// MOViewer.java (c) 2002 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.util.Random;
import java.awt.image.MemoryImageSource;
import java.lang.Math;
import java.awt.event.*;
import java.net.URL;
import java.io.FilterInputStream;
import java.util.StringTokenizer;
import java.lang.reflect.Constructor;
import java.lang.reflect.Method;
class MOViewerCanvas extends Canvas {
MOViewerFrame pg;
MOViewerCanvas(MOViewerFrame p) {
pg = p;
}
public Dimension getPreferredSize() {
return new Dimension(300,400);
}
public void update(Graphics g) {
pg.updateMOViewer(g);
}
public void paint(Graphics g) {
pg.updateMOViewer(g);
}
};
class MOViewerLayout implements LayoutManager {
public MOViewerLayout() {}
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 MOViewer extends Applet implements ComponentListener {
static MOViewerFrame 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 MOViewerFrame(null);
ogf.init();
}
void showFrame() {
if (ogf == null) {
started = true;
ogf = new MOViewerFrame(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 MOViewerFrame extends Frame
implements ComponentListener, ActionListener, AdjustmentListener,
MouseMotionListener, MouseListener, ItemListener {
Thread engine = null;
Dimension winSize;
Image dbimage, memimage;
Random random;
int gridSizeX = 200;
int gridSizeY = 200;
public String getAppletInfo() {
return "MOViewer by Paul Falstad";
}
Button blankButton;
Button normalizeButton;
Button maximizeButton;
Checkbox memoryImageSourceCheck;
CheckboxMenuItem colorCheck;
CheckboxMenuItem eCheckItem;
CheckboxMenuItem eSepCheckItem;
CheckboxMenuItem xCheckItem;
CheckboxMenuItem alwaysNormItem;
CheckboxMenuItem nuclearItem;
CheckboxMenuItem showAtomsItem;
CheckboxMenuItem dimensionsItem;
CheckboxMenuItem axesItem;
MenuItem exitItem;
Choice sliceChooser, stateChooser, sampleChooser;
CheckboxMenuItem samplesItems[];
int samplesNums[] = { 9, 15, 25, 35, 45, 55 };
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 resolutionBar;
Scrollbar internalResBar;
Scrollbar brightnessBar;
Scrollbar scaleBar;
Scrollbar sampleBar;
Scrollbar separationBar;
View viewPotential, viewPotentialSep, viewX;
View viewList[];
int viewCount;
int stateNum;
Orbital orbitals[];
int orbCount;
Orbital orbListLeft[];
Orbital orbListRight[];
Orbital orbListCenter[];
int orbCountOffset, orbCountCenter;
double evalues[][];
int basisCount;
boolean changingDerivedStates;
double dragZoomStart;
double zoom; // was 10
double rotmatrix[];
double sep2;
double colorMult;
Rectangle viewAxes;
static final double pi = 3.14159265358979323846;
static final double pi2 = pi*2;
static final float root2 = 1.41421356237309504880f;
static final float root2inv = .70710678118654752440f;
static final double baseEnergy = .55;
int xpoints[];
int ypoints[];
int selectedPaneHandle;
double func[][][];
PhaseColor phaseColors[];
double resadj;
boolean dragging = false;
MemoryImageSource imageSource;
int pixels[];
int sampleCount;
int dataSize;
float modes[];
static int maxModes = 10;
static int maxDispCoefs = 8;
static int viewDistance = 12;
int pause;
MOViewer applet;
int selection = -1;
static final int SEL_NONE = 0;
static final int SEL_POTENTIAL = 1;
static final int SEL_X = 2;
static final int SEL_STATES = 3;
static final int SEL_HANDLE = 4;
static final int MODE_ANGLE = 0;
static final int MODE_SLICE = 1;
int slicerPoints[][];
double sliceFaces[][];
double sliceFace[];
int sliceFaceCount;
double sliceval = 0;
int sampleMult[];
boolean selectedSlice;
boolean settingScale;
double magDragStart;
int dragX, dragY, dragStartX, dragStartY;
double t = 0;
public static final double epsilon = .01;
static final int panePad = 4;
static final int phaseColorCount = 50;
int phiIndex;
boolean manualScale;
Color gray2;
FontMetrics fontMetrics;
int getrand(int x) {
int q = random.nextInt();
if (q < 0) q = -q;
return q % x;
}
MOViewerCanvas cv;
MOViewerFrame(MOViewer a) {
super("Molecular Orbital Viewer v1.5a");
applet = a;
}
boolean useBufferedImage = false;
public void init() {
gray2 = new Color(127, 127, 127);
String jv = System.getProperty("java.class.version");
double jvf = new Double(jv).doubleValue();
if (jvf >= 48)
useBufferedImage = true;
int res = 68;
setLayout(new MOViewerLayout());
cv = new MOViewerCanvas(this);
cv.addComponentListener(this);
cv.addMouseMotionListener(this);
cv.addMouseListener(this);
add(cv);
MenuBar mb = new MenuBar();
Menu m = new Menu("File");
mb.add(m);
m.add(exitItem = getMenuItem("Exit"));
m = new Menu("View");
mb.add(m);
//m.add(eCheckItem = getCheckItem("Energy"));
m.add(eSepCheckItem = getCheckItem("Energy"));
eSepCheckItem.setState(true);
m.add(xCheckItem = getCheckItem("Position"));
