTER));
add(speedBar = new Scrollbar(Scrollbar.HORIZONTAL, 40, 1, 1, 200));
speedBar.addAdjustmentListener(this);
add(new Label("Brightness", Label.CENTER));
add(brightnessBar = new Scrollbar(Scrollbar.HORIZONTAL, 28,
1, 1, 200));
brightnessBar.addAdjustmentListener(this);
add(new Label("Image Resolution", Label.CENTER));
add(resolutionBar =
new Scrollbar(Scrollbar.HORIZONTAL, res, 2, 20, 300));
resolutionBar.addAdjustmentListener(this);
add(new Label("Width", Label.CENTER));
add(widthBar = new Scrollbar(Scrollbar.HORIZONTAL, 10, 1, 5, 31));
widthBar.addAdjustmentListener(this);
add(new Label("Height", Label.CENTER));
add(heightBar = new Scrollbar(Scrollbar.HORIZONTAL, 10, 1, 5, 31));
heightBar.addAdjustmentListener(this);
add(new Label("", Label.CENTER));
try {
String param = applet.getParameter("PAUSE");
if (param != null)
pause = Integer.parseInt(param);
} catch (Exception e) { }
modes = new Mode[maxModes];
addMode(1, 0, 0).magcoef = 1;
rotmatrix = new double[9];
rotmatrix[0] = rotmatrix[4] = rotmatrix[8] = 1;
xpoints = new int[2];
ypoints = new int[2];
// generate table of sample multipliers for efficient Simpson's rule
int i;
sampleMult = new int[sampleCount];
for (i = 1; i < sampleCount; i += 2) {
sampleMult[i ] = 4;
sampleMult[i+1] = 2;
}
sampleMult[0] = sampleMult[sampleCount-1] = 1;
random = new Random();
reinit();
cv.setBackground(Color.black);
cv.setForeground(Color.white);
resize(800,700);
handleResize();
show();
}
void handleResize() {
reinit();
// XXX
}
void reinit() {
setMaxTerms();
Dimension d = winSize = cv.getSize();
if (winSize.width == 0)
return;
calcSpectrum();
dbimage = createImage(d.width, d.height);
setupDisplay();
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);
}
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;
data = new double[maxTerms][maxTerms][maxTerms];
func = new double[gridSizeX][gridSizeY][2];
}
// set view rectangles for the various subwindows
void setupDisplay() {
int perColumn = 2;
int perRow = 4;
int freqHeight = getTermWidth() * (maxDispCoefs+1) * perColumn;
int spectrumHeight = (spectrumCheck.getState()) ?
getTermWidth()*6 : 0;
view3d = new Rectangle(0, 0, winSize.width,
winSize.height-freqHeight-spectrumHeight);
if (spectrumCheck.getState())
viewSpectrum = new Rectangle(0, view3d.height,
winSize.width, spectrumHeight);
else
viewSpectrum = null;
viewFreq = new Rectangle[maxDispCoefs];
int i;
int winw = getTermWidth() * maxDispCoefs;
int winh = winw;
int pad = getTermWidth();
int x = (winSize.width-(winw*4+pad*3))/2;
for (i = 0; i != maxDispCoefs; i++)
viewFreq[i] = new Rectangle(x+(i%perRow)*(winw+pad),
view3d.height+spectrumHeight+
(i/perRow)*(winh+pad),
winw, winh);
}
// compute func[][][] array (2-d view) by raytracing through a
// 3-d dataset (data[][][])
void computeFunction() {
int i, j;
genData(false);
double q = 3.14159265/maxTerms;
double cost = java.lang.Math.cos(t);
double izoom = 1/zoom;
double rotm[] = rotmatrix;
double boxhalfwidth = boxwidth/2;
double boxhalfheight = boxheight/2;
double aratio = view3d.width/(double) view3d.height;
for (i = 0; i != gridSizeX; i++)
for (j = 0; j != gridSizeY; j++) {
// calculate camera position and direction
double camx0 = 0;
double camz0 = viewDistance;
double camvx0 = (2*i/(double) gridSizeX - 1)*izoom;
double camvy0 = (2*j/(double) gridSizeY - 1)*izoom;
// preserve aspect ratio no matter what window dimensions
if (aratio < 1)
camvy0 /= aratio;
else
camvx0 *= aratio;
// rotate camera with rotation matrix
double camvz0 = -1;
double camx = rotm[0]*camx0+rotm[2]*camz0;
double camy = rotm[5]*camz0;
double camz = rotm[6]*camx0+rotm[8]*camz0;
double camvx = rotm[0]*camvx0+rotm[1]*camvy0+rotm[2]*camvz0;
