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13
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1 // Draw the graph of a function
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2 // version 1.0 (c) K.Sasano
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3
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4 import java.applet.Applet;
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5 import java.awt.*;
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6 import java.awt.event.*;
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7 import java.awt.BorderLayout;
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8 import java.awt.Frame;
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9 import java.awt.Font;
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10 import java.awt.GraphicsConfiguration;
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11 import java.util.Enumeration;
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12 import javax.media.j3d.*;
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13 import javax.vecmath.*;
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14 import com.sun.j3d.utils.universe.*;
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15 import com.sun.j3d.utils.applet.MainFrame;
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16 import com.sun.j3d.utils.behaviors.mouse.MouseRotate;
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17 import com.sun.j3d.utils.behaviors.mouse.MouseTranslate;
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18 import com.sun.j3d.utils.behaviors.mouse.MouseZoom;
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19 import com.sun.j3d.utils.geometry.Text2D;
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20
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21 public class graff3d extends Applet {
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22
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23 // global variables
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24 float xwidth;
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25 float x0;
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26 float ywidth;
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27 float y0;
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28 float xdelta;
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29 float ydelta;
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30 float z0;
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31 float zwidth;
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32 float zvalue[][];
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33 float zcenter[][];
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34 Shape3D surfaceGraph;
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35 Shape3D meshGraph;
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36 Shape3D xyPlane;
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37 Shape3D xyzAxes;
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38 Shape3D xyzArrowHead;
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39 TransformGroup xyzAxesLabels;
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40
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41 //key behavior
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42 public class KeyBehavior extends Behavior{
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43
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44 private BranchGroup bg;
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45 private WakeupOnAWTEvent wue;
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46
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47 KeyBehavior(BranchGroup bg){
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48 this.bg=bg;
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49 }
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50
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51 public void initialize(){
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52 this.wakeupOn(wue = new WakeupOnAWTEvent(KeyEvent.KEY_PRESSED));
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53 }
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54
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55 public void processStimulus(Enumeration criteria){
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56 AWTEvent ae = (wue.getAWTEvent())[0];
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57 char c=((KeyEvent)ae).getKeyChar();
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58 TransparencyAttributes
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59 surftr = (surfaceGraph.getAppearance()).getTransparencyAttributes();
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60 TransparencyAttributes
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61 meshtr = (meshGraph.getAppearance()).getTransparencyAttributes();
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62 TransparencyAttributes
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63 xytr = (xyPlane.getAppearance()).getTransparencyAttributes();
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64
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65 if(c=='s'){ //Show/Erase surfacegraph
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66 addSurface=!addSurface;
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67 if(addSurface){
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68 surftr = new TransparencyAttributes(TransparencyAttributes.NONE,0.0f);
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69 }else{
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70 surftr = new TransparencyAttributes(TransparencyAttributes.NICEST,1.0f);
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71 }
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72 }
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73 if(c=='m'){ //Show/Erase meshgraph
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74 float tr;
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75 addMesh=!addMesh;
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76 if(addMesh){ tr= 0.0f; } else { tr=1.0f; }
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77 meshtr = new TransparencyAttributes(TransparencyAttributes.NICEST,tr);
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78 }
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79 if(c=='z'){ //Show/Erase xyplane
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80 float tr;
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81 addXYPlane=!addXYPlane;
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82 if(addXYPlane){ tr= 0.6f; } else { tr=1.0f; }
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83 xytr = new TransparencyAttributes(TransparencyAttributes.NICEST,tr);
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84 }
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85 (xyPlane.getAppearance()).setTransparencyAttributes(xytr);
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86 (meshGraph.getAppearance()).setTransparencyAttributes(meshtr);
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87 (surfaceGraph.getAppearance()).setTransparencyAttributes(surftr);
