// base.java (C) 2001 by Paul Falstad, www.falstad.com
// this file must be run through cpp with one of BUILD_E, BUILD_V,
// BUILD_M defined before compiling with java compiler.  This was done
// to reduce class file sizes.

import java.io.InputStream;
import java.awt.*;
import java.awt.image.*;
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.awt.image.MemoryImageSource;
import java.lang.Math;
import java.text.NumberFormat;
import java.lang.reflect.Constructor;
import java.lang.reflect.Method;
import java.awt.event.*;

#ifdef BUILD_E
#define BUILD_CASE_EMV(E,M,V) E
#elif defined(BUILD_M)
#define BUILD_CASE_EMV(E,M,V) M
#else
#define BUILD_CASE_EMV(E,M,V) V
#endif

class VecDemoCanvas extends Canvas {
    VecDemoFrame pg;
    VecDemoCanvas(VecDemoFrame p) {
	pg = p;
    }
    public Dimension getPreferredSize() {
	return new Dimension(300,400);
    }
    public void update(Graphics g) {
	pg.updateVecDemo(g);
    }
    public void paint(Graphics g) {
	pg.updateVecDemo(g);
    }
};

class VecDemoLayout implements LayoutManager {
    public VecDemoLayout() {}
    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 DecentScrollbar || m instanceof TextComponent)
		    d.width = barwidth;
		if (m instanceof Choice && d.width > barwidth)
		    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 VecDemo extends Applet implements ComponentListener {
    static VecDemoFrame 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 VecDemoFrame(null);
        ogf.init();
    }

    void showFrame() {
	if (ogf == null) {
	    started = true;
	    ogf = new VecDemoFrame(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 VecDemoFrame extends Frame
    implements ComponentListener, ActionListener,
	       MouseMotionListener, MouseListener, ItemListener,
	       DecentScrollbarListener {
    
    Thread engine = null;

    Dimension winSize;
    Rectangle viewMain, viewAxes;
    Image dbimage;
    Image backimage;
    MemoryImageSource imageSource;
    int pixels[];
    
    VecDemo applet;
    Random random;
    
    public String getAppletInfo() {
	return "VecDemo by Paul Falstad";
    }

    static final double pi = 3.14159265358979323846;

    int getrand(int x) {
	int q = random.nextInt();
	if (q < 0) q = -q;
	return q % x;
    }
    VecDemoCanvas cv;
    Checkbox stoppedCheck;
    Button resetButton;
    Button kickButton;
    Checkbox reverseCheck;
    Button infoButton;
    Choice functionChooser;
    Choice dispChooser;
    static final int DISP_PART_VELOC    = 0;
    static final int DISP_PART_FORCE    = 1;
    static final int DISP_VECTORS       = 2;
    static final int DISP_NONE          = 3;
    static final int DISP_CURLERS       = 4;
    Label partCountLabel;
    Label textFieldLabel;
    Label strengthLabel;
    DecentScrollbar partCountBar;
    DecentScrollbar strengthBar;
    DecentScrollbar aux1Bar;
    DecentScrollbar aux2Bar;
    DecentScrollbar aux3Bar;
    double fieldStrength, barFieldStrength;
    Color darkYellow = new Color(144, 144, 0);
    final double lineWidth = .001;
    class AuxBar {
	DecentScrollbar bar;
	Label label;
	AuxBar(Label l, DecentScrollbar b) { label = l; bar = b; }
    };
    AuxBar auxBars[];
    Label vecDensityLabel;
    DecentScrollbar vecDensityBar;
    Label potentialLabel;
    DecentScrollbar potentialBar;
    Label lineDensityLabel;
    DecentScrollbar lineDensityBar;
    Choice modeChooser;
    Choice floorColorChooser;
    Choice floorLineChooser;

    TextField textFields[];
    int reverse;
    int xpoints[];
    int ypoints[];
    GridElement grid[][];
    Particle particles[];
    FieldVector vectors[];
    int vecCount;
    int density[][];
    Checkbox flatCheck;
    boolean isFlat;
    double viewAngle, viewAngleDragStart;
    double viewZoom = 1.6, viewZoomDragStart;
    double viewAngleCos = 1, viewAngleSin = 0;
    double viewHeight = 2, viewHeightDragStart;
    double viewDistance = 5;
    int integralX = -1, integralY;
    int vectorSpacing = 16;
    int currentStep;
    boolean showA;
    boolean parseError;
    Color fieldColors[];
    static final int gridsize = 80;

    static final int densitygridsize = 16;
    static final double densitygroupsize = 2./densitygridsize;
    static final int maxParticleCount = 2500;
    boolean functionChanged;
    boolean backgroundChanged;
    boolean dragging, draggingView;
    int oldDragX, oldDragY, dragX, dragY, dragStartX, dragStartY;
    double dragZoomStart;
    Vector functionList;
    VecFunction curfunc;
    int pause = 20;
    static final int MOT_VELOCITY = 0;
    static final int MOT_FORCE    = 1;
    static final int MOT_CURLERS  = 2;
    static final int MOT_EQUIPOTENTIAL = 3;
    static final int FC_FIELD     = 0;
    static final int FC_POTENTIAL = 1;
    static final int FC_NONE      = 2;
    static final int FC_DIV       = 3;
    static final int FC_CURL      = 4;
    static final int FL_NONE      = 0;
    static final int FL_GRID      = 1;
    static final int FL_EQUIP     = 2;
    static final int FL_LINES     = 3;

    static final int MODE_VIEW_ROTATE  = 0;
    static final int MODE_VIEW_ZOOM    = 1;
    static final int MODE_LINE_INT     = 2;
    static final int MODE_SURF_INT     = 3;

    boolean useBufferedImage = false;
    
    VecDemoFrame(VecDemo a) {
	super(BUILD_CASE_EMV("2-D Electrostatic Fields Applet v1.4b", null,
			     "2-D Vector Fields Applet v1.4b"));
	applet = a;
    }

    public void init() {
	try {
	    String param = applet.getParameter("PAUSE");
	    if (param != null)
		pause = Integer.parseInt(param);
	} catch (Exception e) { }

        String jv = System.getProperty("java.class.version");
        double jvf = new Double(jv).doubleValue();
        if (jvf >= 48)
	    useBufferedImage = true;
	
	functionList = new Vector();
	VecFunction vf = new InverseRadial();
	int ct = 0;
	while (vf != null) {
	    functionList.addElement(vf);
	    vf = vf.createNext();
	    if (ct == 1000) {
		System.out.print("setup loop\n");
		return;
	    }
	}

	Color particleColors[] = new Color[27];
	int i;
	for (i = 0; i != 27; i++)
	    particleColors[i] = new Color(((i%3)+1)*85,
					  ((i/3)%3+1)*85,
					  ((i/9)%3+1)*85);

	random = new Random();
	particles = new Particle[maxParticleCount];
	for (i = 0; i != maxParticleCount; i++) {
	    particles[i] = new Particle();
	    particles[i].color = particleColors[i % 27];
	}
	xpoints = new int[4];
	ypoints = new int[4];
	density = new int[densitygridsize][densitygridsize];
	setLayout(new VecDemoLayout());
	cv = new VecDemoCanvas(this);
	cv.addComponentListener(this);
	cv.addMouseMotionListener(this);
	cv.addMouseListener(this);
	add(cv);

	/*infoButton = new Button("Function Info");
	add(infoButton);
	infoButton.addActionListener(this);*/

	functionChooser = new Choice();
	for (i = 0; i != functionList.size(); i++)
	    functionChooser.add("Setup: " +
	       ((VecFunction) functionList.elementAt(i)).getName());
	add(functionChooser);
	functionChooser.addItemListener(this);

	floorColorChooser = new Choice();
	floorColorChooser.add("Color: field magnitude");
	floorColorChooser.add("Color: potential");
	floorColorChooser.add("Color: none");
#ifdef BUILD_E
	floorColorChooser.add("Color: charge");
#else
	floorColorChooser.add("Color: divergence");
	floorColorChooser.add("Color: curl z");
#endif
	floorColorChooser.addItemListener(this);
	add(floorColorChooser);

	floorLineChooser = new Choice();
	floorLineChooser.add("Floor: no lines");
	floorLineChooser.add("Floor: grid");
	floorLineChooser.add("Floor: equipotentials");
#ifdef BUILD_V
	floorLineChooser.add("Floor: streamlines");
#else
	floorLineChooser.add("Floor: field lines");
#endif
	floorLineChooser.addItemListener(this);
	add(floorLineChooser);
	floorLineChooser.select(FL_EQUIP);

	flatCheck = new Checkbox("Flat View");
	flatCheck.addItemListener(this);
	add(flatCheck);

	dispChooser = new Choice();
	dispChooser.addItemListener(this);
	setupDispChooser(true);
	add(dispChooser);

	modeChooser = new Choice();
	modeChooser.add("Mouse = Adjust Angle");
	modeChooser.add("Mouse = Adjust Zoom");
	modeChooser.add("Mouse = Line Integral");
	modeChooser.add("Mouse = Surface Integral");
	modeChooser.addItemListener(this);
	add(modeChooser);
	
	stoppedCheck = new Checkbox("Stopped");
	stoppedCheck.addItemListener(this);
	add(stoppedCheck);

	reverseCheck = new Checkbox("Reverse");
	reverseCheck.addItemListener(this);
	add(reverseCheck);

	resetButton = new Button("Reset");
	add(resetButton);
	resetButton.addActionListener(this);
	kickButton = new Button("Kick");
	add(kickButton);
	kickButton.addActionListener(this);
	kickButton.disable();

	add(strengthLabel = new Label("Field Strength", Label.CENTER));
	add(strengthBar = new DecentScrollbar(this, 80, 1, 120));

	add(partCountLabel = new Label("Number of Particles", Label.CENTER));
	add(partCountBar = new DecentScrollbar(this, 500, 1, maxParticleCount));

	add(vecDensityLabel = new Label("Vector Density", Label.CENTER));
	add(vecDensityBar = new DecentScrollbar(this, 32, 2, 64));

	/*add(lineDensityLabel = new Label("Line Density", Label.CENTER));
	  add(lineDensityBar = new DecentScrollbar(this, 5, 3, 8));*/

	add(potentialLabel = new Label("Potential", Label.CENTER));
	add(potentialBar = new DecentScrollbar(this, 250, 0, 1000));

	Label lb;
	auxBars = new AuxBar[3];
	add(lb = new Label("Aux 1", Label.CENTER));
	add(aux1Bar = new DecentScrollbar(this, 0, 0, 100));
	auxBars[0] = new AuxBar(lb, aux1Bar);

	add(lb = new Label("Aux 2", Label.CENTER));
	add(aux2Bar = new DecentScrollbar(this, 0, 0, 100));
	auxBars[1] = new AuxBar(lb, aux2Bar);

	add(lb = new Label("Aux 3", Label.CENTER));
	add(aux3Bar = new DecentScrollbar(this, 0, 0, 100));
	auxBars[2] = new AuxBar(lb, aux3Bar);

#ifdef BUILD_V
	add(textFieldLabel = new Label("", Label.CENTER));
#endif

	textFields = new TextField[2];
	for (i = 0; i != 2; i++) {
	    add(textFields[i] = new TextField());
	    textFields[i].addActionListener(this);
	}
	fieldColors = new Color[513];
	int grayLevel = 76;
	for (i = 0; i != 256; i++) {
	    int rb = grayLevel+(128-grayLevel)*i/255;
	    int g = grayLevel+(255-grayLevel)*i/255;
	    int col = (255<<24) | (g<<8) | (rb<<16) | (rb);
	    fieldColors[i] = new Color(col);
	}
	for (i = 0; i != 256; i++) {
	    int col = (255<<24) | (255<<8) | ((i/2+128) * (0x10001));
	    fieldColors[i+256] = new Color(col);
	}
	fieldColors[512] = fieldColors[511];

	add(new Label("", Label.CENTER));

	reinit();
	cv.setBackground(Color.black);
	cv.setForeground(Color.lightGray);

	resize(650, 500);
	handleResize();
	Dimension screen = getToolkit().getScreenSize();
	Dimension x = getSize();
	setLocation((screen.width  - x.width)/2,
		    (screen.height - x.height)/2);
	functionChanged();
	dispChooserChanged();
	show();
    }

    void handleResize() {
        Dimension d = winSize = cv.getSize();
	if (winSize.width == 0)
	    return;
	dbimage = createImage(d.width, d.height);
	scaleworld();
	viewMain = new Rectangle(winSize);
	viewAxes = new Rectangle(winSize.width-100, 0, 100, 100);
	backgroundChanged = true;
	
	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)dbimage).
		   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 });
		backimage = (Image) cstr.newInstance(new Object[] {
		    new Integer(d.width), new Integer(d.height),
		    new Integer(BufferedImage.TYPE_INT_RGB)});
		Method m = biclass.getMethod("getRaster", null);
		Object ras = m.invoke(backimage, 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[d.width*d.height];
	    int i;
	    for (i = 0; i != d.width*d.height; i++)
		pixels[i] = 0xFF000000;
	    imageSource = new MemoryImageSource(d.width, d.height, pixels, 0,
						d.width);
	    imageSource.setAnimated(true);
	    imageSource.setFullBufferUpdates(true);
	    backimage = cv.createImage(imageSource);
	}
    }

    void resetDensityGroups() {
	int i, j, k;
	for (i = 0; i != densitygridsize; i++)
	    for (j = 0; j != densitygridsize; j++)
		density[i][j] = 0;
	int pcount = getParticleCount();
	for (i = 0; i != pcount; i++) {
	    Particle p = particles[i];
	    addToDensityGroup(p);
	}

	// invalidate all unused particles so they will be
	// repositioned if the particle slider is moved to the right,
	// rather than just falling in where they happened to be last time
	for (; i != maxParticleCount; i++) {
	    Particle p = particles[i];
	    p.lifetime = -100;
	}
    }

    int addToDensityGroup(Particle p) {
	int a = (int)((p.pos[0]+1)*(densitygridsize/2));
	int b = (int)((p.pos[1]+1)*(densitygridsize/2));
	int n = 0;
	try {
	n = ++density[a][b];
	if (n > maxParticleCount)
	    System.out.print(a + " " + b + " " + density[a][b] + "\n");
	} catch (Exception e) {
	    System.out.print(p.pos[0] + " " + p.pos[1] + "\n");
	    e.printStackTrace();
	}
	return n;
    }

    void removeFromDensityGroup(Particle p) {
	int a = (int)((p.pos[0]+1)*(densitygridsize/2));
	int b = (int)((p.pos[1]+1)*(densitygridsize/2));
	try {
	    if (--density[a][b] < 0)
		System.out.print(a + " " + b + " " + density[a][b] + "\n");
	} catch (Exception e) {
	    System.out.print(p.pos[0] + " " + p.pos[1] + "\n");
	    e.printStackTrace();
	}
    }

    void positionParticle(Particle p) {
	int x, y;
	int bestx = 0, besty = 0;
	int best = 10000;