double camvy = rotm[3]*camvx0+rotm[4]*camvy0+rotm[5]*camvz0;
double camvz = rotm[6]*camvx0+rotm[7]*camvy0+rotm[8]*camvz0;
double camnorm =
java.lang.Math.sqrt(camvx*camvx+camvy*camvy+camvz*camvz);
int n;
double simpr = 0;
double simpg = 0;
// number of simpson's rule samples = 14
int nmax = 14;
// 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
func[i][j][0] = func[i][j][1] = 0;
continue;
}
// sample evenly along intersecting portion
double tstep = (maxt-mint)/(sampleCount-1);
double pathlen = (maxt-mint)*camnorm;
double xmult = maxTerms/boxwidth;
double ymult = maxTerms/boxheight;
double zmult = maxTerms/2.;
for (n = 0; n < sampleCount; n++) {
double t = mint+n*tstep;
double xx = camx+camvx*t;
double yy = camy+camvy*t;
double zz = camz+camvz*t;
// find grid element that contains sampled point
int xxi = (int) ((xx+boxhalfwidth )*xmult);
int yyi = (int) ((yy+boxhalfheight)*ymult);
int zzi = (int) ((zz+1)*zmult);
double f = data[xxi][yyi][zzi];
if (f < 0) {
f = java.lang.Math.abs(f);
simpr += sampleMult[n] * f;
} else
simpg += sampleMult[n] * f;
}
simpr *= pathlen/n;
simpg *= pathlen/n;
func[i][j][0] = simpr;
func[i][j][1] = simpg;
}
}
int sign(double x) {
return x < 0 ? -1 : 1;
}
public void paint(Graphics g) {
cv.repaint();
}
public void updateModeBox(Graphics realg) {
Graphics g = null;
if (winSize == null || winSize.width == 0)
return;
boolean mis = memoryImageSourceCheck.getState();
g = dbimage.getGraphics();
g.setColor(cv.getBackground());
g.fillRect(0, 0, winSize.width, winSize.height);
g.setColor(cv.getForeground());
boolean allQuiet = true;
if (!stoppedCheck.getState()) {
int val = speedBar.getValue();
double tadd = val*(.1/16);
t += tadd;
if (modeCount > 0)
allQuiet = false;
}
int i, j, k;
// evolve modes forward in time
for (i = 0; i != modeCount; i++) {
Mode m = modes[i];
m.phasecoef = (m.omega*t+m.phasecoefadj) % (2*pi);
m.phasecoefcos = java.lang.Math.cos(m.phasecoef);
m.phasemult = m.phasecoefcos * m.magcoef;
}
if (modeCount != 0)
computeFunction();
colorMult = brightnessBar.getValue() * 3;
int winw = view3d.width;
int winh = view3d.height;
if (modeCount > 0) {
for (i = 0; i != gridSizeX; i++)
for (j = 0; j != gridSizeY; j++) {
int x = i*winw/gridSizeX;
int y = j*winh/gridSizeY;
int x2 = (i+1)*winw/gridSizeX;
int y2 = (j+1)*winh/gridSizeY;
int colval = 0xFF000000 +
(getColorValue(i, j, 0) << 16) |
(getColorValue(i, j, 1) << 8);
if (mis) {
int l;
for (k = x; k < x2; k++)
for (l = y; l < y2; l++)
pixels[k+l*view3d.width] = colval;
} else {
g.setColor(new Color(colval));
g.fillRect(x, y, x2-x, y2-y);
}
}
if (mis) {
Image dbimage2 = cv.createImage(imageSource);
g.drawImage(dbimage2, 0, 0, null);
}
}
g.setColor(Color.white);
// find which sides of box are visible and draw the lines
// bounding them. Here we step through all 8 vertices on the box
// and draw a line connecting each vertex to each adjacent vertex
// if one of the faces adjacent to that line is visible.
for (i = 0; i != 8; i++) {
// here we assume the box is cube (with vertices at (+-1,+-1,+-1))
// because the dimensions don't affect visibility.
int sign1 = ((i & 1) == 0) ? -1 : 1;
int sign2 = ((i & 2) == 0) ? -1 : 1;
int sign3 = ((i & 4) == 0) ? -1 : 1;
if (sign1 == -1 &&
(visibleFace(0, sign2, 0) || visibleFace(0, 0, sign3))) {
// draw a line from (-1, sign2, sign3) to (1, sign2, sign3)
// if one of the adjacent faces is visible
map3d(-1, sign2, sign3, xpoints, ypoints, 0);
map3d( 1, sign2, sign3, xpoints, ypoints, 1);
g.drawLine(xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
}
if (sign2 == -1 &&
(visibleFace(sign1, 0, 0) || visibleFace(0, 0, sign3))) {
// draw a line from (sign1, -1, sign3) to (sign1, 1, sign3)
// etc.