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88
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89 this.wakeupOn(wue = new WakeupOnAWTEvent(KeyEvent.KEY_PRESSED));
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90 }
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91 }
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92
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93 //create scene
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94 public BranchGroup createSceneGraph() {
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95 BranchGroup objRoot = new BranchGroup();
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96 BoundingSphere bounds = new BoundingSphere();
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97 bounds.setRadius( 1000.0 );
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98
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99 //prepare for movement
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100 TransformGroup objTrans = new TransformGroup();
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101 objRoot.addChild(objTrans);
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102
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103 objTrans.setCapability( TransformGroup.ALLOW_TRANSFORM_READ );
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104 objTrans.setCapability( TransformGroup.ALLOW_TRANSFORM_WRITE );
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105
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106 MouseRotate rotat = new MouseRotate( objTrans );
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107 MouseTranslate trans = new MouseTranslate( objTrans );
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108 MouseZoom zoom = new MouseZoom( objTrans );
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109
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110 rotat.setSchedulingBounds( bounds );
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111 trans.setSchedulingBounds( bounds );
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112 zoom.setSchedulingBounds( bounds );
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113
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114 objTrans.addChild(rotat);
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115 objTrans.addChild(trans);
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116 objTrans.addChild(zoom);
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117
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118 //add xy-plane
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119 objTrans.addChild(xyPlane);
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120
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121 //add graphs
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122 objTrans.addChild(surfaceGraph);
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123 objTrans.addChild(meshGraph);
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124
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125 //add axes
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126 objTrans.addChild(xyzAxes); //axis
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127 objTrans.addChild(xyzArrowHead); //arrowhead
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128 objTrans.addChild(xyzAxesLabels); //label
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129
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130 //add key behavior
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131 KeyBehavior myKeyBehav=new KeyBehavior(objRoot);
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132 myKeyBehav.setSchedulingBounds( bounds );
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133 objRoot.addChild(myKeyBehav);
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134
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135 //compile the object
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136 objRoot.compile();
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137
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138 return objRoot;
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139 }
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140
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141 //surface graph
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142 private Shape3D graph(){
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143 int totalN=6*n*n;
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144
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145 Point3f coord[] = new Point3f[totalN];
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146 Color3f color[] = new Color3f[totalN];
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147
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148 for(int i=0; i<n; i++){
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149 float xi=xmin+i*xdelta;
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150 float xii=xi+xdelta;
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151 float xcenter=xi+0.5f*xdelta;
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152 for(int j=0; j<n; j++){
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153 int tmp=6*(i*n+j);
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154 float yj=ymin+j*ydelta;
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155 float yjj=yj+ydelta;
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156 float ycenter=yj+0.5f*ydelta;
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157
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158 coord[tmp]=new Point3f(xn(xcenter),yn(ycenter),zn(zcenter[i][j]));
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159 coord[tmp+1]=new Point3f(xn(xi),yn(yj),zn(zvalue[i][j]));
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160 coord[tmp+2]=new Point3f(xn(xii),yn(yj),zn(zvalue[i+1][j]));
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161 coord[tmp+3]=new Point3f(xn(xii),yn(yjj),zn(zvalue[i+1][j+1]));
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162 coord[tmp+4]=new Point3f(xn(xi),yn(yjj),zn(zvalue[i][j+1]));
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163 coord[tmp+5]=coord[tmp+1];
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164
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165 color[tmp]=hcolor(zn(zcenter[i][j]));
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166 color[tmp+1]=hcolor(zn(zvalue[i][j]));
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167 color[tmp+2]=hcolor(zn(zvalue[i+1][j]));
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168 color[tmp+3]=hcolor(zn(zvalue[i+1][j+1]));
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169 color[tmp+4]=hcolor(zn(zvalue[i][j+1]));
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170 color[tmp+5]=color[tmp+1];
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171 }
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172 }
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173
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174 int stripCounts[] = new int[n*n];
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175 for(int i=0; i<n*n; i++){stripCounts[i]=6;}
