Before going through this post you might like to read my previous post, to understand the general things.
Last time, I have discussed about some of the general theory needed to draw a three dimensional Sphere on the computer screen. Today, I am going to demonstrate the actual drawing of the sphere on the screen. The complete working code to draw the sphere will be provided in this post.
For working with Three D graphics, You need a good grasp of two main concepts:
Then on top of the RPoint, You could generate another object with the properties of a sphere. Sphere has a center, radius, and lots of points through its surface. It can rotate, translate etc.
Last time, I have discussed about some of the general theory needed to draw a three dimensional Sphere on the computer screen. Today, I am going to demonstrate the actual drawing of the sphere on the screen. The complete working code to draw the sphere will be provided in this post.
For working with Three D graphics, You need a good grasp of two main concepts:
- Point and its operations ( translations)
- Concept of projections in space geometry
/**
*
* @author Rajan Prasad Upadhyay
* class RPoint.java
*/
public class RPoint {
public double x;
public double y;
public double z;
public RPoint(){}
public RPoint(double x,double y,double z){
this.x=x;
this.y=y;
this.z=z;
}
public void viewPoint(){
System.out.println("("+x+","+y+","+z+")");
}
public int getX(){
int i=(int)Math.rint(x);
return i;
}
public int getY(){
int i=(int)Math.rint(y);
return i;
}
public int getZ(){
int i=(int)Math.rint(z);
return i;
}
public RPoint getRotateAlongTheta(int radius,double theta,RPoint center){
double tx=x-center.x,ty=y-center.y,tz=z-center.z;
double tx1,ty1,tz1;
tx1=tx*Math.cos(Math.toRadians(theta))-tz*Math.sin(Math.toRadians(theta));
tz1=tx*Math.sin(Math.toRadians(theta))+tz*Math.cos(Math.toRadians(theta));
tx=tx1+center.x;
tz=tz1+center.z;
RPoint p=new RPoint(tx,y,tz);
return p;
}
public RPoint getRotateAlongPhi(int radius,double phi, RPoint center){
double tx=x-center.x,ty=y-center.y,tz=z-center.z;
double tx1,ty1,tz1;
tx1=tx*Math.cos(Math.toRadians(phi))-tz*Math.sin(Math.toRadians(phi));
ty1=tx*Math.sin(Math.toRadians(phi))+tz*Math.cos(Math.toRadians(phi));
tx=tx1+center.x;
ty=ty1+center.y;
RPoint p=new RPoint(tx,ty,z);
return p;
}
//unit vectors
public double getL(){
double a=x/Math.sqrt(x*x+y*y+z*z);
return a;
}
public double getM(){
double a=y/Math.sqrt(x*x+y*y+z*z);
return a;
}
public double getN(){
double a=z/Math.sqrt(x*x+y*y+z*z);
return a;
}
//project coordiantes functions
public int getViewX(int cz){
int a=(int)Math.rint(cz*x/z);
return a;
}
public int getViewY(int cz){
int a=(int)Math.rint((cz)*y/z);
return a;
}
public int getViewZ(int cz){
int a=(cz);
return a;
}
//3d translations functions
public RPoint translate( RPoint p){
RPoint a=new RPoint(x-p.x,y=p.y,z-p.z);
return a;
}
public RPoint inverseTranslate( RPoint p){
RPoint a=new RPoint(x+p.x,y+p.y,z+p.z);
return a;
}
public void RotateAlongTheta( double theta, RPoint center){
double tx=(x-center.x)*Math.cos(Math.toRadians(theta))-(z-center.z)*Math.sin(Math.toRadians(theta));
double tz=(x-center.x)*Math.sin(Math.toRadians(theta))+(z-center.z)*Math.cos(Math.toRadians(theta));
x=tx+center.x;
z=tz+center.z;
}
public void RotateAlongPhi( double phi, RPoint center){
double tz=(z-center.z)*Math.cos(Math.toRadians(-phi))-(y-center.y)*Math.sin(Math.toRadians(-phi));
double ty=(z-center.z)*Math.sin(Math.toRadians(-phi))+(y-center.y)*Math.cos(Math.toRadians(-phi));
y=ty+center.y;
z=tz+center.z;
}
public RPoint RotateAlongX(int theta, RPoint center){
//x does not change
double tz=(z-center.z)*Math.cos(Math.toRadians(-theta))-(y-center.y)*Math.sin(Math.toRadians(-theta));