	// we avoid scanning the grid in the same order every time
	// so that we treat equal-density squares as equally as possible.
	int randaddx = getrand(densitygridsize);
	int randaddy = getrand(densitygridsize);
	for (x = 0; x != densitygridsize; x++)
	    for (y = 0; y != densitygridsize; y++) {
		int ix = (randaddx + x) % densitygridsize;
		int iy = (randaddy + y) % densitygridsize;
		if (density[ix][iy] <= best) {
		    bestx = ix;
		    besty = iy;
		    best = density[ix][iy];
		}
	    }
	p.pos[0] = bestx*densitygroupsize +
	    getrand(100)*densitygroupsize/100.0 - 1;
	p.pos[1] = besty*densitygroupsize +
	    getrand(100)*densitygroupsize/100.0 - 1;
	p.lifetime = curfunc.redistribute() ? 500 : 5000;
	p.stepsize = 1;
	p.theta = (getrand(101)-50)*pi/50.;
	p.phi   = (getrand(101)-50)*pi/50.;
	int j;
	for (j = 0; j != 3; j++)
	    p.vel[j] = 0;
    }

    int getParticleCount() {
	return partCountBar.getValue();
    }

    void resetParticles() {
	int pcount = getParticleCount();
	int i, j;
	for (i = 0; i != pcount; i++) {
	    Particle p = particles[i];
	    for (j = 0; j != 2; j++) {
		p.pos[j] = getrand(200)/100.0 - 1;
		p.vel[j] = 0;
	    }
	    p.pos[2] = 0;
	    p.lifetime = i*2;
	    p.stepsize = 1;
	}
	integralX = -1;
	resetDensityGroups();
    }

    void kickParticles() {
	int i, j;
	for (i = 0; i != getParticleCount(); i++) {
	    Particle p = particles[i];
	    for (j = 0; j != 2; j++)
		p.vel[j] += (getrand(100)/99.0 - .5) * .04;
	}
    }

    void generateFunction() {
	int x, y;
	if (grid == null)
	    grid = new GridElement[gridsize+1][gridsize+1];
	curfunc.setupFrame();
	divOffset = curfunc.getDivOffset();
	divRange = curfunc.getDivRange();
	double mu, xx, xx2, yy, yy2, r, r1, r2, r3, r4;
	double levelheight = curfunc.getLevelHeight();
	//System.out.print("gf1\n");
	for (x = 0; x != gridsize+1; x++)
	    for (y = 0; y != gridsize+1; y++) {
		GridElement ge = grid[x][y] = new GridElement();
		ge.curl = ge.div = ge.height = 0;
		curfunc.setGrid(ge, x, y);
		/*ge.normdot = (ge.vecX+ge.vecY+1)*(1/1.73)/
		  java.lang.Math.sqrt(ge.vecX*ge.vecX+ge.vecY*ge.vecY+1);*/
	    }
	curfunc.calcDivergence();
	double zval = 2.0/gridsize;
	for (y = 0; y != gridsize; y++)
	    for (x = 0; x != gridsize; x++) {
		GridElement ge = grid[x][y];
		double vecx = grid[x+1][y].height-ge.height;
		double vecy = grid[x][y+1].height-ge.height;
		// light vector = (1,1,1)/1.73
		// norm vector = (-dzdx, -dzdy, 1)
		ge.normdot = (vecx+vecy+zval)*(1/1.73)/
		    java.lang.Math.sqrt(vecx*vecx+vecy*vecy+zval*zval);
	    }
	for (x = 0; x != gridsize+1; x++) {
	    grid[gridsize][x] = grid[gridsize-1][x];
	    grid[x][gridsize] = grid[x][gridsize-1];
	}
	//System.out.print("gf2\n");
	functionChanged = false;
	backgroundChanged = true;
    }

    double divOffset, divRange;

    int computeColor(GridElement ge, double c) {
	if (c < 0)
	    c = 0;
	if (c > 1)
	    c = 1;
	//System.out.print(c + "\n");
	c = .5 + c * .5;
	double value = 0;
	double range = 10;
	double offset = 4;
	switch (floorColorChooser.getSelectedIndex()) {
	case FC_FIELD:
	    value = ge.vecX*ge.vecX+ge.vecY*ge.vecY;
	    offset = 10;
	    range = 16;
	    if (!ge.valid)
		return 0xFF000080;
	    break;
	case FC_POTENTIAL:
	    value = ge.height-curfunc.getLevelHeight();
	    offset = 1;
	    range = 2;
	    break;
	case FC_CURL:
	    value = ge.curl;
	    offset = 4;
	    range = 10;
	    break;
	case FC_DIV:
	    value = ge.div;
	    offset = divOffset;
	    range = divRange;
	    break;
	case FC_NONE:
	    if (!ge.valid)
		return 0xFF000080;
	    break;
	}
	value *= floorBrightMult;
	double redness =
	    (value < 0) ? (java.lang.Math.log(-value)+offset)/range : 0;
	double grnness =
	    (value > 0) ? (java.lang.Math.log( value)+offset)/range : 0;
	if (redness > 1)
	    redness = 1;
	if (grnness > 1)
	    grnness = 1;
	if (grnness < 0)
	    grnness = 0;
	if (redness < 0)
	    redness = 0;
	/*if (redness > 0)
	  System.out.print(redness + "\n");*/
	double grayness = (1-(redness+grnness))*c;
	double gray = .6;
	int r = (int) ((c*redness+gray*grayness)*255);
	int g = (int) ((c*grnness+gray*grayness)*255);
	int b = (int) ((gray*grayness)*255);
	return (255<<24) | (r<<16) | (g<<8) | b;
    }

    
    void reinit() {
	handleResize();
	resetParticles();
	functionChanged = backgroundChanged = true;
    }

    void centerString(Graphics g, String s, int y) {
	FontMetrics fm = g.getFontMetrics();
        g.drawString(s, (winSize.width-fm.stringWidth(s))/2, y);
    }

    int shadowBufferTop[], shadowBufferBottom[],
	shadowBufferTop2[], shadowBufferBottom2[];

    final double floorBrightMult = 2;

    void drawBackground() {
	if (isFlat) {
	    int x, y;
	    for (y = 0; y < gridsize; y++)
		for (x = 0; x < gridsize; x++) {
		    GridElement ge = grid[x][y];
		    int nx  = x*winSize.width/gridsize;
		    int ny  = winSize.height-(y+1)*winSize.height/gridsize;
		    int nx1 = (x+1)*winSize.width/gridsize;
		    int ny1 = winSize.height-y*winSize.height/gridsize;
		    int col = computeColor(ge, 0);
		    fillRectangle(nx, ny, nx1, ny1, col);
		    ge.visible = true;
		}
	    drawFloor();
	    functionChanged = backgroundChanged = false;
	    if (imageSource != null)
		imageSource.newPixels();
	    return;
	}

	scaleworld();
	int x, y;

	int xdir, xstart, xend;
	int ydir, ystart, yend;
	int sc = gridsize;
	// figure out what order to render the grid elements so that
	// the ones in back are rendered first.
	if (viewAngleCos < 0) {
	    ystart = sc;
	    yend = 0;
	    ydir = -1;
	} else {
	    ystart = 0;
	    yend = sc;
	    ydir = 1;
	}
	if (viewAngleSin < 0) {
	    xstart = 0;
	    xend = sc;
	    xdir = 1;
	} else {
	    xstart = sc;
	    xend = 0;
	    xdir = -1;
	}
	boolean xFirst = (-viewAngleSin * xdir > viewAngleCos * ydir);

	shadowBufferBottom = new int[winSize.width];
	shadowBufferTop = new int[winSize.width];
	shadowBufferBottom2 = new int[winSize.width];
	shadowBufferTop2 = new int[winSize.width];
	for (x = 0; x != winSize.width; x++) {
	    shadowBufferBottom[x] = shadowBufferBottom2[x] = 0;
	    shadowBufferTop[x] = shadowBufferTop2[x] = winSize.height-1;
	}
	for (x = 0; x != winSize.width*winSize.height; x++)
	    pixels[x] = 0xFF000000;

	int goffx = (xdir == 1) ? 0 : -1;
	int goffy = (ydir == 1) ? 0 : -1;

	//System.out.print("drawing 1\n");
	for (x = xstart; x != xend; x += xdir) {
	    for (y = ystart; y != yend; y += ydir) {
		if (!xFirst)
		    x = xstart;
		for (; x != xend; x += xdir) {
		    double nx  = x*(2.0/gridsize)-1;
		    double ny  = y*(2.0/gridsize)-1;
		    double nx1 = (x+xdir)*(2.0/gridsize)-1;
		    double ny1 = (y+ydir)*(2.0/gridsize)-1;
		    map3d(nx,  ny,  grid[x]  [y].height, xpoints, ypoints, 0);
		    map3d(nx1, ny,  grid[x+xdir][y].height, xpoints, ypoints, 1);
		    map3d(nx,  ny1, grid[x][y+ydir].height, xpoints, ypoints, 2);
		    map3d(nx1, ny1, grid[x+xdir][y+ydir].height, xpoints, ypoints, 3);
		    GridElement ge = grid[x+goffx][y+goffy];
		    int col = computeColor(ge, ge.normdot);
		    // if (((x&1)^(y&1)) == 0) col ^= 0xff;
		    fillTriangle(xpoints[0], ypoints[0],
				 xpoints[1], ypoints[1],
				 xpoints[3], ypoints[3], col);
		    fillTriangle(xpoints[0], ypoints[0],
				 xpoints[2], ypoints[2],
				 xpoints[3], ypoints[3], col);

		    int cx = (xpoints[0]+xpoints[3])/2;
		    int cy = (ypoints[0]+ypoints[3])/2;
		    boolean vis = false;
		    if (cx >= 0 && cx < winSize.width &&
			cy <= shadowBufferTop[cx] && cy >= 0)
			vis = true;
		    ge.visible = vis;

		    if (xFirst)
			break;
		}
		if (!xFirst) {
		    int i;
		    for (i = 0; i != winSize.width; i++) {
			shadowBufferTop[i] = shadowBufferTop2[i];
			shadowBufferBottom[i] = shadowBufferBottom2[i];
		    }
		}
	    }
	    if (!xFirst)
		break;
	    int i;
	    for (i = 0; i != winSize.width; i++) {
		shadowBufferTop[i] = shadowBufferTop2[i];
		shadowBufferBottom[i] = shadowBufferBottom2[i];
	    }
	}

	//System.out.print("drawing 2\n");
	drawFloor();
	//System.out.print("drawing 3\n");

	functionChanged = backgroundChanged = false;
	if (imageSource != null)
	    imageSource.newPixels();
    }

    void drawFloor() {
	int x, y;
	switch (floorLineChooser.getSelectedIndex()) {
	case FL_NONE:
	    break;
	case FL_GRID:
	    for (x = 0; x != gridsize; x++)
		for (y = 0; y != gridsize; y += 10) {
		    double nx  = x*(2.0/gridsize)-1;
		    double nx1 = (x+1)*(2.0/gridsize)-1;
		    double ny  = y*(2.0/gridsize)-1;
		    if (grid[x][y].visible) {
			map3d(nx,  ny, grid[x]  [y].height,
			      xpoints, ypoints, 0);
			map3d(nx1, ny, grid[x+1][y].height,
			      xpoints, ypoints, 1);
			drawLine(xpoints[0], ypoints[0],
				 xpoints[1], ypoints[1]);
		    }
		    if (grid[y][x].visible) {
			map3d(ny, nx,  grid[y][x].height,
			      xpoints, ypoints, 0);
			map3d(ny, nx1, grid[y][x+1].height,
			      xpoints, ypoints, 1);
			drawLine(xpoints[0], ypoints[0],
				 xpoints[1], ypoints[1]);
		    }
		}
	    break;
	case FL_EQUIP:
	    if (!curfunc.nonGradient())
		renderEquips(); 
	    break;
	case FL_LINES:
	   genLines();
	   break;
	}
    }

    void fillTriangle(int x1, int y1, int x2, int y2, int x3, int y3,
		      int col) {
	if (x1 > x2) {
	    if (x2 > x3) {
		// x1 > x2 > x3
		int ay = interp(x1, y1, x3, y3, x2);
		fillTriangle1(x3, y3, x2, y2, ay, col);
		fillTriangle1(x1, y1, x2, y2, ay, col);
	    } else if (x1 > x3) {
		// x1 > x3 > x2
		int ay = interp(x1, y1, x2, y2, x3);
		fillTriangle1(x2, y2, x3, y3, ay, col);
		fillTriangle1(x1, y1, x3, y3, ay, col);
	    } else {
		// x3 > x1 > x2
		int ay = interp(x3, y3, x2, y2, x1);
		fillTriangle1(x2, y2, x1, y1, ay, col);
		fillTriangle1(x3, y3, x1, y1, ay, col);
	    }
	} else {
	    if (x1 > x3) {
		// x2 > x1 > x3
		int ay = interp(x2, y2, x3, y3, x1);
		fillTriangle1(x3, y3, x1, y1, ay, col);
		fillTriangle1(x2, y2, x1, y1, ay, col);
	    } else if (x2 > x3) {
		// x2 > x3 > x1
		int ay = interp(x2, y2, x1, y1, x3);
		fillTriangle1(x1, y1, x3, y3, ay, col);
		fillTriangle1(x2, y2, x3, y3, ay, col);
	    } else {
		// x3 > x2 > x1
		int ay = interp(x3, y3, x1, y1, x2);
		fillTriangle1(x1, y1, x2, y2, ay, col);
		fillTriangle1(x3, y3, x2, y2, ay, col);
	    }
	}
    }

    int interp(int x1, int y1, int x2, int y2, int x) {
	if (x1 == x2)
	    return y1;
	if (x < x1 && x < x2 || x > x1 && x > x2)
	    System.out.print("interp out of bounds\n");
	return (int) (y1+((double) x-x1)*(y2-y1)/(x2-x1));
    }

    void fillTriangle1(int x1, int y1, int x2, int y2, int y3, int col) {
	// x2 == x3
	int dir = (x1 > x2) ? -1 : 1;
	int x = x1;
	if (x < 0) {
	    x = 0;
	    if (x2 < 0)
		return;
	}
	if (x >= winSize.width) {
	    x = winSize.width-1;
	    if (x2 >= winSize.width)
		return;
	}
	if (y2 > y3) {
	    int q = y2;
	    y2 = y3; y3 = q;
	}
	// y2 < y3
	while (x != x2+dir) {
	    // XXX this could be speeded up
	    int ya = interp(x1, y1, x2, y2, x);
	    int yb = interp(x1, y1, x2, y3, x);
	    if (ya < 0)
		ya = 0;
	    if (yb >= winSize.height)
		yb = winSize.height-1;

	    if (shadowBufferTop2[x] > ya)
		shadowBufferTop2[x] = ya;
	    if (shadowBufferBottom2[x] < yb)
		shadowBufferBottom2[x] = yb;

	    int sb1 = shadowBufferTop[x];
	    int sb2 = shadowBufferBottom[x];
	    if (!(ya >= sb1 && yb <= sb2)) {
		for (; ya <= yb; ya++) {
		    if (ya < sb1 || ya > sb2)
			pixels[x+ya*winSize.width] = col;
		}
	    }
	    x += dir;
	    if (x < 0 || x >= winSize.width)
		return;
	}
    }

    void fillRectangle(int x1, int y1, int x2, int y2, int col) {
	int x, y;
	for (y = y1; y < y2; y++)
	    for (x = x1; x < x2; x++)
		pixels[x+y*winSize.width] = col;
    }

    void drawLine(int x1, int y1, int x2, int y2) {
	if (x1 == x2 && y1 == y2)
	    return;
	if (abs(y2-y1) > abs(x2-x1)) {
	    // y difference is greater, so we step along y's
	    // from min to max y and calculate x for each step
	    int sgn = sign(y2-y1);
	    int x, y;
	    for (y = y1; y != y2+sgn; y += sgn) {
		x = x1+(x2-x1)*(y-y1)/(y2-y1);
		if (x >= 0 && y >= 0 &&
		    x < winSize.width && y < winSize.height)
		    pixels[x+y*winSize.width] = 0xFFC0C0C0;
	    }
	} else {
	    // x difference is greater, so we step along x's
	    // from min to max x and calculate y for each step
	    int sgn = sign(x2-x1);
	    int x, y;
	    for (x = x1; x != x2+sgn; x += sgn) {
		y = y1+(y2-y1)*(x-x1)/(x2-x1);
		if (x >= 0 && y >= 0 &&
		    x < winSize.width && y < winSize.height)
		    pixels[x+y*winSize.width] = 0xFFC0C0C0;
	    }
	}
    }

    int abs(int x) { return x < 0 ? -x : x; }
    int sign(int x) { return (x < 0) ? -1 : (x == 0) ? 0 : 1; }
    int min(int a, int b) { return (a < b) ? a : b; }
    int max(int a, int b) { return (a > b) ? a : b; }
    double min(double a, double b) { return (a < b) ? a : b; }
    double max(double a, double b) { return (a > b) ? a : b; }

    // render equipotentials
    void renderEquips() {
	int x, y;
	for (x = 0; x != gridsize; x++)
	    for (y = 0; y != gridsize; y++) {
		if (!grid[x][y].visible)
		    continue;
		// try all possible edge combinations
		tryEdge(x, y,  x+1, y,  x, y+1,  x+1, y+1);
		tryEdge(x, y,  x+1, y,  x, y,    x, y+1);
		tryEdge(x, y,  x+1, y,  x+1, y,  x+1, y+1);
		tryEdge(x, y,  x, y+1,  x+1, y,  x+1, y+1);
		tryEdge(x, y,  x, y+1,  x, y+1,  x+1, y+1);
		tryEdge(x+1, y, x+1, y+1, x, y+1, x+1, y+1);
	    }
    }

    class FloatPair { public double x, y; }

    // interpolate between two points
    void interpPoint(GridElement ep1, GridElement ep2,
		     int x1, int y1, int x2, int y2, double pval,
		     FloatPair pos) {
	double interp2 = (pval-ep1.height)/(ep2.height-ep1.height);
	double interp1 = 1-interp2;
	pos.x = (x1*interp1 + x2*interp2) * 2./gridsize - 1;
	pos.y = (y1*interp1 + y2*interp2) * 2./gridsize - 1;
    }

    // check to see if pval is between the potential at ep1 and ep2
    boolean spanning(GridElement ep1, GridElement ep2, double pval) {
	if (ep1.height == ep2.height)
	    return false;
	return !((ep1.height < pval && ep2.height < pval) ||
		 (ep1.height > pval && ep2.height > pval));
    }