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176
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177 TriangleFanArray tfa =
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178 new TriangleFanArray(
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179 totalN,
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180 TriangleFanArray.COORDINATES|TriangleFanArray.COLOR_3,
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181 stripCounts
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182 );
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183 tfa.setCoordinates(0,coord);
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184 tfa.setColors(0,color);
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185
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186 //construct appearence
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187 TransparencyAttributes surftr;
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188 if(addSurface){
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189 surftr = new TransparencyAttributes(TransparencyAttributes.NONE,0.0f);
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190 }else{
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191 surftr = new TransparencyAttributes(TransparencyAttributes.NICEST,1.0f);
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192 }
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193 PolygonAttributes attr = new PolygonAttributes();
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194 attr.setCullFace(PolygonAttributes.CULL_NONE);
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195 attr.setPolygonMode(PolygonAttributes.POLYGON_FILL);
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196
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197 Appearance appear = new Appearance();
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198 appear.setPolygonAttributes(attr);
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199 appear.setCapability(Appearance.ALLOW_TRANSPARENCY_ATTRIBUTES_READ);
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200 appear.setCapability(Appearance.ALLOW_TRANSPARENCY_ATTRIBUTES_WRITE);
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201 appear.setTransparencyAttributes(surftr);
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202
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203 //construct Shape3D for surface graph
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204 Shape3D graphshape=new Shape3D();
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205 graphshape.removeGeometry(0);
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206 graphshape.addGeometry(tfa);
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207 graphshape.setAppearance(appear);
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208 graphshape.setCapability(Shape3D.ALLOW_APPEARANCE_WRITE);
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209 graphshape.setCapability(Shape3D.ALLOW_APPEARANCE_READ);
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210
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211 return graphshape;
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212 }
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213
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214 //color data corresponding to the height
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215 private Color3f hcolor(float h){
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216 float r,g,b;
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217 h=h*2;
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218 if(h>1){ r=1.0f; g=0.5f; b=0.0f; }
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219 else if(h>0){ r=h*1.0f; g=0.75f-h*0.25f; b=0.0f; }
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220 else if(h>-1){ r=0.0f; g=(1+h)*0.75f; b= -h*0.75f; }
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221 else{ r=0.0f; g=0.0f; b=0.75f;}
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222 return new Color3f(r,g,b);
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223 }
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224
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225 //mesh graph
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226 private Shape3D meshgraph(){
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227 //construct coordinat data
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228 int totalN=2*(nmesh+1)*(nmesh+1);
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229
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230 Point3f coord[] = new Point3f[totalN];
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231 Color3f color[] = new Color3f[totalN];
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232 Color3f lcolor = new Color3f(1.0f, 1.0f, 1.0f);
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233
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234 for(int i=0; i<=nmesh; i++){
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235 float xi=xmin+i*(xmax-xmin)/nmesh;
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236
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237 for(int j=0; j<=nmesh; j++){
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238 int tmp=i*(nmesh+1)+j;
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239 int tmp1=j*(nmesh+1)+i+(nmesh+1)*(nmesh+1);
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240 float yj=ymin+j*(ymax-ymin)/nmesh;
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241
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242 coord[tmp]=new Point3f(xn(xi),yn(yj),zn(f(xi,yj)));
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243 color[tmp]=lcolor;
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244
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245 coord[tmp1]=coord[tmp];
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246 color[tmp1]=color[tmp];
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247 }
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248 }
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249
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250 int stripCounts[];
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251 stripCounts= new int[2*(nmesh+1)];
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252 for(int i=0; i<=2*nmesh+1; i++){stripCounts[i]=nmesh+1;}
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253
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254 LineStripArray lsa =
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255 new LineStripArray(
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256 totalN,
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257 LineStripArray.COORDINATES|LineStripArray.COLOR_3,
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258 stripCounts
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259 );
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260 lsa.setCoordinates(0,coord);
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261 lsa.setColors(0,color);
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262