xCheckItem.setState(true);
xCheckItem.disable();
m.addSeparator();
m.add(colorCheck = getCheckItem("Phase as Color"));
colorCheck.setState(true);
m = new Menu("Options");
mb.add(m);
m.add(nuclearItem = getCheckItem("Include Nuclear E"));
nuclearItem.setState(true);
m.add(showAtomsItem = getCheckItem("Show Nuclei"));
showAtomsItem.setState(true);
m.add(dimensionsItem = getCheckItem("Show Dimensions"));
m.add(axesItem = getCheckItem("Show Axes"));
axesItem.setState(true);
setMenuBar(mb);
m = new Menu("Samples");
mb.add(m);
samplesItems = new CheckboxMenuItem[6];
m.add(samplesItems[0] = getCheckItem("Samples = 9 (fastest)"));
m.add(samplesItems[1] = getCheckItem("Samples = 15 (default)"));
m.add(samplesItems[2] = getCheckItem("Samples = 25"));
m.add(samplesItems[3] = getCheckItem("Samples = 35"));
m.add(samplesItems[4] = getCheckItem("Samples = 45"));
m.add(samplesItems[5] = getCheckItem("Samples = 55 (best)"));
samplesItems[1].setState(true);
int i;
stateChooser = new Choice();
stateChooser.add("sigma g 1s");
stateChooser.add("sigma*u 1s");
stateChooser.add("pi u 2px");
stateChooser.add("pi u 2py");
stateChooser.add("sigma g 2s");
stateChooser.add("sigma g 2pz");
stateChooser.add("sigma*u 2s");
stateChooser.add("pi*g 2px");
stateChooser.add("pi*g 2py");
stateChooser.add("sigma*u 2pz");
stateChooser.addItemListener(this);
add(stateChooser);
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("Brightness", Label.CENTER));
add(brightnessBar = new Scrollbar(Scrollbar.HORIZONTAL, 1385,
1, 1000, 1800));
brightnessBar.addAdjustmentListener(this);
add(new Label("Image Resolution", Label.CENTER));
add(resolutionBar =
new Scrollbar(Scrollbar.HORIZONTAL, res, 2, 20, 200));
resolutionBar.addAdjustmentListener(this);
/*add(new Label("Internal Resolution", Label.CENTER));
add(internalResBar =
new Scrollbar(Scrollbar.HORIZONTAL, res, 2, 20, 200));
internalResBar.addAdjustmentListener(this);*/
add(new Label("Scale", Label.CENTER));
add(scaleBar = new Scrollbar(Scrollbar.HORIZONTAL, 24, 1, 5, 52));
scaleBar.addAdjustmentListener(this);
/*add(new Label("Samples", Label.CENTER));
add(sampleBar = new Scrollbar(Scrollbar.HORIZONTAL, 7, 1, 0, 20));
sampleBar.addAdjustmentListener(this);*/
add(new Label("Separation", Label.CENTER));
add(separationBar = new Scrollbar(Scrollbar.HORIZONTAL,
12, 1, 0, 21));
separationBar.addAdjustmentListener(this);
add(new Label(""));
try {
String param = applet.getParameter("PAUSE");
if (param != null)
pause = Integer.parseInt(param);
} catch (Exception e) { }
int j;
phaseColors = new PhaseColor[8*phaseColorCount];
for (i = 0; i != 8; i++)
for (j = 0; j != phaseColorCount; j++) {
double ang = Math.atan(j/(double) phaseColorCount);
phaseColors[i*phaseColorCount+j] = genPhaseColor(i, ang);
}
slicerPoints = new int[2][5*2];
sliceFaces = new double[4][3];
rotmatrix = new double[9];
rotmatrix[0] = rotmatrix[4] = rotmatrix[8] = 1;
rotate(-pi/2, 0);
rotate(0, pi/2);
xpoints = new int[4];
ypoints = new int[4];
setupSimpson();
random = new Random();
readModes();
getEnergyValues();
createOrbitals();
reinit();
cv.setBackground(Color.black);
cv.setForeground(Color.white);
resize(550, 530);
handleResize();
Dimension x = getSize();
Dimension screen = getToolkit().getScreenSize();
setLocation((screen.width - x.width)/2,
(screen.height - x.height)/2);
show();
}
MenuItem getMenuItem(String s) {
MenuItem mi = new MenuItem(s);
mi.addActionListener(this);
return mi;
}
CheckboxMenuItem getCheckItem(String s) {
CheckboxMenuItem mi = new CheckboxMenuItem(s);
mi.addItemListener(this);
return mi;
}
PhaseColor genPhaseColor(int sec, double ang) {
// convert to 0 .. 2*pi angle
ang += sec*pi/4;
// convert to 0 .. 6
ang *= 3/pi;
int hsec = (int) ang;
double a2 = ang % 1;
double a3 = 1.-a2;
PhaseColor c = null;
switch (hsec) {
case 6:
case 0: c = new PhaseColor(1, a2, 0); break;
case 1: c = new PhaseColor(a3, 1, 0); break;
case 2: c = new PhaseColor(0, 1, a2); break;
case 3: c = new PhaseColor(0, a3, 1); break;
case 4: c = new PhaseColor(a2, 0, 1); break;
case 5: c = new PhaseColor(1, 0, a3); break;
}
return c;
}
void setupSimpson() {
sampleCount = 15;
//sampleCount = sampleBar.getValue()*2+1;
int i;
for (i = 0; i != samplesNums.length; i++) {
if (samplesItems[i].getState())
sampleCount = samplesNums[i];
}
// generate table of sample multipliers for efficient Simpson's rule
sampleMult = new int[sampleCount];
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() {
setResolution();
Dimension d = winSize = cv.getSize();
if (winSize.width == 0)
return;
dbimage = createImage(d.width, d.height);
setupDisplay();
}
void setupDisplay() {
if (winSize == null)
return;
int potsize = (viewPotentialSep == null) ?