    // try to draw any equipotentials between edge (x1,y1)-(x2,y2)
    // and edge (x3,y3)-(x4,y4).
    void tryEdge(int x1, int y1, int x2, int y2,
		 int x3, int y3, int x4, int y4) {
	int i;
	double emult = 5;
	double mult = 1/(40 * emult * .1);
	GridElement ep1 = grid[x1][y1];
	GridElement ep2 = grid[x2][y2];
	GridElement ep3 = grid[x3][y3];
	GridElement ep4 = grid[x4][y4];
	double pmin = min(min(ep1.height, ep2.height), min(ep3.height, ep4.height));
	double pmax = max(max(ep1.height, ep2.height), max(ep3.height, ep4.height));
	if (pmin < -5) // was 10
	    pmin = -5;
	if (pmax > 5)
	    pmax = 5;
	int imin = (int) (pmin/mult);
	int imax = (int) (pmax/mult);
	for (i = imin; i <= imax; i++) {
	    double pval = i*mult;
	    if (!(spanning(ep1, ep2, pval) && spanning(ep3, ep4, pval)))
		continue;
	    FloatPair pa = new FloatPair();
	    FloatPair pb = new FloatPair();
	    interpPoint(ep1, ep2, x1, y1, x2, y2, pval, pa);
	    interpPoint(ep3, ep4, x3, y3, x4, y4, pval, pb);
	    map3d(pa.x, pa.y, pval, xpoints, ypoints, 0);
	    map3d(pb.x, pb.y, pval, xpoints, ypoints, 1);
	    drawLine(xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
	}
    }

    void drawLineBackground(Graphics g) {
	int x, y;
	for (x = 0; x != gridsize; x++)
	    for (y = 0; y != gridsize; y++)
		grid[x][y].visible = true;
	if (isFlat)
	    return;
	for (y = gridsize-1; y >= 0; y--) {
	    for (x = 0; x < gridsize; x += 5) {
		double ny  = y*(2.0/gridsize)-1;
		double nx1 = (x+1)*(2.0/gridsize)-1;
		double ny1 = (y+1)*(2.0/gridsize)-1;
		map3d(nx1, ny,  grid[x][y].height, xpoints, ypoints, 1);
		map3d(nx1, ny1, grid[x][y+1].height, xpoints, ypoints, 2);
		ypoints[1] = bound_y(ypoints[1]);
		ypoints[2] = bound_y(ypoints[2]);
		g.drawLine(xpoints[1], ypoints[1], xpoints[2], ypoints[2]);
	    }
	}
	for (y = 0; y < gridsize; y += 5) {
	    for (x = gridsize-1; x >= 0; x--) {
		double nx  = x*(2.0/gridsize)-1;
		double nx1 = (x+1)*(2.0/gridsize)-1;
		double ny1 = (y+1)*(2.0/gridsize)-1;
		map3d(nx,  ny1, grid[x]  [y].height, xpoints, ypoints, 3);
		map3d(nx1, ny1, grid[x+1][y].height, xpoints, ypoints, 2);
		ypoints[3] = bound_y(ypoints[3]);
		ypoints[2] = bound_y(ypoints[2]);
		g.drawLine(xpoints[3], ypoints[3], xpoints[2], ypoints[2]);
	    }
	}
    }

    int bound_y(int y) {
	if (y < -100)
	    y = -100;
	if (y > winSize.height+100)
	    y = winSize.height+100;
	return y;
    }

    public void paint(Graphics g) {
	cv.repaint();
    }

    static final double root2 = 1.4142135623730950488016887242096981;
    double scalex, scaley;

    void map3d(double x, double y, double z, int xpoints[], int ypoints[],
	       int pt) {
	map3d(x, y, z, xpoints, ypoints, pt, viewMain);
    }

    void map3d(double x, double y, double z, int xpoints[], int ypoints[],
	       int pt, Rectangle view) {
	if (isFlat) {
	    xpoints[pt] = view.x+(int) ((x+1)*view.width/2);
	    ypoints[pt] = view.y+(int) ((1-y)*view.height/2);
	    return;
	}
	if (z < -1000)
	    z = -1000;
	if (z > 1000)
	    z = 1000;
	/*if (!(z > -2000 && z < 2000))
	  System.out.print(z + " in map3d\n");*/
	double realx = x*viewAngleCos + y*viewAngleSin; // range: [-10,10]
	double realy = z-viewHeight;
	double realz = y*viewAngleCos - x*viewAngleSin + viewDistance;
	scalex = viewZoom * (view.width/4) * viewDistance;
	scaley = scalex;
	int yoff = (int)
	    (scaley*(viewHeight-curfunc.getLevelHeight())/viewDistance);
	xpoints[pt] = view.x+view.width/2 + (int) (scalex*realx/realz);
	ypoints[pt] = view.y+view.height/2 - yoff - (int) (scaley*realy/realz);
    }

    void scaleworld() {
	// scalex = viewZoom * (winSize.width/4) * viewDistance;
	// scaley = scalex;
    }

    double getHeight(double x, double y) {
	x = (x+1)*(gridsize/2);
	y = (y+1)*(gridsize/2);
	int ix = (int) x;
	int iy = (int) y;
	if (ix >= gridsize || iy >= gridsize)
	    return grid[ix][iy].height;
	double fracx = x-ix;
	double fracy = y-iy;
	return grid[ix][iy].height * (1-fracx) * (1-fracy) +
	    grid[ix+1][iy].height * fracx * (1-fracy) +
	    grid[ix][iy+1].height * (1-fracx) * fracy +
	    grid[ix+1][iy+1].height * fracx * fracy;
    }

    void sayCalculating(Graphics realg) {
	realg.setColor(cv.getBackground());
	FontMetrics fm = realg.getFontMetrics();
	String s = "Calculating...";
	realg.fillRect(0, winSize.height-30,
		       20+fm.stringWidth(s), 30);
	realg.setColor(Color.white);
	realg.drawString(s, 10, winSize.height-10);
    }

    long lastTime;
    double timeStep, partMult;
    boolean slowDragView = true;
    
    public void updateVecDemo(Graphics realg) {
	Graphics g = dbimage.getGraphics();
	if (winSize == null || winSize.width == 0)
	    return;
	if (xpoints == null)
	    return;
	checkFlatState();
	barFieldStrength = fieldStrength =
	    java.lang.Math.exp((strengthBar.getValue()-50)/10.);
	if (functionChanged || backgroundChanged) {
	    if (functionChanged) { // && !(draggingView && isFlat)) {
		sayCalculating(realg);
		generateFunction();
	    }
	    if (!slowDragView || !draggingView) {
		long tm1 = System.currentTimeMillis();
		sayCalculating(realg);
		drawBackground();
		long tm2 = System.currentTimeMillis();
		slowDragView = (tm2-tm1 > 40);
	    }
	}

	scaleworld();
	if ((draggingView && slowDragView) || functionChanged) {
	    g.setColor(isFlat ? fieldColors[0] : cv.getBackground());
	    g.fillRect(0, 0, winSize.width, winSize.height);
	    g.setColor(cv.getForeground());
	    drawLineBackground(g);
	} else
	    g.drawImage(backimage, 0, 0, this);

	boolean allquiet = true;

	curfunc.setupFrame();
	fieldStrength = barFieldStrength;
	partMult = fieldStrength * reverse * timeStep;
	int disp = dispChooser.getSelectedIndex();
	timeStep = 1;
	if (!stoppedCheck.getState()) {
	    if (lastTime > 0)
		timeStep = (System.currentTimeMillis()-lastTime)*.03;
	    if (timeStep > 3)
		timeStep = 3;
	    lastTime = System.currentTimeMillis();
	    if (disp != DISP_VECTORS && disp != DISP_NONE) {
		moveParticles();
		allquiet = false;
	    }
	    currentStep += reverse;
	    if (currentStep < 0)
		currentStep += 800;
	} else
	    lastTime = 0;

	if (disp == DISP_VECTORS)
	    drawVectors(g);
	else if (disp != DISP_NONE)
	    drawParticles(g);

	g.setColor(Color.gray);

	if (!isFlat)
	    drawAxes(g);
	curfunc.finishFrame();

	int mode = modeChooser.getSelectedIndex();
	if (mode == MODE_LINE_INT)
	    lineIntegral(g, true);
	else if (mode == MODE_SURF_INT)
	    lineIntegral(g, false);

	if (parseError)
	    centerString(g, "Can't parse expression", winSize.height-20);

	//g.drawString("FR: " + framerate, 0, 10);
	realg.drawImage(dbimage, 0, 0, this);
	long t = System.currentTimeMillis();
	frames++;
	if (firsttime == 0)
	    firsttime = t;
	else if (t-firsttime > 1000) {
	    framerate = frames;
	    firsttime = t;
	    frames = 0;
	}
	if (!stoppedCheck.getState() && !allquiet)
	    cv.repaint(pause);
    }

    void drawAxes(Graphics g) {
	g.setColor(Color.white);
	map3d(0, 0, 0, xpoints, ypoints, 0, viewAxes);
	map3d(1, 0, 0, xpoints, ypoints, 1, viewAxes);
	drawArrow(g, "x", xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
	map3d(0, 1, 0, xpoints, ypoints, 1, viewAxes);
	drawArrow(g, "y", xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
	map3d(0, 0, 1, xpoints, ypoints, 1, viewAxes);
	drawArrow(g, "z", xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
    }

    void drawVectors(Graphics g) {
	int x, y, z;
	DrawData dd = new DrawData();
	dd.mult = barFieldStrength*40;
	dd.g = g;
	dd.field = new double[3];
	dd.vv = new double[3];
	vectorSpacing = vecDensityBar.getValue();
	double vec[] = new double[3];

	vecCount = 0;

	for (x = 0; x != vectorSpacing; x++) {
	    vec[0] = x*(2.0/(vectorSpacing-1))-1;
	    for (y = 0; y != vectorSpacing; y++) {
		vec[1] = y*(2.0/(vectorSpacing-1))-1;
		drawVector(dd, vec);
	    }
	}
    }

    void lineIntegral(Graphics g, boolean line) {
	if (integralX == -1)
	    return;
	if (dragStartX == integralX || dragStartY == integralY)
	    return;
	int x1 = min(dragStartX, integralX);
	int y1 = min(dragStartY, integralY);
	int x2 = max(dragStartX, integralX);
	int y2 = max(dragStartY, integralY);
	int step = 15;
	int x;
	double pos[] = rk_k2;
	if (!line) {
	    g.setColor(Color.white);
	    g.drawRect(x1, y1, x2-x1+1, y2-y1+1);
	}
	double y1p = 1 - 2.*y1/winSize.height;
	double y2p = 1 - 2.*y2/winSize.height;
	for (x = x1; x <= x2; x += step) {
	    int step1 = x2-x;
	    if (step1 > step)
		step1 = step;
	    pos[0] = 2.*x/winSize.width - 1;
	    pos[1] = y1p;
	    lineIntegralStep(g, x, y1, pos, step1, 0, line);
	    pos[1] = y2p;
	    lineIntegralStep(g, x+step1, y2, pos, -step1, 0, line);
	}
	int y;
	double x1p = 2.*x1/winSize.width - 1;
	double x2p = 2.*x2/winSize.width - 1;
	for (y = y2; y >= y1; y -= step) {
	    int step1 = y-y1;
	    if (step1 > step)
		step1 = step;
	    pos[0] = x1p;
	    pos[1] = 1 - 2.*y/winSize.height;
	    lineIntegralStep(g, x1, y, pos, 0, step1, line);
	    pos[0] = x2p;
	    lineIntegralStep(g, x2, y-step1, pos, 0, -step1, line);
	}
	boundCheck = false;
	pos[1] = y1p;
	double iv1 = numIntegrate(pos, 0, x1p, x2p, line);
	pos[1] = y2p;
	double iv2 = numIntegrate(pos, 0, x1p, x2p, line);
	pos[0] = x1p;
	double iv3 = numIntegrate(pos, 1, y1p, y2p, line);
	pos[0] = x2p;
	double iv4 = numIntegrate(pos, 1, y1p, y2p, line);
	double ivtot = -iv1+iv2+iv3-iv4;
	NumberFormat nf = NumberFormat.getInstance();
	nf.setMaximumFractionDigits(3);
	if (ivtot < 1e-7 && ivtot > -1e-7)
	    ivtot = 0;
	ivtot *= reverse;
	String s = ((!line) ? "Flux = " : "Circulation = ");
	s += nf.format(ivtot*1e5);
	g.setColor(cv.getBackground());
	FontMetrics fm = g.getFontMetrics();
	g.fillRect(0, winSize.height-30, 20+fm.stringWidth(s), 30);
	g.setColor(Color.white);
	g.drawString(s, 10, winSize.height-10);
    }

    double numIntegrate(double pos[], int n1,
			double x1, double x2, boolean line) {
	int steps = 8;
	double lastres = 0;
	double res = 0;
	int n2 = (line) ? n1 : 1-n1;
	while (true) {
	    int i;
	    double h = (x2-x1)/steps;
	    res = 0;
	    for (i = 0; i <= steps; i++) {
		pos[n1] = x1+i*h;
		double field[] = rk_k1;
		curfunc.getField(field, pos);
		int ss = (i == 0 || i == steps) ? 1 :
		    ((i & 1) == 1) ? 4 : 2;
		res += field[n2]*h*ss;
	    }
	    res /= 3;
	    if (java.lang.Math.abs(lastres-res) < 1e-7)
		break;
	    lastres = res;
	    steps *= 2;
	    if (steps == 65536)
		break;
	}
	if (!line && n1 == 0)
	    res = -res;
	return res;
    }

    void lineIntegralStep(Graphics g, int x, int y,
			  double pos[], int dx, int dy, boolean line) {
	double field[] = rk_k1;
	curfunc.getField(field, pos);
	double f = (line) ? field[0]*dx+field[1]*dy :
	    field[0]*dy - field[1]*dx;
	f *= reverse;
	double dn = java.lang.Math.abs(f*100);
	if (dn > 1)
	    dn = 1;
	int col1 = (int) (dn*128+127);
	int col2 = (int) (127-dn*127);
	if (!line) {
	    x += dx/2;
	    y -= dy/2;
	}
	if (f == 0) {
	    g.setColor(new Color(col2, col2, col2));
	    g.drawLine(x, y, x+dx, y-dy);
	} else if (f > 0) {
	    g.setColor(new Color(col1, col2, col2));
	    if (line)
		drawArrow(g, null, x, y, x+dx, y-dy);
	    else
		drawArrow(g, null, x, y, x+dy, y+dx);
	} else {
	    g.setColor(new Color(col2, col1, col2));
	    if (line)
		drawArrow(g, null, x+dx, y-dy, x, y);
	    else
		drawArrow(g, null, x, y, x-dy, y-dx);
	}
    }

    void genLines() {
	int i;
	
	int lineGridSize = 8; // lineDensityBar.getValue();
	if (lineGridSize < 3)
	    lineGridSize = 3;
	if (lineGridSize > 8)
	    lineGridSize = 8;
	lineGridSize *= 2;
	int ct = 30*lineGridSize*lineGridSize;
	double brightmult = 80*barFieldStrength;
	fieldStrength = 10;

	boolean lineGrid[][] =
	    new boolean[lineGridSize][lineGridSize];
	double lineGridMult = lineGridSize/2.;

	double origp[] = new double[3];
	double field[] = new double[3];
	Particle p = new Particle();
	p.lifetime = -1;
	p.stepsize = 10;
	int dir = -1;
	int segs = 0;
	double lastdist = 0;
	for (i = 0; i != ct; i++) {
	    if (p.lifetime < 0) {
		p.lifetime = 1;
		p.stepsize = 10;
		segs = 0;
		lastdist = 0;
		if (dir == 1) {
		    int j;
		    for (j = 0; j != 3; j++)
			p.pos[j] = origp[j];
		    dir = -1;
		    continue;
		}
		dir = 1;
		int px = 0, py = 0;
		while (true) {
		    if (!lineGrid[px][py])
			break;
		    if (++px < lineGridSize)
			continue;
		    px = 0;
		    if (++py < lineGridSize)
			continue;
		    break;
		}
		if (py == lineGridSize)
		    break;
		lineGrid[px][py] = true;
		double offs = .5/lineGridMult;
		origp[0] = p.pos[0] = px/lineGridMult-1+offs;
		origp[1] = p.pos[1] = py/lineGridMult-1+offs;
	    }

	    double p1x = p.pos[0];
	    double p1y = p.pos[1];
	    double p1z = getHeight(p1x, p1y);
	    GridElement ge = grid[(int) ((p1x+1)*gridsize/2)]
		[(int) ((p1y+1)*gridsize/2)];
	    if (!ge.visible) {
		p.lifetime = -1;
		continue;
	    }
	    
	    double x[] = p.pos;
	    lineSegment(p, dir);
	    //System.out.print(x[0] + " " + x[1] + " " + x[2] + "\n");
	    if (p.lifetime < 0)
		continue;
	    int gx = (int) ((x[0]+1)*lineGridMult);
	    int gy = (int) ((x[1]+1)*lineGridMult);
	    if (!lineGrid[gx][gy])
		segs--;
	    lineGrid[gx][gy] = true;

	    ge = grid[(int) ((p.pos[0]+1)*gridsize/2)]
		[(int) ((p.pos[1]+1)*gridsize/2)];
	    if (!ge.visible) {
		p.lifetime = -1;
		continue;
	    }
	    
	    double dn = brightmult*p.phi;
	    if (dn > 2)
		dn = 2;
	    // fv.col = (int) (dn*255);
	    map3d(p1x, p1y, p1z, xpoints, ypoints, 0);
	    map3d(p.pos[0], p.pos[1], getHeight(p.pos[0], p.pos[1]),
		  xpoints, ypoints, 1);
	    drawLine(xpoints[0], ypoints[0], xpoints[1], ypoints[1]);

	    double d2 = dist2(origp, x);
	    if (d2 > lastdist)
		lastdist = d2;
	    else
		segs++;
	    if (segs > 10 || d2 < .001)
		p.lifetime = -1;
	}
	//System.out.print("vc " + vecCount + " " + ct + "\n");
    }