map3d(sign1, -1, sign3, xpoints, ypoints, 0);
map3d(sign1, 1, sign3, xpoints, ypoints, 1);
g.drawLine(xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
}
if (sign3 == -1 &&
(visibleFace(sign1, 0, 0) || visibleFace(0, sign2, 0))) {
map3d(sign1, sign2, -1, xpoints, ypoints, 0);
map3d(sign1, sign2, 1, xpoints, ypoints, 1);
g.drawLine(xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
}
}
g.setColor(Color.black);
g.fillRect(0, view3d.height,
winSize.width, winSize.height-view3d.height);
for (i = 0; i != maxDispCoefs; i++)
drawFrequencies(g, i);
if (viewSpectrum != null) {
// draw spectrum
// modes can be identified either individually or by a
// frequency range. We highlight whichever ones are selected.
double selw = (selectedCoefX == -1) ? 0 :
getOmega(selectedCoefX, selectedCoefY, selectedCoefZ);
int selx = (int) (selw * spectrumSpacing);
int selmin = (int) (selectedMinOmega * spectrumSpacing);
int selmax = (int) (selectedMaxOmega * spectrumSpacing);
int ym = viewSpectrum.height - 10;
int y = viewSpectrum.y + viewSpectrum.height - 5;
for (i = 1; i != winSize.width; i++) {
if (spectrum[i] == 0)
continue;
int h = (int) (ym * (.2+java.lang.Math.log(spectrum[i])/4));
if (h > ym)
h = ym;
g.setColor((i == selx || (i >= selmin && i < selmax))
? Color.yellow : Color.gray);
g.drawLine(i, y, i, y-h);
}
}
if (selectedCoefX != -1) {
String s = "Selected mode = (" + selectedCoefX + "," +
selectedCoefY + "," + selectedCoefZ + ")";
FontMetrics fm = g.getFontMetrics();
g.setColor(Color.yellow);
int y = view3d.y + view3d.height - fm.getDescent() - 2;
g.drawString(s, (winSize.width-fm.stringWidth(s))/2, y);
}
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;
}
// 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);
}
void drawFrequencies(Graphics g, int z) {
// draw one frequency grid for a particular z
Rectangle view = viewFreq[z];
int termWidth = getTermWidth();
g.setColor(Color.white);
int starti = 0;
int i, j, x, y;
for (i = starti; i <= maxDispCoefs; i++) {
x = i*termWidth;
g.drawLine(view.x+starti*termWidth, x+view.y,
view.x+termWidth*maxDispCoefs, x+view.y);
g.drawLine(view.x+x, view.y+starti*termWidth,
view.x+x, view.y+termWidth*maxDispCoefs);
}
int rcol = 0x00010000;
int gcol = 0x00000100;
for (i = 0; i != modeCount; i++) {
Mode m = modes[i];
if (m.z != z)
continue;
x = view.x+m.x*termWidth;
y = view.y+m.y*termWidth;
int val = logcoef(m.magcoef);
if (val < -255)
val = -255;
if (val > 255)
val = 255;
if (val < 0)
g.setColor(new Color(0xFF000000 + rcol * -val));
else
g.setColor(new Color(0xFF000000 + gcol * val));
g.fillRect(x+1, y+1, termWidth-1, termWidth-1);
int phx = (int) (m.phasecoefadj * termWidth * (1/(pi*2)));
if (phx > 0) {
// show phase line
g.setColor(Color.blue);
g.drawLine(x+phx, y+1,
x+phx, y+termWidth);
}
}
if (selectedCoefX != -1) {
// draw yellow square around degenerate modes
double selOmega =
getOmega(selectedCoefX, selectedCoefY, selectedCoefZ);
g.setColor(Color.yellow);
for (i = starti; i != maxDispCoefs; i++)
for (j = starti; j != maxDispCoefs; j++) {
x = view.x+i*termWidth;
y = view.y+j*termWidth;
if (getOmega(i, j, z) == selOmega)
g.drawRect(x, y, termWidth, termWidth);
}
}
if (selectedMinOmega > 0 && selectedMaxOmega > 0) {
// draw yellow square around modes in selected range
g.setColor(Color.yellow);
for (i = starti; i != maxDispCoefs; i++)
for (j = starti; j != maxDispCoefs; j++) {