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263 //construct appearence
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264 LineAttributes attr = new LineAttributes();
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265 attr.setLineWidth(meshLineWidth);
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266
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267 float tr;
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268 if(addMesh){ tr= 0.0f; } else { tr=1.0f; }
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269 TransparencyAttributes transAttrib;
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270 transAttrib = new TransparencyAttributes(TransparencyAttributes.NICEST,tr);
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271
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272 Appearance appear = new Appearance();
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273 appear.setLineAttributes(attr);
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274 appear.setTransparencyAttributes(transAttrib);
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275 appear.setCapability(Appearance.ALLOW_TRANSPARENCY_ATTRIBUTES_READ);
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276 appear.setCapability(Appearance.ALLOW_TRANSPARENCY_ATTRIBUTES_WRITE);
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277
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278 //construct Shape3D for meshgraph
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279 Shape3D graphshape=new Shape3D();
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280 graphshape.removeGeometry(0);
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281 graphshape.addGeometry(lsa);
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282 graphshape.setAppearance(appear);
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283 graphshape.setCapability(Shape3D.ALLOW_APPEARANCE_WRITE);
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284 graphshape.setCapability(Shape3D.ALLOW_APPEARANCE_READ);
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285
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286 return graphshape;
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287 }
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288
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289 //xy-plane
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290 private Shape3D xyplane(){
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291 QuadArray xyp= new QuadArray(4,QuadArray.COORDINATES|QuadArray.COLOR_3);
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292 xyp.setCoordinate(0,new Point3f(0.5f,0.5f,zn(0.0f)));
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293 xyp.setCoordinate(1,new Point3f(-0.5f,0.5f,zn(0.0f)));
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294 xyp.setCoordinate(2,new Point3f(-0.5f,-0.5f,zn(0.0f)));
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295 xyp.setCoordinate(3,new Point3f(0.5f,-0.5f,zn(0.0f)));
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296 for(int i=0; i<4; i++){xyp.setColor(i, new Color3f(1.0f,1.0f,1.0f));}
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297
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298 PolygonAttributes attrib = new PolygonAttributes();
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299 attrib.setCullFace(PolygonAttributes.CULL_NONE);
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300 attrib.setPolygonMode(PolygonAttributes.POLYGON_FILL);
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301
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302 TransparencyAttributes transAttrib;
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303 float tr;
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304 if(addXYPlane){ tr= 0.6f; } else { tr=1.0f; }
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305 transAttrib = new TransparencyAttributes(TransparencyAttributes.NICEST,tr);
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306
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307 Appearance appear = new Appearance();
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308 appear.setPolygonAttributes(attrib);
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309 appear.setTransparencyAttributes(transAttrib);
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310 appear.setCapability(Appearance.ALLOW_TRANSPARENCY_ATTRIBUTES_READ);
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311 appear.setCapability(Appearance.ALLOW_TRANSPARENCY_ATTRIBUTES_WRITE);
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312
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313 Shape3D xyplaneshape=new Shape3D();
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314 xyplaneshape.removeGeometry(0);
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315 xyplaneshape.addGeometry(xyp);
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316 xyplaneshape.setAppearance(appear);
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317 xyplaneshape.setCapability(Shape3D.ALLOW_APPEARANCE_WRITE);
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318 xyplaneshape.setCapability(Shape3D.ALLOW_APPEARANCE_READ);
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319
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320 return xyplaneshape;
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321 }
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322
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323 //axes
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324 private Shape3D axes(){
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325 LineArray a=new LineArray(6,LineArray.COORDINATES|LineArray.COLOR_3);
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326 a.setCoordinate(0,new Point3f(0.6f,yn(0.0f),zn(0.0f)));
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327 a.setCoordinate(1,new Point3f(-0.6f,yn(0.0f),zn(0.0f)));
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328 a.setCoordinate(2,new Point3f(xn(0.0f),0.6f,zn(0.0f)));
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329 a.setCoordinate(3,new Point3f(xn(0.0f),-0.6f,zn(0.0f)));
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330 a.setCoordinate(4,new Point3f(xn(0.0f),yn(0.0f),0.6f));
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331 a.setCoordinate(5,new Point3f(xn(0.0f),yn(0.0f),-0.6f));
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332 for(int i=0; i<6; i++){ a.setColor(i,new Color3f(1.0f,1.0f,0.0f));}
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333
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334 LineAttributes att=new LineAttributes();
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335 att.setLineWidth(2.0f);
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336 Appearance appear = new Appearance();
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337 appear.setLineAttributes(att);
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338
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339 Shape3D ax=new Shape3D();
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340 ax.removeGeometry(0);
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341 ax.addGeometry(a);
