2.2.1 A simple 3D projection routine | JAVA 3D Programming | Chapter 2

2.2.1 A simple 3D projection routine

Here is my simple 3D−projection routine. The projectPoint method takes two Point3d instances, the first is the input 3D−coordinate while the second will be used to store the result of the projection from 3D to 2D coordinates (the z attribute will be 0). Point3d is one of the classes defined by Java 3D. Refer to the Java 3D JavaDoc for details. Essentially, it has three public members, x, y, and z that store the coordinates in the three axes.

From AwtRenderingEngine.java

       
private int xScreenCenter = 320/2;
private int yScreenCenter = 240/2;
private Vector3d screenPosition = new Vector3d( 0, 0, 20 );
private Vector3d viewAngle = new Vector3d( 0, 90, 180 );
private static final double DEG_TO_RAD = 0.017453292;
private double modelScale = 10;
CT = Math.cos( DEG_TO_RAD * viewAngle.x );
ST = Math.sin( DEG_TO_RAD * viewAngle.x );
CP = Math.cos( DEG_TO_RAD * viewAngle.y );
SP = Math.sin( DEG_TO_RAD * viewAngle.y );
public void projectPoint( Point3d input, Point3d output )
{
double x = screenPosition.x + input.x * CT − input.y * ST;
double y = screenPosition.y + input.x * ST * SP + input.y * CT * SP
+ input.z * CP;
double temp = viewAngle.z / (screenPosition.z + input.x * ST * CP
+ input.y * CT * CP − input.z * SP );
output.x = xScreenCenter + modelScale * temp * x;
output.y = yScreenCenter − modelScale * temp * y;
output.z = 0;
}

       
 

Let’s quickly project some points using this routine to see if it makes sense. The result of running seven 3D points through the projectPoint method is listed in table 2.1.

CT: 1

ST: 0

SP: 1

CP: 0

Table 2.1 Sample output from the projectPoint method to project points from 3D−world coordinates to 2D−screen Coordinates

WX	WY	WZ	SX	SY
1	1	0	250	30
-1	1	0	70	30
1	-1	0	250	210
-1	-1	0	70	210
0	0	0	160	120
1	1	1	255	25
-1	-1	1	65	215

 

Figure 2.3 The positions of some projected points

Plotting these points by hand using a 2D graphics program (figure 2.3), you can see that they seem to make sense. Projecting the point 0,0,0 places a point at the center of the screen (160,120). While you have symmetry about the corners of the cube, increasing the Z−coordinate appears to move the two opposing corners (1,1,1 and −1,−1,1) closer to the viewer.

Taking a look at the projectPoint function again, you can see it uses the following parameters:

• Input point x, y, and z coordinates

• Center of the screen

• Sin and cosine of the viewer’s angle of view

• Distance of the screen from the viewer

• Model scaling factor

This very simple projection function is adequate for simple 3D projection. As you become more familiar with Java 3D, you will see that it includes far more powerful projection abilities. These allow you to render to stereo displays (such as head−mounted displays) or perform parallel projections. (In parallel projections, parallel lines remain parallel after projection.)