    // draw the appropriate field vector at xx,yy,zz
    void drawVector(DrawData dd, double vec[]) {
	double field[] = dd.field;

	// calculate field vector
	curfunc.getField(field, vec);
	double dn = java.lang.Math.sqrt(field[0]*field[0]+field[1]*field[1]);
	double dnr = dn*reverse;
	if (dn > 0) {
	    field[0] /= dnr;
	    field[1] /= dnr;
	}
	dn *= dd.mult;
	if (dn > 2)
	    dn = 2;
	int col = (int) (dn*255);
	double sw2 = 1./(vectorSpacing-1);
	map3d(vec[0], vec[1], 0, xpoints, ypoints, 0);
	map3d(vec[0]+sw2*field[0], vec[1]+sw2*field[1], 0,
	      xpoints, ypoints, 1);
	dd.g.setColor(fieldColors[col]);
	drawArrow(dd.g, null,
		  xpoints[0], ypoints[0], xpoints[1], ypoints[1], 2);
    }

    void moveParticles() {
	int bestd = 0;
	int i;
	int pcount = getParticleCount();
	for (i = 0; i != pcount; i++) {
	    Particle pt = particles[i];
	    removeFromDensityGroup(pt);
	    moveParticle(pt);
	    double x[] = pt.pos;
	    if (!(x[0] >= -1 && x[0] < 1 &&
		  x[1] >= -1 && x[1] < 1) ||
		(pt.lifetime -= timeStep) < 0)
		positionParticle(pt);
	    int d = addToDensityGroup(pt);
	    if (d > bestd)
		bestd = d;
	}
	boolean withforce =
	    (dispChooser.getSelectedIndex() == DISP_PART_FORCE);
	int maxd =  (6*getParticleCount()/(densitygridsize*densitygridsize));
	if (!withforce && curfunc.redistribute() && bestd > maxd)
	    redistribute(bestd);
    }

    static int frames = 0;
    static int framerate = 0;
    static long firsttime = 0;

    void drawParticles(Graphics g) {
	g.setColor(Color.white);
	int disp = dispChooser.getSelectedIndex();
	if (disp == DISP_VECTORS) {
	    int i;
	    for (i = 0; i != vecCount; i++) {
		FieldVector fv = vectors[i];
		g.setColor(fieldColors[fv.col]);
		drawArrow(g, null, fv.sx1, fv.sy1, fv.sx2, fv.sy2, 2);
	    }
	    return;
	}
	int pcount = getParticleCount();
	int i;
	wooft += .3;
	if (disp == DISP_CURLERS)
	    pcount = (pcount+4)/5;
	for (i = 0; i < pcount; i++) {
	    Particle p = particles[i];
	    double pos[] = p.pos;
	    GridElement ge = grid[(int) ((pos[0]+1)*gridsize/2)]
		[(int) ((pos[1]+1)*gridsize/2)];
	    map3d(pos[0], pos[1], getHeight(pos[0], pos[1]),
					    xpoints, ypoints, 0);
	    if (xpoints[0] < 0 || xpoints[0] >= winSize.width ||
		ypoints[0] < 0 || ypoints[0] >= winSize.height)
		continue;
	    if (disp == DISP_CURLERS) {
		g.setColor(p.color);
		final double len = .02;
		double ax = java.lang.Math.cos(p.theta)*len;
		double ay = java.lang.Math.sin(p.theta)*len;
		double offx = ax;
		double offy = ay;
		double a1 = curlcalc(p.pos[0]+offx, p.pos[1]+offy, -ay, ax);
		double a2 = curlcalc(p.pos[0]-offy, p.pos[1]+offx, -ax, -ay);
		double a3 = curlcalc(p.pos[0]-offx, p.pos[1]-offy, ay, -ax);
		double a4 = curlcalc(p.pos[0]+offy, p.pos[1]-offx, ax, ay);
		p.theta += (a1+a2+a3+a4)/(4*len*len);
		map3d(p.pos[0]-offx, p.pos[1]-offy, 0, xpoints, ypoints, 0);
		map3d(p.pos[0]+offx, p.pos[1]+offy, 0, xpoints, ypoints, 1);
		map3d(p.pos[0]-offy, p.pos[1]+offx, 0, xpoints, ypoints, 2);
		map3d(p.pos[0]+offy, p.pos[1]-offx, 0, xpoints, ypoints, 3);
		g.drawLine(xpoints[0], ypoints[0], xpoints[1], ypoints[1]);
		g.drawLine(xpoints[2], ypoints[2], xpoints[3], ypoints[3]);
		g.fillOval(xpoints[0]-1, ypoints[0]-1, 3, 3);
	    } else if (ge.visible && ge.valid)
		g.fillRect(xpoints[0], ypoints[0]-1, 2, 2);
	}
    }

	double wooft = 0;

    void drawPlane(Graphics g, double sizex, double sizey, double z) {
	g.setColor(darkYellow);
	map3d(-sizex, -sizey, z, xpoints, ypoints, 0);
	map3d(+sizex, -sizey, z, xpoints, ypoints, 1);
	map3d(+sizex, +sizey, z, xpoints, ypoints, 2);
	map3d(-sizex, +sizey, z, xpoints, ypoints, 3);
	g.fillPolygon(xpoints, ypoints, 4);
    }

    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 = java.lang.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));
	}
    }

    int rediscount;
    void redistribute(int mostd) {
	if (mostd < 5)
	    return;
	rediscount++;
	int maxd = (6*getParticleCount()/
		    (densitygridsize*densitygridsize));
	int i;
	int pn = 0;
	int pcount = getParticleCount();
	for (i = rediscount % 4; i < pcount; i+=4) {
	    Particle p = particles[i];
	    int a = (int)((p.pos[0]+1)*(densitygridsize/2));
	    int b = (int)((p.pos[1]+1)*(densitygridsize/2));
	    if (density[a][b] <= maxd)
		continue;
	    p.lifetime = -1;
	    pn++;
	}
	//System.out.print("redist " + mostd + " " + pn + "\n");
    }

    double curlcalc(double x, double y, double ax, double ay) {
	rk_yn[0] = x;
	rk_yn[1] = y;
	curfunc.getField(rk_k1, rk_yn);
	return partMult*(rk_k1[0]*ax + rk_k1[1]*ay);
    }

    double distance(Particle p) {
	return distance(p.pos[0], p.pos[1]);
    }

    double distance(double y[]) {
	return distance(y[0], y[1]);
    }

    double distance(double x, double y) {
	return java.lang.Math.sqrt(x*x+y*y+.000000001);
    }

    void rotateParticleAdd(double result[], double y[], double mult,
			double cx, double cy) { 
	result[0] += -mult*(y[1]-cy);
	result[1] +=  mult*(y[0]-cx);
    }

    void rotateParticle(double result[], double y[], double mult) {
	result[0] = -mult*y[1];
	result[1] =  mult*y[0];
	result[2] = 0;
    }

    void edit(MouseEvent e) {
	int x = e.getX();
	int y = e.getY();
	editView(x, y);
    }

    void editView(int x, int y) {
	if (modeChooser.getSelectedIndex() == MODE_VIEW_ROTATE) {
	    if (isFlat)
		return;
	    viewAngle = (dragStartX-x)/40. + viewAngleDragStart;
	    while (viewAngle < 0)
		viewAngle += 2*pi;
	    while (viewAngle >= 2*pi)
		viewAngle -= 2*pi;
	    viewAngleCos = java.lang.Math.cos(viewAngle);
	    viewAngleSin = java.lang.Math.sin(viewAngle);
	    viewHeight = -(dragStartY-y)/10. + viewHeightDragStart;
	    if (viewHeight > 9)
		viewHeight = 9;
	    if (viewHeight < -9)
		viewHeight = -9;
	    draggingView = backgroundChanged = true;
	    cv.repaint(pause);
	    return;
	}
	if (modeChooser.getSelectedIndex() == MODE_VIEW_ZOOM) {
	    if (isFlat)
		return;
	    viewZoom = (x-dragStartX)/40. + viewZoomDragStart;
	    if (viewZoom < .1)
		viewZoom = .1;
	    draggingView = backgroundChanged = true;
	    cv.repaint(pause);
	    return;
	}
	if (modeChooser.getSelectedIndex() == MODE_LINE_INT ||
	    modeChooser.getSelectedIndex() == MODE_SURF_INT) {
	    integralX = x;
	    integralY = y;
	    cv.repaint(pause);
	}
    }

    public void componentHidden(ComponentEvent e){}
    public void componentMoved(ComponentEvent e){}
    public void componentShown(ComponentEvent e) {
	cv.repaint(pause);
    }

    public void componentResized(ComponentEvent e) {
	handleResize();
	cv.repaint(pause);
    }
    public void actionPerformed(ActionEvent e) {
	vectors = null;
	if (e.getSource() == resetButton)
	    resetParticles();
	if (e.getSource() == kickButton)
	    kickParticles();
	if (e.getSource() == infoButton) {
	    String s = curfunc.getClass().getName();
	    try {
		s = s.substring(s.lastIndexOf('.')+1);
		applet.getAppletContext().showDocument(
			new URL(applet.getCodeBase(),
				"functions.html" + '#' + s),
			"functionHelp");
	    } catch (Exception ex) {
	    }
	}
	curfunc.actionPerformed();
	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();
    }

    public void scrollbarValueChanged(DecentScrollbar ds) {
	vectors = null;
	System.out.print(ds.getValue() + "\n");
	if (ds == partCountBar)
	    resetDensityGroups();
	if (ds == aux1Bar || ds == aux2Bar || ds == aux3Bar) {
	    functionChanged = true;
	    draggingView = true;
	}
	cv.repaint(pause);
    }

    public void scrollbarFinished(DecentScrollbar ds) {
	draggingView = false;
	cv.repaint(pause);
    }

    public void mouseDragged(MouseEvent e) {
	dragging = true;
	edit(e);
    }
    public void mouseMoved(MouseEvent e) {
    }

    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;
	dragStartX = e.getX();
	dragStartY = e.getY();
	viewAngleDragStart = viewAngle;
	viewHeightDragStart = viewHeight;
	viewZoomDragStart = viewZoom;
	dragging = true;
	edit(e);
    }
    public void mouseReleased(MouseEvent e) {
	if ((e.getModifiers() & MouseEvent.BUTTON1_MASK) == 0)
	    return;
	dragging = draggingView = false;
	cv.repaint(pause);
    }

    void dispChooserChanged() {
	int disp = dispChooser.getSelectedIndex();
	showA = false; // XXX
	if (disp == DISP_PART_FORCE)
	    kickButton.enable();
	else
	    kickButton.disable();
	potentialLabel.hide();
	potentialBar.hide();
	vecDensityLabel.hide();
	vecDensityBar.hide();
	/*lineDensityLabel.hide();
	  lineDensityBar.hide();*/
	partCountLabel.hide();
	partCountBar.hide();
	strengthLabel.show();
	strengthBar.show();
	if (disp == DISP_VECTORS) {
	    vecDensityLabel.show();
	    vecDensityBar.show();
	} else {
	    partCountLabel.show();
	    partCountBar.show();
	}
	validate();
	resetParticles();
    }

    public void itemStateChanged(ItemEvent e) {
	vectors = null;
	cv.repaint(pause);
	reverse = (reverseCheck.getState()) ? -1 : 1;
	if (e.getItemSelectable() == dispChooser) {
	    dispChooserChanged();
	    resetParticles();
	}
	if (e.getItemSelectable() == functionChooser)
	    functionChanged();
	if (e.getItemSelectable() == reverseCheck)
	    functionChanged = true;
	if (e.getItemSelectable() == floorColorChooser ||
	    e.getItemSelectable() == floorLineChooser)
	    backgroundChanged = true;
    }

    void checkFlatState() {
	boolean oldFlat = isFlat;
	int disp = dispChooser.getSelectedIndex();
	isFlat = flatCheck.getState() || curfunc.nonGradient() ||
	    disp == DISP_VECTORS || disp == DISP_CURLERS;
	int mode = modeChooser.getSelectedIndex();
	if (mode == MODE_LINE_INT || mode == MODE_SURF_INT)
	    isFlat = true;
	if (isFlat != oldFlat)
	    backgroundChanged = true;
    }

    void functionChanged() {
	reverse = 1;
	reverseCheck.setState(false);
	parseError = false;
	curfunc = (VecFunction)
	    functionList.elementAt(functionChooser.getSelectedIndex());
	int i;
	for (i = 0; i != 3; i++) {
	    auxBars[i].label.hide();
	    auxBars[i].bar.hide();
	}
	for (i = 0; i != 2; i++)
	    textFields[i].hide();
	if (textFieldLabel != null)
	    textFieldLabel.hide();
	strengthBar.setValue(80);
	//setupDispChooser(!curfunc.nonGradient());
	curfunc.setup();
	validate();
	resetParticles();
	dispChooserChanged();
	functionChanged = true;
	integralX = -1;
    }

    void setupDispChooser(boolean potential) {
	dispChooser.removeAll();
	dispChooser.add("Display: Particles (Vel.)");
	dispChooser.add("Display: Particles (Force)");
	dispChooser.add("Display: Field Vectors");
	dispChooser.add("Display: None");
#ifdef BUILD_V
	dispChooser.add("Display: Curl Detectors");
#endif
    }

    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();
    }

    void cross(double res[], double v1[], double v2[]) {
	res[0] = v1[1]*v2[2] - v1[2]*v2[1];
	res[1] = v1[2]*v2[0] - v1[0]*v2[2];
	res[2] = v1[0]*v2[1] - v1[1]*v2[0];
    }

    double dot(double v1[], double v2[]) {
	return v1[0]*v2[0] + v1[1]*v2[1];
    }

    boolean boundCheck;
    double oldY[];
    double rk_k1[] = new double[6];
    double rk_k2[] = new double[6];
    double rk_k3[] = new double[6];
    double rk_k4[] = new double[6];
    double rk_yn[] = new double[6];

    void rk(int order, double x, double Y[], double stepsize) {
	int i;

	// x is not used...

	if (order == 2) {
	    // velocity-based motion
	    double fmult = stepsize * partMult;
	    for (i = 0; i != order; i++)
		rk_yn[i] = Y[i];
	    curfunc.getField(rk_k1, rk_yn);
	    for (i = 0; i != order; i++)
		rk_yn[i] = (Y[i] + 0.5*fmult*rk_k1[i]);
	    curfunc.getField(rk_k2, rk_yn);
	    for (i = 0; i != order; i++)
		rk_yn[i] = (Y[i] + 0.5*fmult*rk_k2[i]);
	    curfunc.getField(rk_k3, rk_yn);
	    
	    for (i = 0; i != order; i++)
		rk_yn[i] = (Y[i] + fmult*rk_k3[i]);
	    curfunc.getField(rk_k4, rk_yn);
	    for (i = 0; i != order; i++)
		Y[i] = Y[i] + fmult*(rk_k1[i]+2*(rk_k2[i]+rk_k3[i])+rk_k4[i])/6;
	    Y[2] = rk_k4[2];
	} else {
	    // force-based (could share more code with above, but this is
	    // called a lot so we want it to be fast)
	    double fmult = stepsize * partMult;
	    for (i = 0; i != order; i++)
		rk_yn[i] = Y[i];
	    getForceField(rk_k1, rk_yn, stepsize, fmult);
	    for (i = 0; i != order; i++)
		rk_yn[i] = (Y[i] + 0.5*rk_k1[i]);
	    getForceField(rk_k2, rk_yn, stepsize, fmult);
	    for (i = 0; i != order; i++)
		rk_yn[i] = (Y[i] + 0.5*rk_k2[i]);
	    getForceField(rk_k3, rk_yn, stepsize, fmult);
	    
	    for (i = 0; i != order; i++)
		rk_yn[i] = (Y[i] + rk_k3[i]);
	    getForceField(rk_k4, rk_yn, stepsize, fmult);
	    for (i = 0; i != order; i++)
		Y[i] = Y[i] + (rk_k1[i]+2*(rk_k2[i]+rk_k3[i])+rk_k4[i])/6;
	    Y[4] = rk_k4[4];
	}
    }

    void getForceField(double result[], double y[],
		       double stepsize, double fmult) {
	// get the field vector for the current function
	curfunc.getField(result, y);