100 : viewPotentialSep.height;
viewX = viewPotential = viewPotentialSep = null;
viewList = new View[10];
int i = 0;
if (eSepCheckItem.getState())
viewList[i++] = viewPotentialSep = new View();
if (xCheckItem.getState())
viewList[i++] = viewX = new View();
viewCount = i;
int sizenum = viewCount;
int toth = winSize.height;
// preserve size of potential and state panes if possible
if (potsize > 0 && viewPotentialSep != null) {
sizenum--;
toth -= potsize;
}
toth -= panePad*2*(viewCount-1);
int cury = 0;
for (i = 0; i != viewCount; i++) {
View v = viewList[i];
int h = (sizenum == 0) ? toth : toth/sizenum;
if (v == viewPotentialSep && potsize > 0)
h = potsize;
v.paneY = cury;
if (cury > 0)
cury += panePad;
v.x = 0;
v.width = winSize.width;
v.y = cury;
v.height = h;
cury += h+panePad;
}
setSubViews();
}
void setSubViews() {
int i;
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(viewX.width), new Integer(viewX.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[viewX.width*viewX.height];
for (i = 0; i != viewX.width*viewX.height; i++)
pixels[i] = 0xFF000000;
imageSource = new MemoryImageSource(viewX.width, viewX.height,
pixels, 0, viewX.width);
imageSource.setAnimated(true);
imageSource.setFullBufferUpdates(true);
memimage = cv.createImage(imageSource);
}
int asize = (int) (min(viewX.width, viewX.height)/3);
viewAxes = new Rectangle(viewX.x+winSize.width-asize, viewX.y,
asize, asize);
}
int getTermWidth() {
return 8;
}
// multiply rotation matrix by rotations through angle1 and angle2
void rotate(double angle1, double angle2) {
double r1cos = Math.cos(angle1);
double r1sin = Math.sin(angle1);
double r2cos = Math.cos(angle2);
double r2sin = 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 setResolution() {
int og = gridSizeX;
gridSizeX = gridSizeY = (resolutionBar.getValue() & ~1);
if (og == gridSizeX)
return;
dataSize = gridSizeX*4; // (internalResBar.getValue() & ~1);
System.out.print("setResolution " + dataSize + " " +
gridSizeX + "\n");
// was 50
resadj = 50./dataSize;
precomputeAll();
func = new double[gridSizeX][gridSizeY][3];
}
// compute func[][][] array (2-d view) by raytracing through a
// 3-d dataset (data[][][])
void computeView(double normmult) {
int i, j;
double q = 3.14159265/dataSize;
boolean color = colorCheck.getState();
for (i = 0; i != orbCount; i++)
orbitals[i].setupFrame(normmult);
double izoom = 1/zoom;
double rotm[] = rotmatrix;
double aratio = viewX.width/(double) viewX.height;
double xmult = dataSize/2.;
double ymult = dataSize/2.;
double zmult = dataSize/2.;
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();
/*double boundRadius2 = 0;
for (i = 0; i != orbCount; i++) {
Orbital oo = orbitals[i];
double br = oo.getBoundRadius(colorMult);
if (br > boundRadius2)
boundRadius2 = br;
}*/
double boundRadius2 = 1.22;
boundRadius2 *= boundRadius2;
double scalemult = scaleBar.getValue() / 50.;
//double sep = separationBar.getValue() * .001 / scalemult;
double sep = sep2 * .5 / (zmult*scalemult*resadj);
//System.out.println(2*sep*zmult*scalemult*resadj);
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 =
Math.sqrt(camvx0*camvx0+camvy0*camvy0+1);
int n;
float simpr = 0;
float simpg = 0;
// calculate intersections with bounding spheres
double a = camvx*camvx+camvy*camvy+camvz*camvz;
double b = 2*(camvx*camx+camvy*camy+camvz*camz);
double c = camx*camx+camy*camy+camz*camz-boundRadius2;
double discrim = b*b-4*a*c;
func[i][j][0] = func[i][j][1] = func[i][j][2] = 0;
if (discrim < 0) {
// doesn't hit it
fillSquare(i, j, 0, 0, 0);
continue;
}
discrim = Math.sqrt(discrim);
double mint = (-b-discrim)/(2*a);
double maxt = (-b+discrim)/(2*a);
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-1;
n = 1;
double xx = (camx + camvx * mint) * xmult;
double yy = (camy + camvy * mint) * ymult;
double zz = (camz + camvz * mint) * zmult;
if (slice != SLICE_NONE) {
maxn = 1;
n = 0;
pathlen = 2;
if (xx > xmult || yy > ymult || zz > zmult ||
xx < -xmult || yy < -ymult || zz < -zmult) {
fillSquare(i, j, 0, 0, 0);
continue;
}
}
camvx *= tstep*xmult;
camvy *= tstep*ymult;
camvz *= tstep*zmult;
int dshalf = dataSize/2;
int oi;
double msep = sep*zmult;
for (; n < maxn; n++) {
double xy2 = xx*xx+yy*yy;
double zz1 = zz+msep;
double r = Math.sqrt(xy2+zz1*zz1);
double costh = zz1/r;
int ri = (int) r;
int costhi = (int) (costh*dshalf+dshalf);
float fr = 0;
calcPhiComponent(xx, yy);
for (oi = 0; oi != orbCountOffset; oi++) {
Orbital oo = orbListLeft[oi];
fr += oo.computePoint(ri, costhi);
}
double zz2 = zz-msep;
r = Math.sqrt(xy2+zz2*zz2);
costh = zz2/r;
ri = (int) r;
costhi = (int) (costh*dshalf+dshalf);
for (oi = 0; oi != orbCountOffset; oi++) {
Orbital oo = orbListRight[oi];
fr += oo.computePoint(ri, costhi);
}
if (orbCountCenter != 0) {
r = Math.sqrt(xy2+zz*zz);
costh = zz/r;
ri = (int) r;
costhi = (int) (costh*dshalf+dshalf);
for (oi = 0; oi != orbCountCenter; oi++) {
Orbital oo = orbListCenter[oi];
fr += oo.computePoint(ri, costhi);
}
}
float fv = fr*fr * sampleMult[n];
if (color) {
/*if (fv > 1)
System.out.print("fv = " + fv + "\n");*/
if (fr > 0)
simpr += fv;
else
simpg += fv;
} else {
simpr = (simpg += fv);
}
xx += camvx;
yy += camvy;
zz += camvz;
}
simpr *= pathlen/n;
simpg *= pathlen/n;
fillSquare(i, j, simpr, simpg, simpg);
}
}
void fillSquare(int i, int j, float cr, float cg, float cb) {
int winw = viewX.width;
int winh = viewX.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*viewX.width;