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342 ax.setAppearance(appear);
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343
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344 return ax;
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345 }
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346
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347 //arrowhead
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348 private Shape3D arrowhead(){
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349 int scounts[]= new int[3];
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350 for(int i=0; i<3; i++){scounts[i]=10;}
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351
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352 TriangleFanArray ah=new TriangleFanArray(30,
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353 TriangleFanArray.COORDINATES|TriangleFanArray.COLOR_3,
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354 scounts);
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355 ah.setCoordinate(0,new Point3f(0.6f, yn(0.0f), zn(0.0f)));
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356 ah.setCoordinate(10,new Point3f(xn(0.0f),0.6f, zn(0.0f)));
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357 ah.setCoordinate(20,new Point3f(xn(0.0f), yn(0.0f), 0.6f));
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358 float d=(float)Math.PI/4;
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359 for(int i=0 ; i<=8; i++){
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360 ah.setCoordinate(i+1,
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361 new Point3f(0.55f, yn(0.0f)+0.02f * (float)Math.cos(d*i), zn(0.0f)+0.02f *(float)Math.sin(d*i)));
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362 ah.setCoordinate(i+11,
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363 new Point3f(xn(0.0f)+0.02f * (float)Math.cos(d*i), 0.55f, zn(0.0f)+0.02f *(float)Math.sin(d*i)));
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364 ah.setCoordinate(i+21,
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365 new Point3f(xn(0.0f)+0.02f * (float)Math.cos(d*i), yn(0.0f)+0.02f *(float)Math.sin(d*i), 0.55f));
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366 }
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367 Color3f color[]=new Color3f[30];
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368 for(int i=0; i<30; i++){ color[i]=new Color3f(1.0f, 1.0f, 0.0f);}
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369 ah.setColors(0,color);
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370
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371 return new Shape3D(ah);
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372 }
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373
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374 //axes labels
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375 TransformGroup axeslabels(){
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376 TransformGroup tmp = new TransformGroup();
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377
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378 PolygonAttributes polyAttrib = new PolygonAttributes();
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379 polyAttrib.setCullFace(PolygonAttributes.CULL_NONE);
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380 polyAttrib.setBackFaceNormalFlip(true);
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381
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382 Transform3D xmov= (new Transform3D());
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383 xmov.set(new Vector3f(0.63f,yn(0.0f)-0.05f,zn(0.0f)));
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384 Text2D xlbl=new Text2D("x",new Color3f(1.0f,1.0f,0.0f),"Helvetica",24,Font.BOLD);
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385 (xlbl.getAppearance()).setPolygonAttributes(polyAttrib);
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386 TransformGroup xmovg=new TransformGroup(xmov);
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387 xmovg.addChild(xlbl);
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388
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389 Transform3D ymov= new Transform3D();
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390 Transform3D tmpymov=new Transform3D();
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391 tmpymov.rotZ(Math.PI/2.0d);
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392 ymov.set(new Vector3f(xn(0.0f)+0.05f,0.63f,zn(0.0f)));
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393 ymov.mul(tmpymov);
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394 Text2D ylbl=new Text2D("y",new Color3f(1.0f,1.0f,0.0f),"Helvetica",24,Font.BOLD);
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395 (ylbl.getAppearance()).setPolygonAttributes(polyAttrib);
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396 TransformGroup ymovg=new TransformGroup(ymov);
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397 ymovg.addChild(ylbl);
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398
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399 Transform3D zmov= new Transform3D();
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400 Transform3D tmpzmov=new Transform3D();
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401 tmpzmov.rotX(Math.PI/2.0d);
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402 zmov.set(new Vector3f(xn(0.0f)-0.02f,yn(0.0f),0.63f));
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403 zmov.mul(tmpzmov);
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404 Text2D zlbl=new Text2D("z",new Color3f(1.0f,1.0f,0.0f),"Helvetica",24,Font.BOLD);
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405 (zlbl.getAppearance()).setPolygonAttributes(polyAttrib);
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406 TransformGroup zmovg=new TransformGroup(zmov);
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407 zmovg.addChild(zlbl);
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408
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409 tmp.addChild(xmovg);
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410 tmp.addChild(ymovg);
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411 tmp.addChild(zmovg);
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412
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413 return tmp;
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414 }
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415
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416 //get normalized coordinate
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417 float xn(float x){ return (x-x0)/xwidth;}
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418 float yn(float y){ return (y-y0)/ywidth;}
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419 float zn(float z){ return (z-z0)/zwidth;}
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420
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421 //////////// main class ///////////////
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422 public graph3d() {