	// copy height information
	result[4] = result[2];

	// the field data has been written into result[0:1] where it will
	// directly influence the position (y[0:1]), but we want it to
	// influence the velocity (y[2:3]), so we move it.  In the
	// process, we multiply by fmult (to get the reverse button
	// and field strength slider to work).  It would be nice if we
	// could just say getField(result+2, y), but that's java for you.
	int i;
	for (i = 0; i != 2; i++)
	    result[i+2] = fmult*result[i]*.1;

	// here we fill in result[0:1] so that the particle position will
	// change according to the velocity.
	for (i = 0; i != 2; i++)
	    result[i] = stepsize*timeStep*rk_yn[i+2];
    }

    double rk_Y[] = new double[6];
    double rk_Yhalf[] = new double[6];
    double rk_oldY[] = new double[6];
    double ls_fieldavg[] = new double[3];

    void moveParticle(Particle p)
    {
	int disp = dispChooser.getSelectedIndex();
	int numIter=0;
	double maxh=1;
	double error=0.0, E = .001, localError;
	boolean useForce = (disp == DISP_PART_FORCE);
	int order = useForce ? 4 : 2;
	double Y[] = rk_Y;
	double Yhalf[] = rk_Yhalf;
	oldY = rk_oldY;
	int i;

	for (i = 0; i != 2; i++)
	    oldY[i] = Y[i] = Yhalf[i] = p.pos[i];
	if (useForce)
	    for (i = 0; i != 2; i++)
		Y[i+2] = Yhalf[i+2] = p.vel[i];
	double t = 0;

	if (!curfunc.useRungeKutta()) {
	    boundCheck = false;
	    curfunc.getField(Yhalf, Y);
	    if (boundCheck && (!useForce || curfunc.checkBoundsWithForce())) {
		p.pos[0] = -100;
		return;
	    }
	    double fmult = partMult;
	    if (useForce) {
		fmult *= .1;
		for (i = 0; i != 2; i++) {
		    p.vel[i] += fmult*Yhalf[i];
		    p.pos[i] += p.vel[i]*timeStep;
		}
	    } else {
		for (i = 0; i != 2; i++)
		    p.pos[i] += fmult*Yhalf[i];
	    }
	    p.pos[2] = Yhalf[2];
	    for (i = 0; i != 2; i++)
		Y[i] = p.pos[i];
	    if (curfunc.checkBounds(Y, oldY))
		p.pos[0] = -100;
	    return;
	}

	boolean adapt = curfunc.useAdaptiveRungeKutta();
	double h = (adapt) ? p.stepsize : 1;

	int steps = 0;
	double minh = .0001;
	while (t >= 0 && t < 1) {
	    if (t+h > 1)
		h = 1-t;

	    boundCheck = false;

	    // estimate one full step
	    rk(order, 0, Y, h);
	    
	    // bail out after one iteration for some slow fields
	    if (!adapt)
		break;

	    // estimate two half steps
	    rk(order, 0, Yhalf, h*0.5);
	    rk(order, 0, Yhalf, h*0.5);

	    if (boundCheck && (!useForce || curfunc.checkBoundsWithForce())) {
		p.pos[0] = -100;
		return;
	    }

	    // estimate the local error
	    localError = java.lang.Math.abs(Y[0] - Yhalf[0]) +
		java.lang.Math.abs(Y[1] - Yhalf[1]);
	    
	    if (localError > E && h > minh) {
		//System.out.print(E + " " + t + " " + localError + " " + h + "\n");
		h *= 0.75; // decrease the step size
		if (h < minh)
		    h = minh;
		for (i = 0; i != order; i++)
		    Y[i] = Yhalf[i] = oldY[i]; 
		continue;
	    } else if (localError < (E * 0.5)) {
		h *= 1.25; // increase the step size
		if (h > maxh)
		    h = maxh;
	    }
	    
	    for (i = 0; i != order; i++)
		oldY[i] = Yhalf[i] = Y[i]; 

	    t += h;
	    steps++;
	}
	
	if (boundCheck && (!useForce || curfunc.checkBoundsWithForce())) {
	    p.pos[0] = -100;
	    return;
	}
	
	p.stepsize = h;
	for (i = 0; i != 3; i++)
	    p.pos[i] = Y[i];
	if (useForce) {
	    for (i = 0; i != 2; i++)
		p.vel[i] = Y[i+2];
	    p.pos[2] = Y[4];
	}
    }

    double dist2(double a[], double b[]) {
	double c0 = a[0]-b[0];
	double c1 = a[1]-b[1];
	return c0*c0+c1*c1;
    }

    void lineSegment(Particle p, int dir)
    {
	int numIter=0;
	double maxh=20;
	double error=0.0, E = .001, localError;
	int order = 2;
	double Y[] = rk_Y;
	double Yhalf[] = rk_Yhalf;
	oldY = rk_oldY;
	int i;

	for (i = 0; i != 2; i++)
	    oldY[i] = Y[i] = Yhalf[i] = p.pos[i];
	double h = p.stepsize;
	ls_fieldavg[0] = ls_fieldavg[1] = ls_fieldavg[2] = 0;

	int steps = 0;
	double minh = .1;
	double segSize2max = 1./gridsize;
	double segSize2min = segSize2max/4;
	double lastd = 0;
	int avgct = 0;
	while (true) {
	    boundCheck = false;
	    steps++;
	    if (steps > 100) {
		System.out.print("maxsteps\n");
		p.lifetime = -1;
		return;
	    }
	    //System.out.print(h + " " + boundCheck + "/\n");

	    // estimate one full step
	    rk(order, 0, Y, dir*h);

	    // estimate two half steps
	    rk(order, 0, Yhalf, dir*h*0.5);
	    rk(order, 0, Yhalf, dir*h*0.5);

	    //System.out.print(h + " " + boundCheck + "\n");
	    if (boundCheck) {
		for (i = 0; i != order; i++)
		    Y[i] = Yhalf[i] = oldY[i]; 
		h /= 2;
		if (h < minh) {
		    p.lifetime = -1;
		    return;
		}
		continue;
	    }
	    if (Y[0] < -1 || Y[0] >= .999 ||
		Y[1] < -1 || Y[1] >= .999) {
		for (i = 0; i != order; i++)
		    Y[i] = Yhalf[i] = oldY[i]; 
		h /= 2;
		if (h < minh) {
		    p.lifetime = -1;
		    return;
		}
		continue;
	    }

	    // estimate the local error
	    localError =
		java.lang.Math.abs(Y[0] - Yhalf[0]) +
		java.lang.Math.abs(Y[1] - Yhalf[1]);
	    
	    if (localError > E && h > minh) {
		h *= 0.75; // decrease the step size
		if (h < minh)
		    h = minh;
		for (i = 0; i != order; i++)
		    Y[i] = Yhalf[i] = oldY[i]; 
		continue;
	    } else if (localError < (E * 0.5)) {
		h *= 1.25; // increase the step size
		if (h > maxh)
		    h = maxh;
	    }
	    
	    double d = dist2(p.pos, Y);
	    if (!(d-lastd > 1e-10)) {
		// we're not getting anywhere!
		//System.out.print("nga " + d + " " + lastd + "\n");
		p.lifetime = -1;
		return;
	    }
	    if (d > segSize2max) {
		h /= 2;
		if (h < minh) {
		    p.lifetime = -1;
		    return;
		}
		for (i = 0; i != order; i++)
		    Y[i] = Yhalf[i] = oldY[i]; 
		continue;
	    }
	    ls_fieldavg[0] += rk_k1[0];
	    ls_fieldavg[1] += rk_k1[1];
	    avgct++;

	    if (d > segSize2min)
		break;
	    lastd = d;

	    for (i = 0; i != order; i++)
		oldY[i] = Yhalf[i] = Y[i]; 
	}

	//System.out.print(steps + " ss\n");
	p.stepsize = h;
	for (i = 0; i != 3; i++)
	    p.pos[i] = Y[i];
	p.phi = java.lang.Math.sqrt(ls_fieldavg[0]*ls_fieldavg[0]+
				    ls_fieldavg[1]*ls_fieldavg[1])/avgct;
    }

    int doubleToGrid(double x) {
	return (int) ((x+1)*gridsize/2);
    }

    double gridToDouble(int x) {
	return (x*2./gridsize)-1;
    }

    abstract class VecFunction {
	abstract String getName();
	abstract VecFunction createNext();
	boolean nonGradient() { return false; }
	boolean useRungeKutta() { return true; }
	boolean useAdaptiveRungeKutta() { return true; }
	boolean checkBoundsWithForce() { return true; }
	boolean checkBounds(double y[], double oldY[]) { return false; }
	abstract void getField(double result[], double y[]);
	boolean redistribute() { return true; }
	void setup() {}
	void setupFrame() {}
	void finishFrame() {}
	void actionPerformed() {}
	void calcDivergence() {}
	double getLevelHeight() { return 0; }
	void setGrid(GridElement ge, int x, int y) {
	    double xx[] = rk_k1;
	    double res[] = rk_k2;
	    double res1[] = rk_k3;
	    xx[0] = (x*2./gridsize)-1;
	    xx[1] = (y*2./gridsize)-1;
	    xx[2] = 0;
	    boundCheck = false;
	    getField(res, xx);
	    ge.vecX = reverse*res[0]*70;
	    ge.vecY = reverse*res[1]*70;
	    ge.height = reverse*res[2]*.625;
	    ge.valid = !boundCheck;
	    /*if (!(ge.height >= -9999 && ge.height <= 9999))
		System.out.print(xx[0] + " " + xx[1] + " " +
		ge.height + "\n"); */
	    double xorig0 = xx[0];
	    xx[0] += 1e-8;
	    getField(res1, xx);
	    ge.div = res1[0] - res[0];
	    ge.curl = res1[1] - res[1];
	    xx[0] = xorig0;
	    xx[1] += 1e-8;
	    getField(res1, xx);
	    ge.div = (ge.div + res1[1] - res[1])*1e10*reverse;
	    ge.curl = (ge.curl - (res1[0] - res[0]))*1e10*reverse;
	}
	double getDivOffset() { return 4; }
	double getDivRange() { return 11; }
    };

    class InverseRadial extends VecFunction {
	double lineLen;
	String getName() { return BUILD_CASE_EMV("charged line",
						 null, "1/r single line"); }
	void getField(double result[], double y[]) {
	    double r = distance(y[0], y[1]);
	    if (r < lineWidth)
		boundCheck = true;
	    double r2 = r*r;
	    result[0] = -.0002*y[0]/r2;
	    result[1] = -.0002*y[1]/r2;
	    result[2] = .4*java.lang.Math.log(r+1e-300);
	}
	void setup() {
	    lineLen = 1;
	}
	VecFunction createNext() { return new InverseRadialDouble(); }
    };

    class InverseRadialDouble extends VecFunction {
	InverseRadialDouble() { sign = 1; }
	String getName() { return BUILD_CASE_EMV("line charge double",
						 null, "1/r double lines"); }
	double sign;
	void getField(double result[], double y[]) {
	    // we want to make sure sep is a multiple of the grid spacing
	    // so that the divergence gets calculated correctly.
	    double sep = gridToDouble(gridsize/2+
				      aux1Bar.getValue()*gridsize/200);
	    double xx1 = y[0] - sep;
	    double xx2 = y[0] + sep;
	    double r1 = distance(xx1, y[1]);
	    double r2 = distance(xx2, y[1]);
	    if (r1 < lineWidth || r2 < lineWidth)
		boundCheck = true;
	    double q = .0002;
	    double r1s = 1/(r1*r1);
	    double r2s = 1/(r2*r2*sign);
	    result[0] = q*(-xx1 *r1s-xx2 *r2s);
	    result[1] = q*(-y[1]*r1s-y[1]*r2s);
	    result[2] = .2*(java.lang.Math.log(r1+1e-20)+
			    sign*java.lang.Math.log(r2+1e-20));
	}
	void setup() {
	    setupBar(0, "Line Separation", 30);
	}
	VecFunction createNext() { return
	    BUILD_CASE_EMV(new InverseRadialDipole(), null,
			   new InverseSquaredRadial()); }
    };

#ifdef BUILD_E
    class InverseRadialDipole extends InverseRadialDouble {
	InverseRadialDipole() { sign = -1; }
	String getName() { return "dipole lines"; }
	VecFunction createNext() { return new InverseRadialQuad(); }
    };

    class InverseRadialQuad extends VecFunction {
	String getName() { return "quad lines"; }
	void getField(double result[], double y[]) {
	    // we want to make sure sep is a multiple of the grid spacing
	    // so that the divergence gets calculated correctly.
	    double sep = gridToDouble(gridsize/2+
				      aux1Bar.getValue()*gridsize/200);
	    double xx1 = y[0] + sep;
	    double xx2 = y[0] - sep;
	    double yy1 = y[1] + sep;
	    double yy2 = y[1] - sep;
	    double r1 = distance(xx1, yy1);
	    double r2 = distance(xx2, yy1);
	    double r3 = distance(xx1, yy2);
	    double r4 = distance(xx2, yy2);
	    if (r1 < lineWidth || r2 < lineWidth ||
		r3 < lineWidth || r4 < lineWidth)
		boundCheck = true;
	    double q = .0003;
	    result[0] = q*(-xx1/(r1*r1)-xx2/(r4*r4) +xx2/(r2*r2)+xx1/(r3*r3));
	    result[1] = q*(-yy1/(r1*r1)-yy2/(r4*r4) +yy1/(r2*r2)+yy2/(r3*r3));
	    result[2] = .2*(+java.lang.Math.log(r1+1e-20)
			    -java.lang.Math.log(r2+1e-20)
			    -java.lang.Math.log(r3+1e-20)
			    +java.lang.Math.log(r4+1e-20));
	}
	void setup() {
	    setupBar(0, "Line Separation", 30);
	}
	VecFunction createNext() { return new InverseSquaredRadial(); }
    };
#endif /* BUILD_E */

    class InverseSquaredRadial extends VecFunction {
	String getName() { return BUILD_CASE_EMV("point charge",
						 null, "1/r^2 single"); }
	void getField(double result[], double y[]) {
	    double r = distance(y);
	    if (r < chargeSize)
		boundCheck = true;
	    double r3 = r*r*r;
	    double q = .0003/r3;
	    result[0] = -y[0]*q;
	    result[1] = -y[1]*q;
	    result[2] = -.3/r;
	}

	static final double chargeSize = .001;

	VecFunction createNext() { return new InverseSquaredRadialDouble(); }
    };

    class InverseSquaredRadialDouble extends InverseSquaredRadial {
	String getName() { return BUILD_CASE_EMV("point charge double", null,
						 "1/r^2 double"); }
	double sign2;
	void getField(double result[], double y[]) {
	    // we want to make sure sep is a multiple of the grid spacing
	    // so that the divergence gets calculated correctly.
	    double sep = gridToDouble(gridsize/2+
				      aux1Bar.getValue()*gridsize/200);
	    double xx1 = y[0]-sep;
	    double xx2 = y[0]+sep;
	    double r1 = distance(xx1, y[1]);
	    if (r1 < chargeSize)
		boundCheck = true;
	    double r2 = distance(xx2, y[1]);
	    if (r2 < chargeSize)
		boundCheck = true;
	    double q = .0003;
	    double rq1 = q/(r1*r1*r1);
	    double rq2 = q/(r2*r2*r2) * sign2;
	    result[0] = -xx1 *rq1-xx2 *rq2;
	    result[1] = -y[1]*rq1-y[1]*rq2;
	    result[2] = -.05/r1 - .05*sign2/r2;
	    if (sign2 == -1)
		result[2] *= 2;
	}
	void setup() {
	    sign2 = 1;
	    setupBar(0, "Charge Separation", 30);
	}
	VecFunction createNext() { return
	    BUILD_CASE_EMV(new InverseSquaredRadialDipole(),
			   null, new InverseRotational()); }
    };