for (k = x; k < x2; k++)
for (l = y*viewX.width; l < y2l; l += viewX.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*viewX.width;
for (k = x; k < x2; k++)
for (l = y*viewX.width; l < y2l; l += viewX.width)
pixels[k+l] = colval;
}
PhaseColor getPhaseColor(double x, double y) {
double val = 0;
if (x == 0 && y == 0)
return phaseColors[0];
int offset = 0;
if (y >= 0) {
if (x >= 0) {
if (x >= y) {
offset = 0;
val = y/x;
} else {
offset = phaseColorCount;
val = 1-x/y;
}
} else {
if (-x <= y) {
offset = 2*phaseColorCount;
val = -x/y;
} else {
offset = 3*phaseColorCount;
val = 1+y/x;
}
}
} else {
if (x <= 0) {
if (y >= x) {
offset = 4*phaseColorCount;
val = y/x;
} else {
offset = 5*phaseColorCount;
val = 1-x/y;
}
} else {
if (-y >= x) {
offset = 6*phaseColorCount;
val = -x/y;
} else {
offset = 7*phaseColorCount;
val = 1+y/x;
}
}
}
return phaseColors[offset+(int) (val*(phaseColorCount-1))];
}
void calcPhiComponent(double x, double y) {
int phiSector = 0;
double val = 0;
if (x == 0 && y == 0) {
phiIndex = 0;
return;
}
if (y >= 0) {
if (x >= 0) {
if (x >= y) {
phiSector = 0;
val = y/x;
} else {
phiSector = 1;
val = 1-x/y;
}
} else {
if (-x <= y) {
phiSector = 2;
val = -x/y;
} else {
phiSector = 3;
val = 1+y/x;
}
}
} else {
if (x <= 0) {
if (y >= x) {
phiSector = 4;
val = y/x;
} else {
phiSector = 5;
val = 1-x/y;
}
} else {
if (-y >= x) {
phiSector = 6;
val = -x/y;
} else {
phiSector = 7;
val = 1+y/x;
}
}
}
phiIndex = (phiSector*(dataSize+1))+(int) (val*dataSize);
}
URL getCodeBase() {
try {
if (applet != null)
return applet.getCodeBase();
File f = new File(".");
return new URL("file:" + f.getCanonicalPath() + "/");
} catch (Exception e) {
e.printStackTrace();
return null;
}
}
void readModes() {
try {
URL url = new URL(getCodeBase() + "states.txt");
Object o = url.getContent();
FilterInputStream fis = (FilterInputStream) o;
byte b[] = new byte[42000];
int off = 0;
while (true) {
int n = fis.read(b, off, 2048);
if (n <= 0)
break;
off += n;
}
int len = off;
int p;
int mm = 0;
modes = new float[10101];
for (p = 0; p < len; ) {
int l;
for (l = 0; l != len-p; l++)
if (b[l+p] == '\n') {
l++;
break;
}
String line = new String(b, p, l-1);
StringTokenizer st = new StringTokenizer(line);
while (st.hasMoreTokens())
modes[mm++] = new Float(st.nextToken()).floatValue();
p += l;
}
} catch (Exception e) {
e.printStackTrace();
}
}
int precount;
void precomputeAll() {
int i;
for (i = 0; i != orbCount; i++) {
Orbital orb = orbitals[i];
orb.precompute();
}
sep2 = separationBar.getValue()/2.;
if (sep2 < 0)
sep2 = 0;
if (sep2 > 10)
sep2 = 10;
int ma = 0;
for (; ; ma++) {
if (modes[ma] == 99999)
break;
if (modes[ma] == 99000+sep2)
break;
}
if (modes[ma] == 99999)
return;
ma++;
stateNum = 0;
orbitals[4].setReal();
orbitals[5].setReal();
orbitals[9].setReal();
switch (stateChooser.getSelectedIndex()) {
case 0: stateNum = 0; break;
case 1: stateNum = 1; break;
case 2: stateNum = 2; break;
case 3:
stateNum = 2;
orbitals[4].setIm();
orbitals[5].setIm();
orbitals[9].setIm();
break;
case 4: stateNum = 3; break;
case 5: stateNum = 4; break;
case 6: stateNum = 5; break;
case 7: stateNum = 6; break;
case 8:
stateNum = 6;
orbitals[4].setIm();
orbitals[5].setIm();
orbitals[9].setIm();
break;
case 9: stateNum = 7; break;
}
for (i = 0; i != orbCount; i++)
orbitals[i].used = false;
while (modes[ma] < 99000 && modes[ma] != stateNum)
ma += 59;
if (modes[ma] >= 99000)
return;
ma++;
sep2 = modes[ma++];
int sgn = 1;
if (sep2 < 0) {
sep2 = -sep2;
sgn = -1;
}
//System.out.println(sep2 + " " + modes[ma++]);
ma++;
// 1S orbitals
precount = 0;
orbitals[0].precomputeR(1, 1, sgn*modes[ma++]);
orbitals[1].precomputeR(1, 1, sgn*modes[ma++]);
orbitals[0].precomputeR(1.5, 1, sgn*modes[ma++]);
orbitals[1].precomputeR(1.5, 1, sgn*modes[ma++]);
orbitals[0].precomputeR(2, 1, sgn*modes[ma++]);
orbitals[1].precomputeR(2, 1, sgn*modes[ma++]);
orbitals[0].precomputeR(.4, 1, sgn*modes[ma++]);
orbitals[1].precomputeR(.4, 1, sgn*modes[ma++]);
orbitals[0].precomputeR(.7, 1, sgn*modes[ma++]);
orbitals[1].precomputeR(.7, 1, sgn*modes[ma++]);
// 2S orbitals
orbitals[0].precomputeR(1, 2, sgn*modes[ma++]);
orbitals[1].precomputeR(1, 2, sgn*modes[ma++]);
orbitals[0].precomputeR(1.5, 2, sgn*modes[ma++]);
orbitals[1].precomputeR(1.5, 2, sgn*modes[ma++]);
orbitals[0].precomputeR(2, 2, sgn*modes[ma++]);
orbitals[1].precomputeR(2, 2, sgn*modes[ma++]);
orbitals[0].precomputeR(.4, 2, sgn*modes[ma++]);
orbitals[1].precomputeR(.4, 2, sgn*modes[ma++]);
orbitals[0].precomputeR(.7, 2, sgn*modes[ma++]);
orbitals[1].precomputeR(.7, 2, sgn*modes[ma++]);
// 2Px orbitals
orbitals[4].precomputeR(1, 2, sgn*modes[ma++]);
orbitals[5].precomputeR(1, 2, sgn*modes[ma++]);
orbitals[4].precomputeR(1.5, 2, sgn*modes[ma++]);
orbitals[5].precomputeR(1.5, 2, sgn*modes[ma++]);
orbitals[4].precomputeR(2, 2, sgn*modes[ma++]);
orbitals[5].precomputeR(2, 2, sgn*modes[ma++]);
orbitals[4].precomputeR(.4, 2, sgn*modes[ma++]);
orbitals[5].precomputeR(.4, 2, sgn*modes[ma++]);
orbitals[4].precomputeR(.7, 2, sgn*modes[ma++]);
orbitals[5].precomputeR(.7, 2, sgn*modes[ma++]);
// 2Py orbitals
/*orbitals[6].precomputeR(1, 2, sgn*modes[ma++]);
orbitals[7].precomputeR(1, 2, sgn*modes[ma++]);
orbitals[6].precomputeR(1.5, 2, sgn*modes[ma++]);
orbitals[7].precomputeR(1.5, 2, sgn*modes[ma++]);
orbitals[6].precomputeR(2, 2, sgn*modes[ma++]);