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423 // preparation for numeric data
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424 xwidth=xmax-xmin;
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425 x0=(xmax+xmin)/2;
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426 ywidth=ymax-ymin;
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427 y0=(ymax+ymin)/2;
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428 xdelta=xwidth/n;
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429 ydelta=ywidth/n;
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430
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431 zvalue = new float[n+1][n+1];
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432 zcenter = new float[n][n];
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433
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434 int i; int j;
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435
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436 for(i=0; i<=n; i++){
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437 for(j=0; j<=n; j++){
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438 zvalue[i][j]=f(xmin+i*xdelta, ymin+j*ydelta);
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439 }
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440 }
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441 for(i=0; i<n; i++){
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442 for(j=0; j<n; j++){
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443 zcenter[i][j]=f(xmin+(i+0.5f)*xdelta, ymin+(j+0.5f)*ydelta);
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444 }
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445 }
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446
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447 // if necessary, determine zmin and zmax automatically
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448 if(zmin==0.0f && zmax==0.0f){
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449 zmin=Float.POSITIVE_INFINITY; zmax=Float.NEGATIVE_INFINITY;
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450 for(i=0; i<=n; i++){
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451 for(j=0; j<=n; j++){
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452 zmin=Math.min(zmin,zvalue[i][j]);
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453 zmax=Math.max(zmax,zvalue[i][j]);
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454 }
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455 }
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456 for(i=0; i<n; i++){
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457 for(j=0; j<n; j++){
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458 zmin=Math.min(zmin,zcenter[i][j]);
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459 zmax=Math.max(zmax,zcenter[i][j]);
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460 }
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461 }
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462 }
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463
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464 zwidth=zmax-zmin;
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465 z0=(zmax+zmin)/2;
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466
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467 /////////// main part ///////////
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468 setLayout(new BorderLayout());
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469
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470 GraphicsConfiguration config = SimpleUniverse.getPreferredConfiguration();
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471
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472 Canvas3D canvas = new Canvas3D(config);
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473 add("Center", canvas);
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474
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475 SimpleUniverse universe = new SimpleUniverse(canvas);
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476 universe.getViewingPlatform().setNominalViewingTransform();
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477
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478 //construct graphic objects
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479 surfaceGraph = graph();
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480 meshGraph = meshgraph();
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481 xyPlane = xyplane();
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482 xyzAxes = axes();
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483 xyzArrowHead = arrowhead();
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484 xyzAxesLabels = axeslabels();
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485
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486 BranchGroup scene = createSceneGraph();
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487 universe.addBranchGraph(scene);
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488 }
|
|
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489
|
|
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490 //main method to make both of Application and Applet
|
|
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491 public static void main(String[] args) {
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492 Frame frame = new MainFrame(new graff3d(), 480, 480);
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493 }
|
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494
|
|
|
495 /////////////////////////////////////////////////
|
|
|
496 // define our function and give necessary data //
|
|
|
497 /////////////////////////////////////////////////
|
|
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498
|
|
|
499 // our function
|
|
|
500 float f(float x, float y){
|
|
|
501 return x*x-y*y;
|
|
|
502 //return x*x*x + y*y*y - 3*x*y;
|
|
|
503 //return (y-x*x)*(y-2*x*x);
|
|
|
504 //return (float)Math.sin(x*x+y*y);
|
|
|
505 //if(x==0.0f){ return 0.0f; } else { return y*y/x; }
|
|
|
506 //if((x==0.0f) && (y==0.0f)){ return 0.5f; } else {return x*y/(x*x+y*y);}
|
|
|
507 }
|
|
|
508
|
|
|
509 // domain of definition
|
|
|
510 float xmin=-1.0f; // min of x
|
|
|
511 float xmax=1.0f; // max of x
|
|
|
512 float ymin=-1.0f; // min of y
|
|
|
513 float ymax=1.0f; // max of y
|
|
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514
|
|
|
515 // range of the value
|
|
|
516 // If both of zmin and zmax are set to 0.0f, then zmin and zmax
|
|
|
517 // are calculated automatically.
|
|
|
518 float zmin=0.0f; // min of z
|
|
|
519 float zmax=0.0f; // max of z
|
|
|
520
|
|
|
521 int n=20; // number of divisions for surface graph
|
|
|
522 int nmesh=20; // number of divisions for mesh graph
|
|
|
523
|
|
|
524 float meshLineWidth=2.0f; // width of lines in mesh graph
|
|
|
525
|
|
|
526 boolean addSurface=true; // FLAG : show/erase surface graph
|
|
|
527 boolean addMesh=true; // FLAG : show/erase mesh graph
|
|
|
528 boolean addXYPlane=false; // FLAG : show/erase xy-plane
|
|
|
529 }
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