#ifdef BUILD_E
    class InverseSquaredRadialDipole extends InverseSquaredRadialDouble {
	String getName() { return "dipole"; }
	void setup() {
	    super.setup();
	    sign2 = -1;
	}
	VecFunction createNext() { return new InverseSquaredRadialQuad(); }
    };
    class InverseSquaredRadialQuad extends InverseSquaredRadial {
	String getName() { return "quadrupole"; }
	void getField(double result[], double y[]) {
	    // we want to make sure sep is a multiple of the grid spacing
	    // so that the divergence gets calculated correctly.
	    double sep = gridToDouble(gridsize/2+
				      aux1Bar.getValue()*gridsize/200);
	    double xx1 = y[0] - sep;
	    double xx2 = y[0] + sep;
	    double yy1 = y[1] - sep;
	    double yy2 = y[1] + sep;
	    double r1 = distance(xx1, yy1);
	    double r2 = distance(xx2, yy1);
	    double r3 = distance(xx1, yy2);
	    double r4 = distance(xx2, yy2);
	    if (r1 < chargeSize || r2 < chargeSize ||
		r3 < chargeSize || r4 < chargeSize)
		boundCheck = true;
	    double q = .0003;
	    double rq1 = q/(r1*r1*r1);
	    double rq2 = q/(r2*r2*r2);
	    double rq3 = q/(r3*r3*r3);
	    double rq4 = q/(r4*r4*r4);
	    result[0] = -xx1*rq1-xx2*rq4+xx2*rq2+xx1*rq3;
	    result[1] = -yy1*rq1-yy2*rq4+yy1*rq2+yy2*rq3;
	    result[2] = .05*(-1/r1+1/r2+1/r3-1/r4);
	}
	void setup() {
	    super.setup();
	    setupBar(0, "Charge Separation", 30);
	}
	VecFunction createNext() { return new ConductingPlate(); }
    };

    class ConductingPlate extends VecFunction {
	String getName() { return "conducting plate"; }
	Complex z, z2;
	boolean plate;
	double a, base;
	ConductingPlate() {
	    z = new Complex();
	    z2 = new Complex();
	    plate = true;
	}
	void setupFrame() {
	    a = (aux1Bar.getValue()+1)/100.;
	    z.set(0, 1/a);
	    z.arcsin();
	    base = z.b;
	}
	void getField(double result[], double y[]) {
	    // smythe p89
	    if (y[1] >= -.02 && y[1] <= .02) {
		if ((plate  && y[0] >= -a && y[0] <= a) ||
		    (!plate && (y[0] >= a || y[0] <= -a)))
		boundCheck = true;
	    }
	    z.set(y[0]/a, y[1]/a);
	    if (y[1] < 0 && plate)
		z.b = -z.b;
	    z2.set(z);
	    z2.arcsin();
	    result[2] = (plate) ? z2.b/base-1 : -z2.a*.6;

	    // here we calculate ((1-(z/a)^2)^(-1/2))/a, which is
	    // d/dz arcsin(z/a)
	    z.square();
	    z.mult(-1);
	    z.add(1);
	    z.pow(-.5);
	    z.mult(1/a);
	    if (plate) {
		// field = (Im dw/dz, Re dw/dz)
		result[1] = z.a * -.0007;
		result[0] = z.b * -.0007;
		if (y[1] <= 0)
		    result[1] = -result[1];
	    } else {
		// field = (Re dw/dz, -Im dw/dz)
		result[0] = z.a * .0007;
		result[1] = -z.b * .0007;
		if (y[1] == 0)
		    result[1] = -result[1];
	    }
	}
	void setup() {
	    setupBar(0, "Plate Size", 60);
	}
	double getDivOffset() { return -17.3; }
	double getDivRange() { return 2.5; }
	VecFunction createNext() { return new ChargedPlate(); }
    };
    class ChargedPlate extends ConductingPlate {
	Complex cz;
	ChargedPlate() { cz = new Complex(); }
	String getName() { return "charged plate"; }
	double getDivOffset() { return 4; }
	double getDivRange() { return 11; }
	double getPot(double a1, double a2, double y) {
	    cz.set (y, -a1);
	    cz.mult(y,  a2);
	    cz.log();
	    double b1 = cz.b;
	    cz.set (y,  a1);
	    cz.mult(y, -a2);
	    cz.log();
	    double y2 = y*y;
	    if (y2 == 0)
		y2 = 1e-8;
	    return .3*(2*(a1-a2) + (b1-cz.b)*y +
		       a2*java.lang.Math.log(a2*a2+y2) -
		       a1*java.lang.Math.log(a1*a1+y2));
	}
	void calcDivergence() {
	    double sep = aux2Bar.getValue()/100.;
	    int x, y;
	    for (x = 0; x != gridsize; x++) {
		double xx = gridToDouble(x);
		if (xx < -a || xx > a)
		    continue;
		grid[x][gridsize/2].div = -reverse;
	    }
	}
	void getField(double result[], double y[]) {
	    if (y[1] >= -.01 && y[1] <= .01 &&
		(y[0] >= -a && y[0] <= a))
		boundCheck = true;
	    double a1 = -a-y[0];
	    double a2 =  a-y[0];
	    double y2 = y[1]*y[1];
	    if (y2 == 0)
		y2 = 1e-8;
	    double q = .0003/a;
	    result[0] = .5*q*
	        java.lang.Math.log((y2+a2*a2)/(y2+a1*a1));
	    result[1] = q*
		(java.lang.Math.atan(a1/y[1])-
		 java.lang.Math.atan(a2/y[1]));
	    result[2] = .4*getPot(a1, a2, y[1])/a;
	}
	VecFunction createNext() { return new ChargedPlatePair(); }
    };

    class ChargedPlatePair extends ChargedPlate {
	String getName() { return "charged plate pair"; }
	boolean useRungeKutta() { return false; }
	double dipole;
	ChargedPlatePair() { dipole = 1; }
	void getField(double result[], double y[]) {
	    double sep = aux2Bar.getValue()/100.;
	    if ((y[1] >= -.01+sep && y[1] <= .01+sep ||
		 y[1] >= -.01-sep && y[1] <= .01-sep) &&
		y[0] >= -a && y[0] <= a)
		boundCheck = true;
	    double a1 = -a-y[0];
	    double a2 =  a-y[0];
	    double y1 = y[1]-sep;
	    double y12 = y1*y1;
	    if (y12 == 0)
		y12 = 1e-8;
	    double y2 = y[1]+sep;
	    double y22 = y2*y2;
	    if (y22 == 0)
		y22 = 1e-8;

	    double q = .0003/a;
	    result[0] = .5*q*
	        (java.lang.Math.log((y12+a2*a2)/(y12+a1*a1)) + dipole*
		 java.lang.Math.log((y22+a2*a2)/(y22+a1*a1)));
	    result[1] = q*
		(java.lang.Math.atan(a1/y1)
		-java.lang.Math.atan(a2/y1)
		+dipole*(java.lang.Math.atan(a1/y2)
			-java.lang.Math.atan(a2/y2)));
	    result[2] = .4*(getPot(a1, a2, y1)+dipole*getPot(a1, a2, y2))/a;
	}
	void calcDivergence() {
	    double sep = aux2Bar.getValue()/100.;
	    int x, y;
	    for (x = 0; x != gridsize; x++) {
		double xx = gridToDouble(x);
		if (xx < -a || xx > a)
		    continue;
		y = doubleToGrid(sep);
		grid[x][y].div = -reverse;
		y = doubleToGrid(-sep);
		grid[x][y].div = -dipole*reverse;
	    }
	}
	void setup() {
	    setupBar(0, "Sheet Size", 60);
	    setupBar(1, "Sheet Separation", 33);
	}
	boolean checkBounds(double y[], double oldY[]) {
	    double size = aux1Bar.getValue()/100.;
	    double sep = aux2Bar.getValue()/100.;
	    // check to see if particle has passed through one of plates
	    if (y[0] >= -size && y[0] <= size) {
		if (y[1] > sep) {
		    if (oldY[1] < sep)
			return true;
		} else if (y[1] < -sep) {
		    if (oldY[1] > -sep)
			return true;
		} else if (oldY[1] > sep || oldY[1] < -sep)
		    return true;
	    }
	    return false;
	}
	VecFunction createNext() { return new ChargedPlateDipole(); }
    };

    class ChargedPlateDipole extends ChargedPlatePair {
	String getName() { return "charged plate dipole"; }
	ChargedPlateDipole() { dipole = -1; }
	VecFunction createNext() { return new InfiniteChargedPlane(); }
    };

    class InfiniteChargedPlane extends VecFunction {
	String getName() { return "infinite plane"; }
	void getField(double result[], double y[]) {
	    double alpha = .0004;
	    if (y[1] > -.01 && y[1] < .01)
		boundCheck = true;
	    result[0] = 0;
	    result[1] = (y[1] <= 0) ? alpha : -alpha;
	    result[2] = java.lang.Math.abs(y[1])-1;
	}
	boolean checkBoundsWithForce() { return false; }
	VecFunction createNext() { return new Cylinder(); }
    };
    
    class Cylinder extends VecFunction {
	String getName() { return "conducting cylinder"; }
	double getCylRadius() { return (aux1Bar.getValue()+1)/110.; }
	void setup() {
	    setupBar(0, "Cylinder Size", 30);
	    setupBar(1, "Cylinder Potential", 1);
	}
	void getField(double result[], double y[]) {
	    // Smythe p70
	    double a = getCylRadius();
	    double farpt = 4;

	    double pot = 2*(aux2Bar.getValue()/50.-1);
	    final int mult = 4000;

	    // add in charge that will bring cylinder to specified potential
	    double cq = -pot/
		(mult*(java.lang.Math.log(a)-java.lang.Math.log(farpt)));
	    double pot0 = mult*cq*java.lang.Math.log(farpt);

	    double y0 = y[0];
	    double y1 = y[1];
	    double r1 = distance(y0, y1);
	    if (r1 < a) {
		result[0] = result[1] = 0;
		result[2] = pot;
		boundCheck = true;
		return;
	    }
	    double a1 = 5*cq/(r1*r1);
	    result[0] = y0*a1;
	    result[1] = y1*a1;
	    result[2] = pot0-cq*mult*java.lang.Math.log(r1);
	}
	void calcDivergence() {
	    double a = getCylRadius();
	    int i;
	    for (i = 0; i != 100; i++) {
		double th = 2*pi*i/100.;
		double xx = java.lang.Math.cos(th)*a;
		double yy = java.lang.Math.sin(th)*a;
		grid[doubleToGrid(xx)][doubleToGrid(yy)].div -= reverse/20.;
	    }
	}
	VecFunction createNext() { return new CylinderAndLineCharge(); }
    };

    class CylinderAndLineCharge extends VecFunction {
	String getName() { return "cyl + line charge"; }
	double getCylRadius() { return (aux1Bar.getValue()+1)/110.; }
	double getSeparation() { return aux2Bar.getValue()/100.; }
	double getCylPos() { return getSeparation()/2; }
	double getPointPos() { return -getSeparation()/2-getCylRadius(); }
	void setup() {
	    setupBar(0, "Cylinder Size", 30);
	    setupBar(1, "Separation", 30);
	    setupBar(2, "Cylinder Potential", 50);
	}

	void setupFrame() {
	    // Smythe p70
	    q = -.0003;
	    a = getCylRadius();
	    b = getSeparation() + a;
	    spos = getCylPos();
	    imagePos = spos - a*a/b;

	    double r2_0 = spos+a-imagePos;
	    double r3_0 = spos+a-getPointPos();

	    // Find charge that will eliminate field at far end cylinder.
	    // That's our definition of "ground".  (We can't use the
	    // potential at infinity as ground, since that diverges.)
	    cq = a*a*(q/(r2_0*r2_0) - q/(r3_0*r3_0));

	    // calculate potential on cylinder with that charge.  we will
	    // subtract that value out of the potential everywhere.
	    pot0 = -cq*java.lang.Math.log(a)
		+q*java.lang.Math.log(r2_0)
		-q*java.lang.Math.log(r3_0);

	    // add in charge that will bring cylinder to specified potential
	    cq -= (aux3Bar.getValue()/50.-1)*.0006/java.lang.Math.log(a);
	}

	double q, a, b, spos, imagePos, cq, pot0;

	void calcDivergence() {
	    int i;
	    double pos[] = rk_k1;
	    double res[] = rk_k2;
	    double a1 = getCylRadius()+.001;
	    int x, y;
	    for (x = 0; x != gridsize; x++)
		for (y = 0; y != gridsize; y++)
		    grid[x][y].div = 0;
	    grid[doubleToGrid(getPointPos())][doubleToGrid(0)].div = -reverse;
	    for (i = 0; i != 200; i++) {
		double th = 2*pi*i/200.;
		double costh = java.lang.Math.cos(th);
		double sinth = java.lang.Math.sin(th);
		pos[0] = costh*a1+getCylPos();
		pos[1] = sinth*a1;
		pos[2] = 0;
		curfunc.getField(res, pos);
		grid[doubleToGrid(costh*a+getCylPos())]
		    [doubleToGrid(sinth*a)].div +=
		    (costh*res[0] + sinth*res[1])*60*reverse;
	    }
	}
	void getField(double result[], double y[]) {
	    // Smythe p70
	    double x1 = y[0]-spos;
	    double r1 = distance(x1, y[1]);
	    final int mult = 4000;
	    double y0 = y[0];
	    double y1 = y[1];
	    if (r1 < a) {
		y0 = spos+a;
		y1 = 0;
		x1 = r1 = a;
		boundCheck = true;
	    }
	    double x2 = y0-imagePos;
	    double r2 = distance(x2, y1);
	    double x3 = y0-getPointPos();
	    double r3 = distance(x3, y1);
	    double chargeSize = .001;
	    if (r3 < chargeSize)
		boundCheck = true;
	    double a1 = cq/(r1*r1);
	    double a2 = -q/(r2*r2);
	    double a3 = q/(r3*r3);
	    result[0] = x1*a1 + x2*a2 + x3*a3;
	    result[1] = y1*(a1+a2+a3);
	    result[2] = mult*(-pot0
			      -cq*java.lang.Math.log(r1)
			      +q*java.lang.Math.log(r2+1e-20)
			      -q*java.lang.Math.log(r3+1e-20));
	    if (r1 == a)
		result[0] = result[1] = 0;
	}
	VecFunction createNext() { return new CylinderInField(); }
    };

    class CylinderInField extends VecFunction {
	CylinderInField() { conducting = true; showD = false; }
	String getName() { return "cylinder in field"; }
	boolean conducting, showD;
	double a;
	void setupFrame() {
	    a = aux1Bar.getValue()/100.;
	}
	void getField(double result[], double y[]) {
	    // smythe p67
	    double a2 = a*a;
	    double r = distance(y[0], y[1]);
	    double e1 = aux2Bar.getValue()/10. + 1;
	    double dimult = (conducting) ? 1 : (e1-1)/(e1+1);
	    double fmult = .0006;
	    final double potmult = 3;
	    if (r < a) {
		result[0] = result[1] = result[2] = 0;
		if (conducting)
		    boundCheck = true;
		else
		    result[0] = (showD) ? e1*fmult*(1-dimult) :
		        fmult*(1-dimult);
		result[2] = -potmult*(1-dimult)*y[0];
		return;
	    }
	    double costh = y[0]/r;
	    double sinth = y[1]/r;
	    double r_2 = 1/(r*r);
	    double er  = (1+dimult*a2*r_2)*costh*fmult;
	    double eth = -(1-dimult*a2*r_2)*sinth*fmult;
	    er /= r;
	    result[0] = y[0]*er - eth*sinth;
	    result[1] = y[1]*er + eth*costh;
	    result[2] = -potmult*(1-dimult*a2*r_2)*y[0];
	}
	void setup() {
	    setupBar(0, "Cylinder Size", 40);
	}
	void calcDivergence() {
	    int i;
	    double pos[] = rk_k1;
	    double res[] = rk_k2;
	    double a1 = a+.001;
	    int x, y;
	    for (x = 0; x != gridsize; x++)
		for (y = 0; y != gridsize; y++)
		    grid[x][y].div = 0;
	    for (i = 0; i != 200; i++) {
		double th = 2*pi*i/200.;
		double costh = java.lang.Math.cos(th);
		double sinth = java.lang.Math.sin(th);
		pos[0] = costh*a1;
		pos[1] = sinth*a1;
		pos[2] = 0;
		curfunc.getField(res, pos);
		double rx = res[0];
		double ry = res[1];
		double a2 = a-.001;
		pos[0] = costh*a2;
		pos[1] = sinth*a2;
		pos[2] = 0;
		curfunc.getField(res, pos);
		grid[doubleToGrid(costh*a)][doubleToGrid(sinth*a)].div +=
		    (costh*(rx-res[0]) + sinth*(ry-res[1]))*4e2*reverse;
	    }
	}
	VecFunction createNext() { return new DielectricCylinderInFieldE(); }
    };

    class DielectricCylinderInFieldE extends CylinderInField {
	DielectricCylinderInFieldE() { conducting = false; showD = false; }
	String getName() { return "dielec cyl in field"; }
	void setup() {
	    setupBar(0, "Cylinder Size", 40);
	    setupBar(1, "Dielectric Strength", 60);
	}
	VecFunction createNext() { return new SlottedPlane(); }
    };