orbitals[7].precomputeR(2, 2, sgn*modes[ma++]);
orbitals[6].precomputeR(.4, 2, sgn*modes[ma++]);
orbitals[7].precomputeR(.4, 2, sgn*modes[ma++]);
orbitals[6].precomputeR(.7, 2, sgn*modes[ma++]);
orbitals[7].precomputeR(.7, 2, sgn*modes[ma++]);*/
// 2Pz orbitals
orbitals[2].precomputeR(1, 2, sgn*modes[ma++]);
orbitals[3].precomputeR(1, 2, sgn*modes[ma++]);
orbitals[2].precomputeR(1.5, 2, sgn*modes[ma++]);
orbitals[3].precomputeR(1.5, 2, sgn*modes[ma++]);
orbitals[2].precomputeR(2, 2, sgn*modes[ma++]);
orbitals[3].precomputeR(2, 2, sgn*modes[ma++]);
orbitals[2].precomputeR(.4, 2, sgn*modes[ma++]);
orbitals[3].precomputeR(.4, 2, sgn*modes[ma++]);
orbitals[2].precomputeR(.7, 2, sgn*modes[ma++]);
orbitals[3].precomputeR(.7, 2, sgn*modes[ma++]);
// centered orbitals
orbitals[6].precomputeR(1.5, 1, sgn*modes[ma++]);
orbitals[6].precomputeR(2, 1, sgn*modes[ma++]);
orbitals[6].precomputeR(1.5, 2, sgn*modes[ma++]);
orbitals[6].precomputeR(2, 2, sgn*modes[ma++]);
orbitals[7].precomputeR(1.5, 2, sgn*modes[ma++]);
orbitals[7].precomputeR(2, 2, sgn*modes[ma++]);
orbitals[7].precomputeR(1.5, 3, sgn*modes[ma++]);
orbitals[7].precomputeR(2, 3, sgn*modes[ma++]);
orbitals[8].precomputeR(1.5, 3, sgn*modes[ma++]);
orbitals[8].precomputeR(2, 3, sgn*modes[ma++]);
// definition of 3Dxz is reversed
orbitals[9].precomputeR(1.5, 3, -sgn*modes[ma++]);
orbitals[9].precomputeR(2, 3, -sgn*modes[ma++]);
orbitals[7].precomputeR(1.5, 4, sgn*modes[ma++]);
orbitals[7].precomputeR(2, 4, sgn*modes[ma++]);
orbitals[10].precomputeR(1.5, 4, sgn*modes[ma++]);
orbitals[10].precomputeR(2, 4, sgn*modes[ma++]);
orbCountOffset = orbCountCenter = 0;
orbListLeft = new Orbital[3];
orbListRight = new Orbital[3];
orbListCenter = new Orbital[5];
for (i = 0; i != 6; i += 2) {
if (orbitals[i].used) {
orbListLeft [orbCountOffset] = orbitals[i];
orbListRight[orbCountOffset] = orbitals[i+1];
orbCountOffset++;
}
}
for (i = 6; i != 11; i++) {
if (orbitals[i].used) {
orbListCenter[orbCountCenter] = orbitals[i];
orbCountCenter++;
}
}
//System.out.println(orbCountOffset + " " + orbCountCenter);
}
void getEnergyValues() {
int ma = 0;
evalues = new double[21][8];
while (modes[ma] != 99999) {
int s = (int) ((modes[ma]-99000)*2);
ma++;
while (modes[ma] < 99000) {
evalues[s][(int)modes[ma]] = modes[ma+2];
ma += 59;
}
}
}
int sign(double x) {
return x < 0 ? -1 : 1;
}
public void paint(Graphics g) {
cv.repaint();
}
public void updateMOViewer(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());
if (fontMetrics == null)
fontMetrics = g.getFontMetrics();
boolean sliced = sliceChooser.getSelectedIndex() != SLICE_NONE;
zoom = (sliced) ? 8 : 16.55;
colorMult = Math.exp(brightnessBar.getValue()/100.-2);
//System.out.println(colorMult);
computeView(1);
int i, j, k;
for (i = 1; i != viewCount; i++) {
g.setColor(i == selectedPaneHandle ? Color.yellow : Color.gray);
g.drawLine(0, viewList[i].paneY,
winSize.width, viewList[i].paneY);
}
if (viewPotential != null) {
int sno = (int) (sep2-1);
double ymult = viewPotential.height * 1.9;
g.setColor(Color.darkGray);
int floory = viewPotential.y + viewPotential.height/2;
for (i = 0; i != 21; i++) {
double e = evalues[sno][i];
int y = floory - (int) (ymult * e);
g.drawLine(0, y, winSize.width, y);
}
double xp = getScaler();
/*
g.setColor(Color.white);
int ox = -1, oy = -1;
int x;
for (x = 0; x != winSize.width; x++) {
double xx = (x-winSize.width/2)*xp;
if (xx < 0)
xx = -xx;
if (xx < 1e-3)
xx = 1e-3;
double dy = -1/xx;
int y = viewPotential.y - (int) (ymult * dy);
if (y > floory) {
if (ox == -1)
continue;
g.drawLine(ox, oy, ox, floory);
ox = -1;
continue;
}
if (ox == -1 && x > 0) {
g.drawLine(x, floory, x, y);
ox = x;
oy = y;
continue;
}
if (ox != -1)
g.drawLine(ox, oy, x, y);
ox = x;
oy = y;
}
// calculate expectation value of E
if (norm != 0) {
double expecte = 0;
for (i = 0; i != stateCount; i++) {
State st = states[i];
double prob = st.magSquared()*normmult2;
expecte += prob*st.elevel;
}
int y = viewPotential.y - (int) (ymult * expecte);
g.setColor(Color.red);
g.drawLine(0, y, winSize.width, y);
}
if (selectedState != null && !dragging) {
g.setColor(Color.yellow);
int y = viewPotential.y - (int) (ymult * selectedState.elevel);
g.drawLine(0, y, winSize.width, y);
}
*/
}
if (viewPotentialSep != null) {
int floory = viewPotentialSep.y + viewPotentialSep.height/2;
double ymult = viewPotentialSep.height;
if (nuclearItem.getState()) {
ymult *= .7;
} else {
ymult *= .5;
floory = viewPotentialSep.y;
}
for (i = 0; i != 8; i++)
drawEnergyLine(g, i, floory, ymult);
drawEnergyLine(g, stateNum, floory, ymult);
g.setColor(Color.yellow);
int xx = (int) (sep2*winSize.width/10);
g.drawLine(xx, viewPotentialSep.y,
xx, viewPotentialSep.y+viewPotentialSep.height-1);
}
if (imageSource != null)
imageSource.newPixels();
g.drawImage(memimage, viewX.x, viewX.y, null);
if (showAtomsItem.getState()) {
double scalemult = scaleBar.getValue() / 50.;
double zmult = dataSize/2.;
double sep = sep2 * .5 / (zmult*scalemult*resadj);
g.setColor(Color.yellow);
map3d(0, 0, sep, xpoints, ypoints, 0, viewX);
g.drawOval(xpoints[0]-2, ypoints[0]-2, 4, 4);
map3d(0, 0, -sep, xpoints, ypoints, 0, viewX);
g.drawOval(xpoints[0]-2, ypoints[0]-2, 4, 4);
}
g.setColor(Color.white);
if (sliced)
drawCube(g, false);
if (axesItem.getState())
drawAxes(g);
g.setColor(Color.yellow);
if (dimensionsItem.getState()) {
double w = sep2 * 52.9463;