double ty=(z-center.z)*Math.sin(Math.toRadians(-theta))+(y-center.y)*Math.cos(Math.toRadians(-theta));
return new RPoint(x,ty+center.y,tz+center.z);
}
public RPoint RotateAlongY( int theta, RPoint center){
//ie rotating along y axix , clockwise
double tx=(x-center.x)*Math.cos(Math.toRadians(theta))-(z-center.z)*Math.sin(Math.toRadians(theta));
double tz=(x-center.x)*Math.sin(Math.toRadians(theta))+(z-center.z)*Math.cos(Math.toRadians(theta));
return new RPoint(tx+center.x,y,tz+center.z);
}
public RPoint RotateAlongZ(int theta, RPoint center){
//z constant
double tx=(x-center.x)*Math.cos(Math.toRadians(theta))-(y-center.y)*Math.sin(Math.toRadians(theta));
double ty=(x-center.x)*Math.sin(Math.toRadians(theta))+(y-center.y)*Math.cos(Math.toRadians(theta));
return new RPoint(tx+center.x,ty+center.y,z);
}
//prospective view coordinate giving functions
public void RevolveAlongY(double theta, RPoint sample){
double tx=(x-sample.x)*Math.cos(Math.toRadians(theta))-(z-sample.z)*Math.sin(Math.toRadians(theta));
double tz=(x-sample.x)*Math.sin(Math.toRadians(theta))+(z-sample.z)*Math.cos(Math.toRadians(theta));
x=tx+sample.x;
z=tz+sample.z;
}
public void RevolveAlongX(double theta, RPoint sample){
}
public RPoint getPerspective( RPoint viewPoint){
double xp=x-(-z)/(viewPoint.z-z)*(x-viewPoint.x);
double yp=y-(-z)/(viewPoint.z-z)*(y-viewPoint.y);
double zp=0;
return new RPoint(xp,yp,zp);
}
public RPoint rotateAlongY(double angle){
double x2=x*Math.cos(Math.toRadians(angle))-z*Math.sin(Math.toRadians(angle));
double y2=x*Math.sin(Math.toRadians(angle))+z*Math.cos(Math.toRadians(angle));
return new RPoint(x2,y2,z);
}
}
Then on top of the RPoint, You could generate another object with the properties of a sphere. Sphere has a center, radius, and lots of points through its surface. It can rotate, translate etc.
/**
*
* @author Rajan Prasad Upadhyay
* class RSphere.java
*/
import java.awt.Color;
import java.awt.Graphics;
public class RSphere {
RPoint center;
RPoint viewPoint=new RPoint(600,400,2000);
int radius;
public Graphics g;
int delphi;//used to determine the number of rows in mat[][] ie point matrix
int deltheta;//determine the num of cols in the mat
int numOfRows;
int numOfCols;
RPoint mat[][];//matrix of points// actual world coordinates
RPoint mat1[][];//to hold projected coordinates
RPoint mat2[][];//matrix according to view points angle with the z axis;;
int angle=0;
public RSphere(){
center=new RPoint(0,0,0);
radius=50;
deltheta=20;
delphi=20;
numOfRows=180/delphi;
numOfCols=360/deltheta;
}
public void setGraphics(Graphics gh){
if(gh != null){
this.g = gh;
}else{
System.out.println("Your graphics context is null.");
}
}
public void setColor(Color c){
g.setColor(c);
}
public void set_Center( RPoint p){
//this funciton should be called at the beginning only
center=p;
}
public void set_viewer(int x,int y,int z){
viewPoint=new RPoint(x,y,z);
}
public void set_Center(int x,int y,int z){
center=new RPoint(x,y,z);
}
public void setRadius(int r){
radius=r;
}
public void initialize(){
numOfRows = 180/delphi+1;
numOfCols = 360/deltheta+1;
mat = new RPoint[numOfRows][numOfCols];
mat1 = new RPoint[numOfRows][numOfCols];
mat2 = new RPoint[numOfRows][numOfCols];
System.out.print("center=");
center.viewPoint();
System.out.println("radius="+this.radius);
double theta = 0;
double phi = 90;
for(int row = 0; row<numOfRows; row++){
for(int col = 0;col < numOfCols; col++){
//creating the matrix
mat[row][col] = new RPoint(
center.x+radius*Math.cos(Math.toRadians(theta))*Math.cos(Math.toRadians(phi))
,center.y+radius*Math.sin(Math.toRadians(phi))
,center.z+radius*Math.sin(Math.toRadians(theta))*Math.cos(Math.toRadians(phi))
);
mat1[row][col] = mat[row][col].getPerspective(viewPoint);
theta += deltheta;
theta %= 360;
}
phi -= delphi;
theta = 0;
}