    /*class DielectricBoundaryE extends InverseSquaredRadial {
	boolean showD, conducting;
	double planeY;
	DielectricBoundaryE() { conducting = false; showD = false; }
	String getName() { return "dielec boundary"; }
	void setup() {
	    setupBar(0, "Charge Location", 60);
	    if (!conducting)
		setupBar(1, "Dielectric Strength", 60);
	}
	void getField(double result[], double y[]) {
	    double cx = aux1Bar.getValue()/50.-1.001;
	    double r1 = distance(y[0], y[1]-cx);
	    if (r1 < chargeSize)
		boundCheck = true;
	    double eps1 = 1;
	    double eps2 = aux2Bar.getValue()/10. + 1;
	    if (conducting)
		eps2 = 1e8;
	    if (cx < planeY) {
		eps1 = eps2;
		eps2 = 1;
	    }
	    double q1 = .0003;
	    double q2 = -(eps2-eps1)/(eps2+eps1)*q1;
	    double ep = eps1;
	    if (cx > planeY && y[1] < planeY || cx < planeY && y[1] > planeY) {
		q1 = 2*eps2*q1/(eps2+eps1);
		q2 = 0;
		ep = eps2;
	    }
	    double r2 = distance(y[0], y[1]-planeY*2+cx);
	    result[2] = -2000*(q1/(r1*ep) + q2/(r2*ep));
	    if (!showD) {
		q1 /= ep;
		q2 /= ep;
	    }
	    double rq1 = q1/(r1*r1*r1);
	    double rq2 = q2/(r2*r2*r2);
	    result[0] = -y[0]*(rq1+rq2);
	    result[1] = -(y[1]-cx)*rq1-(y[1]-planeY*2+cx)*rq2;
	}
	VecFunction createNext() { return new ConductingPlane(); }
    };
    class ConductingPlane extends DielectricBoundaryE {
	ConductingPlane() { conducting = true; showD = false; planeY = -1; }
	String getName() { return "conducting plane + pt"; }
	VecFunction createNext() { return new SlottedPlane(); }
	};*/

    class SlottedPlane extends VecFunction {
	String getName() { return "slotted conducting plane"; }
	Complex z, z2, z3;
	double getDivOffset() { return -17.3; }
	double getDivRange() { return 2.5; }
	SlottedPlane() {
	    z = new Complex();
	    z2 = new Complex();
	    z3 = new Complex();
	}
	void getField(double result[], double y[]) {
	    // W = -.5E (z +- (z^2-a^2)^1/2)
	    // dw/dz = -.5E (1 +- z/(z^2-a^2)^1/2)
	    // Smythe p92
	    double a = (aux1Bar.getValue()+1)/101.;
	    z.set(y[0], y[1]);
	    if (y[1] >= -.01 && y[1] <= .01 &&
		(y[0] < -a || y[0] > a)) {
		boundCheck = true;
		if (z.b == 0)
		    z.b = -1e-8;
	    }
	    z2.set(z);
	    z2.square();
	    z2.add(-a*a);
	    z3.set(z2);
	    z3.pow(.5);
	    if (z3.b < 0)
		z3.mult(-1);
	    z3.add(z.a, z.b);
	    result[2] = z3.b*2;

	    z2.pow(-.5);
	    // I can barely understand what Smythe is talking about but
	    // I think he wants the square root to always have a positive
	    // imaginary part.  Here we already took the reciprocal
	    // (by calling pow(-.5) instead of pow(.5)) so we want the
	    // root to have a negative imaginary part instead.
	    if (z2.b > 0)
		z2.mult(-1);
	    z2.mult(z);
	    // field = (Im dw/dz, Re dw/dz)
	    result[1] = -(1+z2.a) * .003;
	    result[0] = -(z2.b) * .003;
	}
	void setup() {
	    setupBar(0, "Slot Size", 30);
	}
	VecFunction createNext() { return new PlanePair(); }
    };
    class PlanePair extends ConductingPlate {
	String getName() { return "conducting planes w/ gap"; }
	PlanePair() { super(); plate = false; }
	void setup() {
	    setupBar(0, "Gap Size", 20);
	}
	double getDivOffset() { return -17; }
	VecFunction createNext() { return null; }
    };

#endif
#ifndef BUILD_E
    class InverseRotational extends InverseRadial {
	String getName() { return BUILD_CASE_EMV(null, "current line",
				  "1/r rotational"); }
	void getField(double result[], double y[]) {
	    double r = distance(y[0], y[1]);
	    if (showA) {
		result[0] = result[1] = 0;
		result[2] = -.001*(java.lang.Math.log(r)-.5);
	    } else {
		if (r < lineWidth*2)
		    boundCheck = true;
		rotateParticle(result, y, .0001/(r*r));
	    }
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new InverseRotationalPotential(); }
    };

    class InverseRotationalPotential extends VecFunction {
	String getName() { return "1/r rotational potential"; }
	void getField(double result[], double y[]) {
	    double r = distance(y[0], y[1]);
	    rotateParticle(result, y, .0001/(r*r));
	    if (r < lineWidth*2)
		boundCheck = true;
	    else if (y[0] >= 0 && y[1] < .001 && y[1] > -.025) {
		boundCheck = true;
		if (y[1] == 0)
		    result[1] = 1e8;
	    }
	    double ang = java.lang.Math.atan2(y[1], y[0]);
	    if (ang < 0)
		ang += 2*pi;
	    result[2] = (pi-ang)*.3;
	}
	VecFunction createNext() { return new InverseRotationalDouble(); }
    };

    class InverseRotationalDouble extends InverseRadialDouble {
	InverseRotationalDouble() { dir2 = 1; ext = false; }
	int dir2;
	boolean ext;
	String getName() { return BUILD_CASE_EMV(null, "current line double",
						 "1/r rotational double"); }
	void getField(double result[], double y[]) {
	    // we want to make sure sep is a multiple of the grid spacing
	    // so that the divergence gets calculated correctly.
	    double sep = gridToDouble(gridsize/2+
				      aux1Bar.getValue()*gridsize/200);
	    double r  = distance(y[0] - sep, y[1]);
	    double r2 = distance(y[0] + sep, y[1]);
	    if (ext) {
		double p = aux3Bar.getValue()*pi/50.;
		double s = aux2Bar.getValue()/6.;
		getDirectionField(result, y, p);
		result[0] *= s;
		result[1] *= s;
		result[2] *= s;
	    } else
		result[0] = result[1] = result[2] = 0;
	    if (showA) {
		if (dir2 == 1)
		    result[2] += -.001*(java.lang.Math.log(r)+
				       java.lang.Math.log(r2)-1);
		else
		    result[2] += .001*(java.lang.Math.log(r)-
				       java.lang.Math.log(r2));
	    } else {
		if (r < lineWidth*2)
		    boundCheck = true;
		rotateParticleAdd(result, y, .0001/(r*r),  sep, 0);
		if (r2 < lineWidth*2)
		    boundCheck = true;
		rotateParticleAdd(result, y, dir2*.0001/(r2*r2), -sep, 0);
	    }
	}
	void setup() {
	    setupBar(0, "Line Separation", 30);
	    if (ext) {
		setupBar(1, "Ext. Strength", 7);
		setupBar(2, "Ext. Direction", 0);
	    }
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new InverseRotationalDoubleExt(); }
    };
    class InverseRotationalDoubleExt extends InverseRotationalDouble {
	InverseRotationalDoubleExt() { ext = true; }
	String getName() { return BUILD_CASE_EMV(null, "cur line double + ext",
						 "1/r rot double + ext"); }
	VecFunction createNext() { return new InverseRotationalDipole(); }
    };
    class InverseRotationalDipole extends InverseRotationalDouble {
	InverseRotationalDipole() { dir2 = -1; }
	String getName() { return BUILD_CASE_EMV(null, "current line dipole",
						 "1/r rotational dipole"); }
	VecFunction createNext() { return new InverseRotationalDipoleExt(); }
    };
    class InverseRotationalDipoleExt extends InverseRotationalDouble {
	InverseRotationalDipoleExt() { dir2 = -1; ext = true; }
	void setup() {
	    super.setup();
	    aux2Bar.setValue(3);
	    aux3Bar.setValue(25);
	}
	String getName() { return BUILD_CASE_EMV(null, "cur line dipole + ext",
						 "1/r rot dipole + ext"); }
	VecFunction createNext() { return new OneDirectionFunction(); }
    };
    class OneDirectionFunction extends VecFunction {
	String getName() { return BUILD_CASE_EMV(null, "uniform field",
						 "one direction"); }
	void getField(double result[], double y[]) {
	    double th = aux1Bar.getValue() * pi /50.;
	    getDirectionField(result, y, th);
	}

	void setup() {
	    setupBar(0, "Theta", 0);
	}
	VecFunction createNext() { return
	    BUILD_CASE_EMV(null, new MovingChargeField(),
			   new InverseSquaredRadialSphere()); }
    };

    void getDirectionField(double result[], double y[], double th) {
	double sinth = java.lang.Math.sin(th);
	double costh = java.lang.Math.cos(th);
	if (!showA) {
	    result[0] = .0003*costh;
	    result[1] = .0003*sinth;
	    result[2] = -.4*(y[0]*costh + y[1]*sinth);
	} else {
	    // The A for this field is a linear rotation around
	    // an axis pointing in the direction of the field.
	    // First calculate the axis.
	    double axis[] = new double[3];
	    axis[0] = costh;
	    axis[1] = sinth;
	    axis[2] = 0;
	    // now project the point we are looking at onto the axis
	    double d = dot(axis, y);
	    // subtract out this projection so we can get the vector
	    // from the point to the axis
	    double r[] = new double[3];
	    int i;
	    for (i = 0; i != 2; i++)
		r[i] = .0006*(y[i] - axis[i]*d);
	    // cross this vector with the axis vector to get the result
	    cross(result, axis, r);
	}
    }

#endif
#ifndef BUILD_V
    class MovingChargeField extends InverseSquaredRadial {
	String getName() { return "moving charge"; }
	void getField(double result[], double y[]) {
	    double rz = distance(y);
	    if (showA) {
		result[0] = result[1] = 0;
		result[2] = .0003/rz;
	    } else {
		double r = distance(y[0], y[1]);
		if (rz < chargeSize)
		    boundCheck = true;
		rotateParticle(result, y, .0001/(rz*rz*rz));
	    }
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return
	       BUILD_CASE_EMV(null, new FastChargeField(), null); }
    };
#endif
#ifdef BUILD_V
    class InverseSquaredRadialSphere extends VecFunction {
	String getName() { return "1/r^2 sphere"; }
	double getSize() { return (aux1Bar.getValue()+1)/110.; }
	void getField(double result[], double y[]) {
	    double r = distance(y);
	    if (r < .01)
		boundCheck = true;
	    double a = getSize();
	    result[2] = .2*((r > a) ? -1/r : -3/(2*a)+r*r/(2*a*a*a));
	    if (r < a)
		r = a;
	    double alpha = .0003/(r*r*r);
	    result[0] = -y[0]*alpha;
	    result[1] = -y[1]*alpha;
	}
	void setup() {
	    setupBar(0, "Sphere Size", 30);
	}

	boolean checkBoundsWithForce() { return false; }
	VecFunction createNext() { return new ConstRadial(); }
    };
    class ConstRadial extends InverseSquaredRadial {
	String getName() { return "const radial"; }
	void getField(double result[], double y[]) {
	    double r = distance(y);
	    if (r < chargeSize)
		boundCheck = true;
	    double q = .0006/r;
	    result[0] = -q*y[0];
	    result[1] = -q*y[1];
	    result[2] = r;
	}
	boolean checkBoundsWithForce() { return false; }
	VecFunction createNext() { return new LinearRadial(); }
    };

    class LinearRadial extends InverseSquaredRadial {
	String getName() { return "linear radial"; }
	void getField(double result[], double y[]) {
	    double r = distance(y);
	    if (r < chargeSize)
		boundCheck = true;
	    double k = .0009;
	    result[0] = -y[0]*k;
	    result[1] = -y[1]*k;
	    result[2] = r*r-1;
	}
	boolean checkBoundsWithForce() { return false; }
	VecFunction createNext() { return new ConstantToYAxis(); }
    };

    class ConstantToYAxis extends InverseRadial {
	String getName() { return "constant to y axis"; }
	void getField(double result[], double y[]) {
	    double alpha = .0004;
	    if (y[0] > -.01 && y[0] < .01)
		boundCheck = true;
	    result[0] = (y[0] <= 0) ? alpha : -alpha;
	    result[1] = 0;
	    result[2] = java.lang.Math.abs(y[0])-1;
	}
	boolean checkBoundsWithForce() { return false; }
	VecFunction createNext() { return new LinearToYAxis(); }
    };
    class LinearToYAxis extends InverseRadial {
	String getName() { return "linear to y axis"; }
	void getField(double result[], double y[]) {
	    double r = java.lang.Math.abs(y[0]);
	    if (r < lineWidth)
		boundCheck = true;
	    double q = .0009;
	    result[0] = -y[0]*q;
	    result[1] = 0;
	    result[2] = r*r-1;
	}
	boolean checkBoundsWithForce() { return false; }
	VecFunction createNext() { return new LinearToXYAxes(); }
    };
    class LinearToXYAxes extends VecFunction {
	String getName() { return "2-dimensional oscillator"; }
	void getField(double result[], double y[]) {
	    double alpha = .0006;
	    double r = java.lang.Math.sqrt((aux1Bar.getValue()+1)/51.);
	    result[0] = -alpha*r*y[0];
	    result[1] = -alpha/r*y[1];
	    result[2] = (y[0]*y[0]*r+y[1]*y[1]/r)-1;
	}
	void setup() {
	    setupBar(0, "X/Y Ratio", 50);
	}
	boolean checkBoundsWithForce() { return false; }
	VecFunction createNext() { return new InverseToYAxis(); }
    };
    class InverseToYAxis extends VecFunction {
	String getName() { return "inverse to y axis"; }
	void getField(double result[], double y[]) {
	    if (y[0] > -.01 && y[0] < .01)
		boundCheck = true;
	    double alpha = .0003;
	    double zz = y[0];
	    if (zz == 0)
		zz = .00001;
	    result[0] = -alpha/zz;
	    result[1] = 0;
	    result[2] = -.01/(zz*zz);
	}
	VecFunction createNext() { return new InverseSquareRotational(); }
    };
    class InverseSquareRotational extends InverseRadial {
	String getName() { return "1/r^2 rotational"; }
	void getField(double result[], double y[]) {
	    double r = distance(y[0], y[1]);
	    if (r < lineWidth*2)
		boundCheck = true;
	    rotateParticle(result, y, .0001/(r*r*r));
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new LinearRotational(); }
    };
    class LinearRotational extends InverseRadial {
	String getName() { return "linear rotational"; }
	void getField(double result[], double y[]) {
	    double q = .0006;
	    result[0] = -q*y[1];
	    result[1] =  q*y[0];
	    result[2] = 0;
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new ConstantRotational(); }
    };

    class ConstantRotational extends InverseRadial {
	String getName() { return "constant rotational"; }
	void getField(double result[], double y[]) {
	    double r = distance(y[0], y[1]);
	    rotateParticle(result, y, .0006/r);
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new FxEqualsYField(); }
    };

    class FxEqualsYField extends VecFunction {
	String getName() { return "(y,0)"; }
	void getField(double result[], double y[]) {
	    result[2] = result[1] = 0;
	    result[0] = y[1] * .0009;
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new FxEqualsY2(); }
    };

    class FxEqualsY2 extends VecFunction {
	String getName() { return "(y^2,0)"; }
	void getField(double result[], double y[]) {
	    result[2] = result[1] = 0;
	    result[0] = y[1]*y[1] * .002;
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new Saddle(); }
    };

    class Saddle extends VecFunction {
	String getName() { return "saddle"; }
	void getField(double result[], double y[]) {
	    double q = .001;
	    result[0] = -q*y[0];
	    result[1] =  q*y[1]*.5;
	    result[2] = 1*(2*y[0]*y[0] - y[1]*y[1]);
	}
	VecFunction createNext() { return new RotationalExpansion(); }
    };

    class RotationalExpansion extends VecFunction {
	String getName() { return "rotation + expansion"; }
	void getField(double result[], double y[]) {
	    double q = .0006;
	    result[0] = q*(y[0]-y[1]);
	    result[1] = q*(y[0]+y[1]);
	    result[2] = 0;
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new Function4Field(); }
    };
    
    class Function4Field extends VecFunction {
	String getName() { return "(x^2-y,x+y^2)"; }
	void getField(double result[], double y[]) {
	    double q = .0003;
	    result[0] = q*(y[0]*y[0]-y[1]);
	    result[1] = q*(y[0]+y[1]*y[1]);
	    result[2] = 0;
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new Function5Field(); }
    };