centerString(g, "Separation = " + (int)w + " pm (" + sep2 + " a0)",
viewX.y+viewX.height-5);
}
realg.drawImage(dbimage, 0, 0, this);
/*if (!allQuiet)
cv.repaint(pause);*/
}
void drawEnergyLine(Graphics g, int i, int floory, double ymult) {
int ox = -1, oy = -1;
g.setColor(stateNum == i ? Color.yellow : Color.darkGray);
int j;
for (j = 0; j != 21; j++) {
int xx = j*winSize.width/20;
double ne = 0;
if (nuclearItem.getState())
ne = (j == 0) ? 10 : 1/(j*.5);
int yy = floory - (int) (ymult*(evalues[j][i]+ne));
if (ox != -1)
g.drawLine(ox, oy, xx, yy);
ox = xx;
oy = yy;
}
}
double getScaler() {
// XXX don't duplicate this
double scalex = viewX.width*zoom/2;
double scaley = viewX.height*zoom/2;
double aratio = viewX.width/(double) viewX.height;
// preserve aspect ratio regardless of window dimensions
if (aratio < 1)
scaley *= aratio;
else
scalex /= aratio;
double xp = 2*scalex/viewDistance;
double mult = scaleBar.getValue() / 50.;
xp /= 50*mult;
xp = 1/xp;
return xp;
}
public void centerString(Graphics g, String str, int ypos) {
g.drawString(str, (winSize.width-fontMetrics.stringWidth(str))/2, ypos);
}
// 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;
}
// 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, viewX);
}
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, viewX);
computeFace(i, 2, pts);
pts[slice-SLICE_X] = sliceval;
map3d(pts[0], pts[1], pts[2],
slicerPoints[0], slicerPoints[1], sp+1, viewX);
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;
}
}
void drawAxes(Graphics g) {
g.setColor(Color.white);
double d = .5;
map3d(0, 0, 0, xpoints, ypoints, 0, viewAxes);
map3d(d, 0, 0, xpoints, ypoints, 1, viewAxes);
drawArrow(g, "x", xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
map3d(0, d, 0, xpoints, ypoints, 1, viewAxes);
drawArrow(g, "y", xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
map3d(0, 0, d, xpoints, ypoints, 1, viewAxes);
drawArrow(g, "z", xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
}
void drawArrow(Graphics g, String text, int x1, int y1, int x2, int y2) {
drawArrow(g, text, x1, y1, x2, y2, 5);
}
void drawArrow(Graphics g, String text,
int x1, int y1, int x2, int y2, int as) {
g.drawLine(x1, y1, x2, y2);
double l = Math.sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
if (l > as/2) { // was as
double hatx = (x2-x1)/l;
double haty = (y2-y1)/l;
g.drawLine(x2, y2,
(int) (haty*as-hatx*as+x2),
(int) (-hatx*as-haty*as+y2));
g.drawLine(x2, y2,
(int) (-haty*as-hatx*as+x2),
(int) (hatx*as-haty*as+y2));
if (text != null)
g.drawString(text, (int) (x2+hatx*10), (int) (y2+haty*10));
}
}
// 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, Rectangle v) {
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 = v.width*zoom/2;
double scaley = v.height*zoom/2;
double aratio = v.width/(double) v.height;
// preserve aspect ratio regardless of window dimensions
if (aratio < 1)
scaley *= aratio;
else
scalex /= aratio;
xpoints[pt] = v.x + v.width /2 + (int) (scalex*realx/realz);
ypoints[pt] = v.y + v.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 = viewX.width*zoom/2;
double scaley = viewX.height*zoom/2;
double aratio = viewX.width/(double) viewX.height;
// preserve aspect ratio regardless of window dimensions
if (aratio < 1)
scaley *= aratio;
else
scalex /= aratio;
double vx = (x-(viewX.x+viewX.width/2))/scalex;
double vy = -(y-(viewX.y+viewX.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;
}
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() == exitItem) {
applet.destroyFrame();
return;
}
cv.repaint();
}
int scaleValue = -1;
int sepValue = -1;
public void adjustmentValueChanged(AdjustmentEvent e) {
System.out.print(((Scrollbar) e.getSource()).getValue() + "\n");
if (e.getSource() == scaleBar) {
if (scaleBar.getValue() == scaleValue)
return;
scaleValue = scaleBar.getValue();
precomputeAll();
manualScale = true;
}
if (e.getSource() == separationBar) {
if (separationBar.getValue() == sepValue)
return;
sepValue = separationBar.getValue();
precomputeAll();
}
if (e.getSource() == resolutionBar)
setResolution();
setupSimpson();
cv.repaint(pause);
}
public void mouseDragged(MouseEvent e) {
dragging = true;
changingDerivedStates = false;
edit(e);
dragX = e.getX(); dragY = e.getY();
}
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 = 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/Math.sqrt(1+b*b);
}
if (d < 6) {
selectedSlice = true;
sliceFace = sliceFaces[n/2];
break;
}
}
}
public void mouseMoved(MouseEvent e) {
if (dragging)
return;
int x = e.getX();
int y = e.getY();
dragX = x; dragY = y;
int oldsph = selectedPaneHandle;
int olds = selection;
boolean oldss = selectedSlice;
selectedPaneHandle = -1;
selection = 0;
int i;
for (i = 1; i != viewCount; i++) {
int dy = y-viewList[i].paneY;
if (dy >= -3 && dy <= 3) {
selectedPaneHandle = i;
selection = SEL_HANDLE;
}
}
if (viewX != null && viewX.inside(x, y)) {
selection = SEL_X;
checkSlice(e.getX(), e.getY());
} else if (viewPotential != null && viewPotential.contains(x, y)) {
selection = SEL_POTENTIAL;
//findStateByEnergy(y);
}
if (oldsph != selectedPaneHandle || olds != selection ||
oldss != selectedSlice)
cv.repaint(pause);
}
public void mouseClicked(MouseEvent e) {
}
public void mouseEntered(MouseEvent e) {
}
public void mouseExited(MouseEvent e) {
if (!dragging && selection != 0) {
selectedPaneHandle = -1;
selection = 0;
cv.repaint(pause);
}
}
public void mousePressed(MouseEvent e) {