}//initialize
public void drawLatitudes(){
int cz = -20;
for(int i=0;i<numOfRows;i++){
for(int j=0;j<(numOfCols-1);j++){
g.drawLine(mat[i][j].getX(), mat[i][j].getY(), mat[i][j+1].getX(), mat[i][j+1].getY());
}
}
}
public void drawLongitudes(){
int cz=0;
for(int i=0;i<numOfRows-1;i++){
for(int j=0;j<numOfCols;j++){
g.drawLine(mat[i][j].getX(), mat[i][j].getY(), mat[i+1][j].getX(), mat[i+1][j].getY());
}
}
}
public void rotateAlongX(int angle){
for(int i=0;i<numOfRows;i++){
for(int j=0;j<numOfCols;j++){
mat[i][j]=mat[i][j].RotateAlongX(angle,center);//perfect
}
}
}
public void rotateAlongY(int angle){
for(int i=0;i<numOfRows;i++){
for(int j=0;j<numOfCols;j++){
mat[i][j]= mat[i][j].RotateAlongY(angle,center);//perfect
}
}
}
public void rotateAlongZ(int angle){
for(int i=0;i<numOfRows;i++){
for(int j=0;j<numOfCols;j++){
mat[i][j]=mat[i][j].RotateAlongZ(angle,center);//perfect
}
}
}
public void updatePerspective(){
for(int i=0;i<numOfRows;i++){
for(int j=0;j<numOfCols;j++){
mat1[i][j]=mat[i][j].getPerspective(viewPoint);
}
}
}
public void calculatePrespective(){
for(int i=0;i<numOfRows;i++){
for(int j=0;j<numOfCols;j++){
mat1[i][j]=mat[i][j].getPerspective(viewPoint);
}
}
}
public void prospectiveView(){
calculatePrespective();
viewTheLines(mat1);
}
public void viewTheLines( RPoint mat1[][]){
//longitute
for(int i=0;i<numOfRows-1;i++){
for(int j=0;j<numOfCols;j++){
g.drawLine(mat1[i][j].getX(), mat1[i][j].getY(), mat1[i+1][j].getX(), mat1[i+1][j].getY());
}
}
//latitude
for(int i=0;i<numOfRows;i++){
for(int j=0;j<(numOfCols-1);j++){
g.drawLine(mat1[i][j].getX(), mat1[i][j].getY(), mat1[i][j+1].getX(), mat1[i][j+1].getY());
}
}
}
}
and finally to display the frame we have
/**
*
* @author Rajan Prasad Upadhyay
* class RFrame.java
*/
import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.event.KeyEvent;
import javax.swing.JFrame;
public class RFrame extends JFrame{
RSphere earth = new RSphere();
RPoint earthCenter=new RPoint(600,400,-1500);
int viewAngle = 0;
Graphics g;
private void arrangeGraphics(){
earth.set_Center(earthCenter);
earth.setRadius(200);
earth.initialize();
g = this.getGraphics();
if(g != null){
earth.setGraphics(g);
}else{
System.out.println("The g is null, Frame.java");
}
if(earth.g != null){
earth.setColor(Color.blue);
}else{
System.out.println("Graphics is null");
}
}
public RFrame(){
initComponents();
arrangeGraphics();
earth.drawLatitudes();
earth.drawLongitudes();
}
private void initComponents(){
setDefaultCloseOperation(javax.swing.WindowConstants.EXIT_ON_CLOSE);
this.setMinimumSize(new Dimension(1000,800));
addKeyListener(new java.awt.event.KeyAdapter() {
public void keyPressed(java.awt.event.KeyEvent evt) {
formKeyPressed(evt);
}
});
javax.swing.GroupLayout layout = new javax.swing.GroupLayout(getContentPane());
getContentPane().setLayout(layout);
layout.setHorizontalGroup(
layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
.addGap(0, 483, Short.MAX_VALUE)
);
layout.setVerticalGroup(
layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
.addGap(0, 320, Short.MAX_VALUE)
);
pack();
}
private void formKeyPressed(java.awt.event.KeyEvent evt){
RPoint p = earth.center;
if(evt.getKeyCode()==KeyEvent.VK_LEFT){
g.clearRect(0, 20, this.getWidth(), this.getHeight());
earth.rotateAlongZ(5);
earth.drawLatitudes();
earth.drawLongitudes();
}if(evt.getKeyCode()==KeyEvent.VK_SPACE){
g.clearRect(0, 20, this.getWidth(), this.getHeight());
earth.rotateAlongY(1);
earth.drawLatitudes();
earth.drawLongitudes();
}
}
@Override
public void paint(Graphics g){
earth.drawLatitudes();
earth.drawLongitudes();
}
public static void main(String [] args){
RFrame f = new RFrame();
f.setVisible(true);
}
}
Now try running the code and press the Space and Left arrow button on the key-board. Have fun.