    class Function5Field extends VecFunction {
	String getName() { return "(x+y^2,x^2-y)"; }
	void getField(double result[], double y[]) {
	    double q = .0003;
	    result[0] = q*(y[0]+y[1]*y[1]);
	    result[1] = q*(y[0]*y[0]-y[1]);
	    result[2] = 0;
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new Function6Field(); }
    };

    class Function6Field extends VecFunction {
	String getName() { return "(x,x^2)"; }
	void getField(double result[], double y[]) {
	    double q = .0006;
	    result[0] = q*y[0];
	    result[1] = q*y[0]*y[0];
	    result[2] = 0;
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return new Function7Field(); }
    };

    class Function7Field extends VecFunction {
	String getName() { return "u=x^2+y"; }
	void getField(double result[], double y[]) {
	    double q = .0003;
	    result[0] = -2*y[0]*q;
	    result[1] = -q;
	    result[2] = (y[0]*y[0]+y[1])*1;
	}
	VecFunction createNext() { return new PendulumPotential(); }
    };

    class PendulumPotential extends VecFunction {
	String getName() { return "pendulum potential"; }
	void getField(double result[], double y[]) {
	    double q = .0006;
	    double xx  = y[0]*3.1;
	    double yy  = y[1]*3.1;
	    double cosx = java.lang.Math.cos(xx);
	    double cosy = java.lang.Math.cos(yy);
	    double sinx = java.lang.Math.sin(xx);
	    double siny = java.lang.Math.sin(yy);
	    result[0] = -q*sinx*cosy;
	    result[1] = -q*cosx*siny;
	    result[2] = -cosx*cosy*.5;
	}
	VecFunction createNext() { return new Function8Field(); }
    };

    class Function8Field extends VecFunction {
	String getName() { return "sin(r2)/r2"; }
	void getField(double result[], double y[]) {
	    double r2 = 23*(y[0]*y[0]+y[1]*y[1])+.00000001;
	    result[2] = java.lang.Math.sin(r2)/r2;
	    double r= java.lang.Math.sqrt(r2);
	    double sinr2 = java.lang.Math.sin(r2);
	    double cosr2 = java.lang.Math.cos(r2);
	    double r4 = r2*r2;
	    double vecR = (sinr2/r4-cosr2/r2)*.01;
	    result[0] = y[0]*vecR;
	    result[1] = y[1]*vecR;
	}
	VecFunction createNext() { return new UserDefinedPotential(); }
    };

    class UserDefinedPotential extends VecFunction {
	Expr expr;
	double y0[];
	String getName() { return "user-defined potential"; }
	void setup() {
	    textFields[0].setText("x*x");
	    textFields[0].show();
	    textFieldLabel.setText("Potential Function");
	    textFieldLabel.show();
	    actionPerformed();
	    y0 = new double[3];
	}
	void actionPerformed() {
	    parseError = false;
	    ExprParser ep = new ExprParser(textFields[0].getText());
	    expr = ep.parseExpression();
	    if (ep.gotError())
		parseError = true;
	    functionChanged = true;
	}
	void getField(double result[], double y[]) {
	    double k = .00001;
	    int i;
	    for (i = 0; i != 3; i++)
		y0[i] = y[i];
	    double pot0 = expr.eval(y0);

	    y0[0] += k;
	    result[0] = pot0-expr.eval(y0);
	    y0[0] = y[0];

	    y0[1] += k;
	    result[1] = pot0-expr.eval(y0);
	    y0[1] = y[1];
	    
	    result[2] = pot0*.01;
	    for (i = 0; i != 2; i++)
		if (!(result[i] > -10 && result[i] < 10))
		    boundCheck = true;
	}
	VecFunction createNext() { return new UserDefinedFunction(); }
    };
    class UserDefinedFunction extends VecFunction {
	Expr exprs[];
	String getName() { return "user-defined field"; }
	void setup() {
	    exprs = new Expr[3];
	    textFields[0].setText("x");
	    textFields[1].setText("y");
	    textFieldLabel.setText("Field Functions");
	    textFieldLabel.show();
	    int i;
	    for (i = 0; i != 2; i++)
		textFields[i].show();
	    actionPerformed();
	}
	void actionPerformed() {
	    int i;
	    parseError = false;
	    for (i = 0; i != 2; i++) {
		ExprParser ep = new ExprParser(textFields[i].getText());
		exprs[i] = ep.parseExpression();
		if (ep.gotError())
		    parseError = true;
	    }
	    functionChanged = true;
	}
	void getField(double result[], double y[]) {
	    double k = .0002;
	    int i;
	    for (i = 0; i != 2; i++) {
		result[i] = k*exprs[i].eval(y);
		if (!(result[i] > -10 && result[i] < 10))
		    boundCheck = true;
	    }
	    result[2] = 0;
	}
	boolean nonGradient() { return true; }
	VecFunction createNext() { return null; }
    };
#endif

    class DrawData {
	public Graphics g;
	public double mult;
	public double field[], vv[];
    };

    class Particle {
	public double pos[];
	public double vel[];
	public double lifetime;
	public double phi, theta, phiv, thetav;
	public double stepsize;
	public Color color;
	Particle() {
	    pos = new double[3]; vel = new double[3];
	    stepsize = 1;
	}
    };

    class FieldVector {
	public int sx1, sy1, sx2, sy2;
	public double p1[], p2[];
	public int col;
	public int viewPri;
    };

    class GridElement {
	public double height, div, curl, normdot, vecX, vecY;
	public boolean visible, valid;
    };

#ifdef BUILD_E    
    // this is a complex number class that avoids creating new objects
    // whenever possible.  Takes a little more effort to use, but it is
    // much faster because we don't have to do constant garbage
    // collection.
    class Complex {
	public double a, b;
	Complex() { a = b = 0; }
	void set(double aa, double bb) { a = aa; b = bb; }
	void set(Complex c) { set(c.a, c.b); }
	void add(double r) { a += r; }
	void add(double r, double i) { a += r; b += i; }
	void square() { set(a*a-b*b, 2*a*b); }
	void mult(double c, double d) { set(a*c-b*d, a*d+b*c); }
	void mult(double c) { a *= c; b *= c; }
	void mult(Complex c) { mult(c.a, c.b); }
	void recip() {
	    double n = a*a+b*b;
	    set(a/n, -b/n);
	}
	void pow(double p) {
	    double arg = java.lang.Math.atan2(b, a);
	    arg *= p;
	    double abs = java.lang.Math.pow(a*a+b*b, p*.5);
	    set(abs*java.lang.Math.cos(arg),
		abs*java.lang.Math.sin(arg));
	}
	void sin() {
	    set(cosh(b)*java.lang.Math.sin(a),
		java.lang.Math.cos(a)*sinh(b));
	}
	void cos() {
	    set(cosh(b)*java.lang.Math.cos(a),
		java.lang.Math.sin(a)*sinh(b));
	}
	void log() {
	    set(java.lang.Math.log(a*a+b*b),
		java.lang.Math.atan2(b, a));
	}
	void arcsin() {
	    Complex z2 = new Complex();
	    z2.set(a, b);
	    z2.square();
	    z2.mult(-1);
	    z2.add(1);
	    z2.pow(.5);
	    mult(0, 1);
	    add(z2.a, z2.b);
	    log();
	    mult(0, -1);
	}
    };

    double cosh(double a) {
	return .5*(java.lang.Math.exp(a)+java.lang.Math.exp(-a));
    }
    double sinh(double a) {
	return .5*(java.lang.Math.exp(a)-java.lang.Math.exp(-a));
    }
#endif
};

#ifdef BUILD_V
class ExprState {
    public double x, y, z;
}

class Expr {
    Expr(Expr e1, Expr e2, int v) {
	left = e1;
	right = e2;
	type = v;
    }
    Expr(int v, double vv) {
	type = v;
	value = vv;
    }
    Expr(int v) {
	type = v;
    }
    double eval(double es[]) {
	switch (type) {
	case E_ADD: return left.eval(es)+right.eval(es);
	case E_SUB: return left.eval(es)-right.eval(es);
	case E_MUL: return left.eval(es)*right.eval(es);
	case E_DIV: return left.eval(es)/right.eval(es);
	case E_POW: return java.lang.Math.pow(left.eval(es), right.eval(es));
	case E_UMINUS: return -left.eval(es);
	case E_VAL: return value;
	case E_X:   return es[0]*10;
	case E_Y:   return es[1]*10;
	case E_R:   return java.lang.Math.sqrt(
			      es[0]*es[0]+es[1]*es[1])*10;
	case E_SIN: return java.lang.Math.sin(left.eval(es));
	case E_COS: return java.lang.Math.cos(left.eval(es));
	case E_ABS: return java.lang.Math.abs(left.eval(es));
	case E_EXP: return java.lang.Math.exp(left.eval(es));
	case E_LOG: return java.lang.Math.log(left.eval(es));
	case E_SQRT: return java.lang.Math.sqrt(left.eval(es));
	case E_TAN: return java.lang.Math.tan(left.eval(es));
	default: System.out.print("unknown\n");
	}
	return 0;
    }
    Expr left, right;
    double value;
    int type;
    static final int E_ADD = 1;
    static final int E_SUB = 2;
    static final int E_X = 3;
    static final int E_Y = 4;
    static final int E_Z = 5;
    static final int E_VAL = 6;
    static final int E_MUL = 7;
    static final int E_DIV = 8;
    static final int E_POW = 9;
    static final int E_UMINUS = 10;
    static final int E_SIN = 11;
    static final int E_COS = 12;
    static final int E_ABS = 13;
    static final int E_EXP = 14;
    static final int E_LOG = 15;
    static final int E_SQRT = 16;
    static final int E_TAN = 17;
    static final int E_R = 18;
};

class ExprParser {
    String text;
    String token;
    int pos;
    int tlen;
    boolean err;

    void getToken() {
	while (pos < tlen && text.charAt(pos) == ' ')
	    pos++;
	if (pos == tlen) {
	    token = "";
	    return;
	}
	int i = pos;
	int c = text.charAt(i);
	if ((c >= '0' && c <= '9') || c == '.') {
	    for (i = pos; i != tlen; i++) {
		if (!((text.charAt(i) >= '0' && text.charAt(i) <= '9') ||
		      text.charAt(i) == '.'))
		    break;
	    }
	} else if (c >= 'a' && c <= 'z') {
	    for (i = pos; i != tlen; i++) {
		if (!(text.charAt(i) >= 'a' && text.charAt(i) <= 'z'))
		    break;
	    }
	} else {
	    i++;
	}
	token = text.substring(pos, i);
	pos = i;
    }

    boolean skip(String s) {
	if (token.compareTo(s) != 0)
	    return false;
	getToken();
	return true;
    }

    void skipOrError(String s) {
	if (!skip(s))
	    err = true;
    }

    Expr parseExpression() {
	if (token.length() == 0)
	    return new Expr(Expr.E_VAL, 0.);
	Expr e = parse();
	if (token.length() > 0)
	    err = true;
	return e;
    }

    Expr parse() {
	Expr e = parseMult();
	while (true) {
	    if (skip("+"))
		e = new Expr(e, parseMult(), Expr.E_ADD);
	    else if (skip("-"))
		e = new Expr(e, parseMult(), Expr.E_SUB);
	    else
		break;
	}
	return e;
    }

    Expr parseMult() {
	Expr e = parseUminus();
	while (true) {
	    if (skip("*"))
		e = new Expr(e, parseUminus(), Expr.E_MUL);
	    else if (skip("/"))
		e = new Expr(e, parseUminus(), Expr.E_DIV);
	    else
		break;
	}
	return e;
    }

    Expr parseUminus() {
	skip("+");
	if (skip("-"))
	    return new Expr(parsePow(), null, Expr.E_UMINUS);
	return parsePow();
    }

    Expr parsePow() {
	Expr e = parseTerm();
	while (true) {
	    if (skip("^"))
		e = new Expr(e, parseTerm(), Expr.E_POW);
	    else
		break;
	}
	return e;
    }

    Expr parseFunc(int t) {
	skipOrError("(");
	Expr e = parse();
	skipOrError(")");
	return new Expr(e, null, t);
    }

    Expr parseTerm() {
	if (skip("(")) {
	    Expr e = parse();
	    skipOrError(")");
	    return e;
	}
	if (skip("x"))
	    return new Expr(Expr.E_X);
	if (skip("y"))
	    return new Expr(Expr.E_Y);
	if (skip("r"))
	    return new Expr(Expr.E_R);
	if (skip("pi"))
	    return new Expr(Expr.E_VAL, 3.14159265358979323846);
	if (skip("e"))
	    return new Expr(Expr.E_VAL, 2.7182818284590452354);
	if (skip("sin"))
	    return parseFunc(Expr.E_SIN);
	if (skip("cos"))
	    return parseFunc(Expr.E_COS);
	if (skip("abs"))
	    return parseFunc(Expr.E_ABS);
	if (skip("exp"))
	    return parseFunc(Expr.E_EXP);
	if (skip("log"))
	    return parseFunc(Expr.E_LOG);
	if (skip("sqrt"))
	    return parseFunc(Expr.E_SQRT);
	if (skip("tan"))
	    return parseFunc(Expr.E_TAN);
	try {
	    Expr e = new Expr(Expr.E_VAL, Double.valueOf(token).doubleValue());
	    getToken();
	    return e;
	} catch (Exception e) {
	    err = true;
	    System.out.print("unrecognized token: " + token + "\n");
	    return new Expr(Expr.E_VAL, 0);
	}
    }

    ExprParser(String s) {
	text = s;
	tlen = text.length();
	pos = 0;
	err = false;
	getToken();
    }
    boolean gotError() { return err; }
};
#endif


interface DecentScrollbarListener {
    abstract void scrollbarValueChanged(DecentScrollbar ds);
    abstract void scrollbarFinished(DecentScrollbar dc);
}

// this is a scrollbar that notifies us when the user is _done_ fiddling
// with the value.
class DecentScrollbar extends Canvas
  implements MouseListener, MouseMotionListener {
    int value, lo, hi;
    DecentScrollbarListener listener;
    DecentScrollbar(DecentScrollbarListener parent, 
		    int start, int lo_, int hi_) {
	value = start;
	lo = lo_;
	hi = hi_;
	listener = parent;
	addMouseListener(this);
	addMouseMotionListener(this);
	gray1 = new Color(104, 104, 104);
	gray2 = new Color(168, 168, 168);
	gray3 = new Color(192, 192, 192);
	gray4 = new Color(224, 224, 224);
    }
    Color gray1, gray2, gray3, gray4;
    public Dimension getPreferredSize() {
	return new Dimension(20,20);
    }
    static final int tw = 8;
    boolean dragging;
    int thumbpos, dragoffset;
    public void paint(Graphics g) {
	Dimension size = getSize();
	int w = size.width;
	int h = size.height;
	int x = thumbpos = (value-lo)*(w-2-tw)/(hi-lo)+1;
	g.setColor(gray2);
	g.fillRect(0, 0, w, h);
	g.setColor(gray3);
	g.fillRect(x, 2, tw, h-4);
	g.setColor(gray4);
	g.drawLine(0, h-1, w, h-1);
	g.drawLine(w-1, 1, w-1, h-1);
	g.drawLine(x, 1, x+tw-1, 1);
	g.drawLine(x, 1, x, h-2);
	g.setColor(gray1);
	g.drawLine(0, 0, w-1, 0);
	g.drawLine(0, 0, 0, h-1);
	g.drawLine(x+tw-1, 2, x+tw-1, h-2);
	g.drawLine(x+1, h-2, x+tw-1, h-2);
    }
    int getValue() { return value; }
    boolean setValue(int v) {
	if (v < lo)
	    v = lo;
	if (v > hi)
	    v = hi;
	if (value == v)
	    return false;
	value = v;
	repaint();
	return true;
    }
    public void mousePressed(MouseEvent e) {
	if (thumbpos <= e.getX() && thumbpos+tw >= e.getX()) {
	    dragging = true;
	    dragoffset = e.getX()-thumbpos;
	}
    }
    public void mouseReleased(MouseEvent e) {
	if (dragging)
	    listener.scrollbarFinished(this);
	dragging = false;
    }
    public void mouseClicked(MouseEvent e) {
    }
    public void mouseEntered(MouseEvent e) {
    }
    public void mouseExited(MouseEvent e) {
    }
    public void mouseDragged(MouseEvent e) {
	if (!dragging)
	    return;
	int x = e.getX()-dragoffset;
	Dimension size = getSize();
	int v = (x-1)*(hi-lo)/(size.width-2-tw)+lo;
	if (setValue(v))
	    listener.scrollbarValueChanged(this);
    }
    public void mouseMoved(MouseEvent e) {
    }
};
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. <a href="http://www.91gouda.com.cn/">HoME</a><a href="http://91gouda.com.cn/">ÁíÀàС˵ߣɫ
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