x = view.x+i*termWidth;
y = view.y+j*termWidth;
double w = getOmega(i, j, z);
if (w >= selectedMinOmega && w < selectedMaxOmega)
g.drawRect(x, y, termWidth, termWidth);
}
}
}
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) {
if (e.getSource() == clearButton) {
while (modeCount > 0)
deleteMode(0);
cv.repaint();
}
}
public void adjustmentValueChanged(AdjustmentEvent e) {
if (e.getSource() == widthBar || e.getSource() == heightBar)
setWidthHeight();
if (e.getSource() == resolutionBar)
setMaxTerms();
cv.repaint(pause);
}
// set the width and/or height of box and adjust omegas to match
void setWidthHeight() {
boxwidth = widthBar.getValue() / 5.;
boxheight = heightBar.getValue() / 5.;
int i;
for (i = 0; i != modeCount; i++) {
Mode m = modes[i];
m.omega = getOmega(m.x, m.y, m.z);
}
calcSpectrum();
}
void calcSpectrum() {
int i, j, k;
if (winSize == null)
return;
spectrum = new int[winSize.width];
for (i = 0; i != maxDispCoefs; i++)
for (j = 0; j != maxDispCoefs; j++)
for (k = 0; k != maxDispCoefs; k++) {
double w = getOmega(i, j, k);
int x = (int) (w*spectrumSpacing);
if (x >= winSize.width)
continue;
spectrum[x]++;
}
}
public void mouseDragged(MouseEvent e) {
dragging = true;
oldDragX = dragX;
oldDragY = dragY;
dragX = e.getX(); dragY = e.getY();
edit(e);
}
public void mouseMoved(MouseEvent e) {
if ((e.getModifiers() & MouseEvent.BUTTON1_MASK) != 0) {
if (selection != -1) {
dragging = true;
}
return;
}
int x = e.getX();
int y = e.getY();
oldDragX = dragX;
oldDragY = dragY;
dragX = x; dragY = y;
int oldCoefX = selectedCoefX;
int oldCoefY = selectedCoefY;
int oldCoefZ = selectedCoefZ;
selectedCoefX = -1;
selectedCoefY = -1;
selectedCoefZ = -1;
selection = 0;
selectedMinOmega = selectedMaxOmega = 0;
int i;
if (view3d.inside(x,y))
selection = SEL_3D;
if (viewSpectrum != null && viewSpectrum.inside(x,y)) {
selection = SEL_SPECTRUM;
selectedMinOmega = (x-2)/(double) spectrumSpacing;
selectedMaxOmega = (x+2)/(double) spectrumSpacing;
}
for (i = 0; i != maxDispCoefs; i++) {
Rectangle vf = viewFreq[i];
if (vf.inside(x, y)) {
int termWidth = getTermWidth();
selectedCoefX = (x-vf.x)/termWidth;
selectedCoefY = (y-vf.y)/termWidth;
selectedCoefZ = i;
if (selectedCoefX >= maxDispCoefs)
selectedCoefX = -1;
if (selectedCoefY >= maxDispCoefs)
selectedCoefX = -1; // sic
if (selectedCoefX != -1)
selection = SEL_MAG;
}
}
if (selectedCoefX != oldCoefX || selectedCoefY != oldCoefY ||
selectedCoefZ != oldCoefZ)
cv.repaint(pause);
}
public void mouseClicked(MouseEvent e) {
if (selection == SEL_MAG)
editMagClick();
}
public void mouseEntered(MouseEvent e) {
}
public void mouseExited(MouseEvent e) {
if (!dragging && selection != -1) {
selectedCoefX = selectedCoefY = selectedCoefZ = -1;
cv.repaint(pause);
}
}
public void mousePressed(MouseEvent e) {
if ((e.getModifiers() & MouseEvent.BUTTON1_MASK) == 0)
return;
oldDragX = dragStartX = e.getX();
oldDragY = dragStartY = e.getY();
dragZoomStart = zoom;
if (selectedCoefX != -1) {
Mode m = findSelectedMode();
magDragStart = m.magcoef;
}
dragging = true;
edit(e);
}
public void mouseReleased(MouseEvent e) {
if (dragging)
cv.repaint();
dragging = false;
}
public void itemStateChanged(ItemEvent e) {
if (e.getItemSelectable() == spectrumCheck)
setupDisplay();
cv.repaint(pause);
}
public boolean handleEvent(Event ev) {
if (ev.id == Event.WINDOW_DESTROY) {
if (applet == null) dispose();