if ((e.getModifiers() & MouseEvent.BUTTON1_MASK) == 0)
return;
dragX = dragStartX = e.getX();
dragY = dragStartY = e.getY();
dragZoomStart = zoom;
dragging = true;
edit(e);
}
public void mouseReleased(MouseEvent e) {
if (dragging)
cv.repaint();
dragging = changingDerivedStates = false;
}
public void itemStateChanged(ItemEvent e) {
if (e.getItemSelectable() instanceof CheckboxMenuItem) {
int i;
for (i = 0; i != samplesNums.length; i++)
if (samplesItems[i] == e.getItemSelectable())
break;
if (i != samplesNums.length) {
int j;
for (j = 0; j != samplesNums.length; j++)
samplesItems[j].setState(i == j);
setupSimpson();
}
setupDisplay();
cv.repaint(pause);
return;
}
if (e.getItemSelectable() == stateChooser)
precomputeAll();
cv.repaint(pause);
}
public boolean handleEvent(Event ev) {
if (ev.id == Event.WINDOW_DESTROY) {
destroyFrame();
return true;
}
return super.handleEvent(ev);
}
void destroyFrame() {
if (applet == null)
dispose();
else
applet.destroyFrame();
}
void edit(MouseEvent e) {
if (selection == SEL_NONE)
return;
int x = e.getX();
int y = e.getY();
switch (selection) {
case SEL_HANDLE: editHandle(y); break;
case SEL_POTENTIAL: break;
case SEL_X: editX(x, y); break;
}
}
void editHandle(int y) {
int dy = y-viewList[selectedPaneHandle].paneY;
View upper = viewList[selectedPaneHandle-1];
View lower = viewList[selectedPaneHandle];
int minheight = 10;
if (upper.height+dy < minheight || lower.height-dy < minheight)
return;
upper.height += dy;
lower.height -= dy;
lower.y += dy;
lower.paneY += dy;
cv.repaint(pause);
setSubViews();
}
void editX(int x, int y) {
int mode = MODE_ANGLE;
if (selectedSlice)
mode = MODE_SLICE;
if (mode == MODE_ANGLE) {
int xo = dragX-x;
int yo = dragY-y;
rotate(xo/40., -yo/40.);
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;
}
if (sliceval < -.99)
sliceval = -.99;
if (sliceval > .99)
sliceval = .99;
cv.repaint(pause);
}
}
void createOrbitals() {
if (orbCount == 11)
return;
orbCount = 11;
orbitals = new Orbital[orbCount];
orbitals[0] = new SOrbital();
orbitals[1] = new SOrbital();
orbitals[2] = new MZeroOrbital(1);
orbitals[3] = new MZeroOrbital(1);
orbitals[4] = new ReImOrbital(1);
orbitals[5] = new ReImOrbital(1);
orbitals[6] = new SOrbital();
orbitals[7] = new MZeroOrbital(1);
orbitals[8] = new MZeroOrbital(2);
orbitals[9] = new ReImOrbital(2);
orbitals[10] = new MZeroOrbital(3);
}
abstract class Orbital {
int l, m;
float reMult, imMult;
boolean used;
void setupFrame(double mult) {
reMult = 1; // state.re*mult;
imMult = 0; // state.im*mult;
}
void setReal() { }
void setIm() { }
float dataR[], dataTh[], dataPhiR[], dataPhiI[];
int dshalf;
double brightnessCache;
double getBoundRadius(double bright) {
int i;
int outer = 1;
/*
double maxThData = 0;
if (l == 0)
maxThData = 1;
else {
for (i = 0; i != dataSize; i++) {
if (dataTh[i] > maxThData)
maxThData = dataTh[i];
if (dataTh[i] < -maxThData)
maxThData = -dataTh[i];
}
}*/
// we need to divide the spherical harmonic norm out of
// dataR[] to get just the radial function. (The spherical
// norm gets multiplied into dataR[] for efficiency.)
int mpos = (m < 0) ? -m : m;
double norm1 = 1/sphericalNorm(l, mpos);
//norm1 *= maxThData;
norm1 *= norm1;
norm1 *= bright;
for (i = 0; i != dataSize; i++) { // XXX
double v = dataR[i]*dataR[i]*norm1;
if (v > 32)
outer = i;
}
//System.out.println(maxThData + " " + outer);
return outer / (dataSize/2.);
}
double getScaleRadius() {
// set scale by solving equation Veff(r) = E, assuming m=0
// Veff(r) = -1/r + l(l+1)/2, E = 1/2n^2
int n = 1; // XXX
double b0 = -n*n*2;
double c0 = l*(l+1)*n*n;
double r0 = .5*(-b0+Math.sqrt(b0*b0-4*c0));
return r0;
}
final int distmult = 4;
void precompute() {
int x, y, z;
dshalf = dataSize/2;
double mult = scaleBar.getValue() / 50.;
int mpos = (m < 0) ? -m : m;
double lgcorrect = Math.pow(-1, m);
dataR = new float[dataSize];
if (l > 0) {
dataTh = new float[dataSize+1];
for (x = 0; x != dataSize+1; x++) {
double th = (x-dshalf)/(double) dshalf;
// we multiply in lgcorrect because plgndr() uses a
// different sign convention than Bransden
dataTh[x] = (float) (lgcorrect*plgndr(l, mpos, th));
}
}
if (m != 0) {
dataPhiR = new float[8*(dataSize+1)];
dataPhiI = new float[8*(dataSize+1)];
int ix = 0;
for (x = 0; x != 8; x++)
for (y = 0; y <= dataSize; y++, ix++) {
double phi = x*pi/4 + y*(pi/4)/dataSize;
dataPhiR[ix] = (float) Math.cos(phi*mpos);
dataPhiI[ix] = (float) Math.sin(phi*mpos);
}
}
brightnessCache = 0;
}
void precomputeR(double charge, int n, double mag) {
if (Math.abs(mag) < .06) {
precount++;
return;
}
used = true;
//System.out.println("precomputing " + precount + " " + n + " " + l + " " + m + " " + charge + " " + mag);
precount++;
int x, y, z;
dshalf = dataSize/2;
double mult = scaleBar.getValue() / 50.;
int mpos = (m < 0) ? -m : m;
double norm = radialNorm(n, l, charge)*sphericalNorm(l, mpos) *
mag;
// r*mult = distance in a0's
for (x = 0; x != dataSize; x++) {
double r = x*resadj + .00000001;
double rho = 2*charge*r*mult/n;
double rhol = Math.pow(rho, l)*norm;
dataR[x] += (float) (hypser(l+1-n, 2*l+2, rho)*rhol*
Math.exp(-rho/2));
}
}
double getBrightness() {
if (brightnessCache != 0)
return brightnessCache;
int x;
double avgsq = 0;
double vol = 0;
// we need to divide the spherical harmonic norm out of
// dataR[] to get just the radial function. (The spherical
// norm gets multiplied into dataR[] for efficiency.)