else 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();
switch (selection) {
case SEL_MAG: editMag(x, y); break;
case SEL_3D: edit3d(x, y); break;
}
}
void edit3d(int x, int y) {
if (modeChooser.getSelectedIndex() == MODE_ANGLE) {
int xo = oldDragX-x;
int yo = oldDragY-y;
rotate(xo/40., yo/40.);
cv.repaint(pause);
} else if (modeChooser.getSelectedIndex() == MODE_ZOOM) {
int xo = x-dragStartX;
zoom = dragZoomStart + xo/20.;
if (zoom < .1)
zoom = .1;
cv.repaint(pause);
}
}
void editMag(int x, int y) {
if (selectedCoefX == -1)
return;
double coef = (dragStartY-y)/20.+magDragStart;
if (coef < -1)
coef = -1;
if (coef > 1)
coef = 1;
double pcoef = (x-dragStartX)/10.;
if (pcoef < 0)
pcoef = 0;
if (pcoef > 2*pi)
pcoef = 2*pi;
Mode m = findSelectedMode();
if (m.magcoef == coef && m.phasecoefadj == pcoef)
return;
m.magcoef = coef;
m.phasecoefadj = pcoef;
cv.repaint(pause);
}
void editMagClick() {
if (selectedCoefX == -1)
return;
Mode m = findSelectedMode();
if (magDragStart < .5)
m.magcoef = 1;
else
m.magcoef = 0;
m.phasecoefadj = 0;
if (m.magcoef == 0)
deleteMode(m);
cv.repaint(pause);
}
// generate 3-d dataset
void genData(boolean fixed) {
double q = 3.14159265/maxTerms;
int x, y, z, mi;
for (mi = 0; mi != modeCount; mi++) {
Mode m = modes[mi];
if (m.tableSize != maxTerms) {
m.xtable = new double[maxTerms];
m.ytable = new double[maxTerms];
m.ztable = new double[maxTerms];
m.tableSize = maxTerms;
}
// precompute cosine tables for speed
for (x = 0; x != maxTerms; x++) {
m.xtable[x] = java.lang.Math.cos(x*m.x*q) * m.phasemult;
m.ytable[x] = java.lang.Math.cos(x*m.y*q);
m.ztable[x] = java.lang.Math.cos(x*m.z*q);
}
if (mi == 0)
for (x = 0; x != maxTerms; x++)
for (y = 0; y != maxTerms; y++)
for (z = 0; z != maxTerms; z++)
data[x][y][z] =
m.xtable[x]*m.ytable[y]*m.ztable[z];
else
for (x = 0; x != maxTerms; x++)
for (y = 0; y != maxTerms; y++)
for (z = 0; z != maxTerms; z++)
data[x][y][z] +=
m.xtable[x]*m.ytable[y]*m.ztable[z];
}
}
void deleteMode(int i) {
for (; i < modeCount-1; i++) {
modes[i] = modes[i+1];
}
modeCount--;
}
void deleteMode(Mode m) {
int i;
for (i = 0; i != modeCount; i++)
if (modes[i] == m) {
deleteMode(i);
return;
}
}
Mode addMode(int x, int y, int z) {
if (modeCount == maxModes) {
// one of the existing modes must be deleted; pick weakest one
int i;
double minmag = 1;
int minmagi = 0;
for (i = 0; i != modeCount; i++) {
Mode m = modes[i];
if (m.magcoef < minmag) {
minmag = m.magcoef;
minmagi = i;
}
}
deleteMode(minmagi);
}
Mode m = new Mode();
m.x = x;
m.y = y;
m.z = z;
m.magcoef = 0;
m.phasecoef = 0;
m.phasecoefcos = 1;
m.phasecoefadj = 0;
m.omega = getOmega(x, y, z);
modes[modeCount++] = m;
return m;
}
// get angular frequency of a particular mode
double getOmega(int x, int y, int z) {
return java.lang.Math.sqrt(x*x/(boxwidth*boxwidth)+
y*y/(boxheight*boxheight)+z*z/4.);
}
Mode findSelectedMode() {
int i;
for (i = 0; i != modeCount; i++) {
Mode m = modes[i];
if (selectedCoefX == m.x && selectedCoefY == m.y &&
selectedCoefZ == m.z)
return m;
}
return addMode(selectedCoefX, selectedCoefY, selectedCoefZ);
}
class Mode {
public int x, y, z;
public double magcoef, phasecoef, phasecoefcos, phasemult,
phasecoefadj, omega;
int tableSize;
public double xtable[], ytable[], ztable[];
};
}
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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