int mpos = (m < 0) ? -m : m;
double norm1 = 1/sphericalNorm(l, mpos);
for (x = 0; x != dataSize; x++) {
double val = dataR[x]*norm1;
val *= val;
avgsq += val*val*x*x;
vol += x*x;
}
brightnessCache = avgsq / vol;
return brightnessCache;
}
double radialNorm(int n, int l, double charge) {
double a0 = factorial(n+l);
return Math.sqrt(4.*charge*charge*charge*factorial(n+l)/
(n*n*n*n*factorial(n-l-1)))/
factorial(2*l+1);
}
double sphericalNorm(int l, int m) {
return Math.sqrt((2*l+1)*factorial(l-m)/
(4*pi*factorial(l+m)));
}
double factorial(int f) {
double res = 1;
while (f > 1)
res *= f--;
return res;
}
abstract float computePoint(int r, int costh);
};
class SOrbital extends Orbital {
float computePoint(int r, int costh) {
try {
float v = (r < dataSize) ? dataR[r] : 0;
return reMult*v;
} catch (Exception e) {
return 0;
//System.out.println("bad " + r + " " + costh);
//funci = 100;
}
}
};
class MZeroOrbital extends Orbital {
MZeroOrbital(int ll) {
l = ll;
}
float computePoint(int r, int costh) {
try {
float v = (r < dataSize) ? dataR[r]*dataTh[costh] : 0;
return v*reMult;
} catch (Exception e) {
return 0;
//System.out.println("bad " + r + " " + costh);
}
}
};
class ReImOrbital extends Orbital {
ReImOrbital(int ll) {
l = ll;
m = 1;
}
float dataPhi[];
void setReal() {
dataPhi = dataPhiR;
}
void setIm() {
dataPhi = dataPhiI;
}
float computePoint(int r, int costh) {
try {
float phiValR = dataPhi[phiIndex];
return (r < dataSize) ? dataR[r]*dataTh[costh]*phiValR*root2
: 0;
} catch (Exception e) {
return 0;
}
}
};
class Complex {
public double re, im, mag, phase;
Complex() { re = im = mag = phase = 0; }
Complex(double r, double i) {
set(r, i);
}
double magSquared() { return mag*mag; }
void set(double aa, double bb) {
re = aa; im = bb;
setMagPhase();
}
void set(double aa) {
re = aa; im = 0;
setMagPhase();
}
void set(Complex c) {
re = c.re;
im = c.im;
mag = c.mag;
phase = c.phase;
}
void add(double r) {
re += r;
setMagPhase();
}
void add(double r, double i) {
re += r; im += i;
setMagPhase();
}
void add(Complex c) {
re += c.re;
im += c.im;
setMagPhase();
}
void square() {
set(re*re-im*im, 2*re*im);
}
void mult(double c, double d) {
set(re*c-im*d, re*d+im*c);
}
void mult(double c) {
re *= c; im *= c;
mag *= c;
}
void mult(Complex c) {
mult(c.re, c.im);
}
void setMagPhase() {
mag = Math.sqrt(re*re+im*im);
phase = Math.atan2(im, re);
}
void setMagPhase(double m, double ph) {
mag = m;
phase = ph;
re = m*Math.cos(ph);
im = m*Math.sin(ph);
}
void rotate(double a) {
setMagPhase(mag, (phase+a) % (2*pi));
}
void conjugate() {
im = -im;
phase = -phase;
}
};
class PhaseColor {
public double r, g, b;
PhaseColor(double rr, double gg, double bb) {
r = rr; g = gg; b = bb;
}
}
double plgndr(int l,int m,double x) {
double fact,pll = 0,pmm,pmmp1,somx2;
int i,ll;
if (m < 0 || m > l || Math.abs(x) > 1.0) {
System.out.print("bad arguments in plgndr\n");
}
pmm=1.0;
if (m > 0) {
somx2=Math.sqrt((1.0-x)*(1.0+x));
fact=1.0;
for (i=1;i<=m;i++) {
pmm *= -fact*somx2;
fact += 2.0;
}
}
if (l == m)
return pmm;
else {
pmmp1=x*(2*m+1)*pmm;
if (l == (m+1))
return pmmp1;
else {
for (ll=(m+2);ll<=l;ll++) {
pll=(x*(2*ll-1)*pmmp1-(ll+m-1)*pmm)/(ll-m);
pmm=pmmp1;
pmmp1=pll;
}
return pll;
}
}
}
double hypser(int a, int c, double z) {
int n;
double fac = 1;
double result = 1;
for (n=1;n<=1000;n++) {
fac *= a*z/((double) n*c);
//System.out.print("fac " + n + " " + fac + " " + z + "\n");
if (fac == 0)
return result;
result += fac;
a++;
c++;
}
System.out.print("convergence failure in hypser\n");
return 0;
}
class View extends Rectangle {
View() { }
View(View v) { super(v); }
double scale;
int paneY;
int pixels[];
}
}
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
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