Screen Projection

This section explains how to perform screen projection of vectors. Screen projection allows you to obtain the X and Y coordinates (i.e., window coordinates) on the graphics display that correspond to arbitrary positions in 3D space.

Screen Projection

Screen Projection of a Vector

If you want to find out where a point in 3D space appears on the screen, you can use screen projection. By applying screen projection to a vector placed in 3D space, you can obtain the corresponding X and Y coordinates in the rendering area -- these are known as window coordinates.

Origin Is at the Bottom-Left

One important point to note is the position of the origin in the rendering area.

In many fields outside of 3DCG, the top-left corner of the screen is treated as the origin. However, in certain 3DCG contexts that use right-handed coordinate systems, the bottom-left corner is often used instead, due to various technical conventions (though the top-left origin is still used in some cases).

VCSSL Graphics3D adopts a right-handed coordinate system, so the origin of the rendering area is considered to be at the bottom-left.

As a result:

• In VCSSL GUI and VCSSL Graphics2D, the origin is at the top-left.
• In VCSSL Graphics3D, the origin is at the bottom-left.

Keep this difference in mind when combining these systems.

Projecting a Vector onto the Screen

To perform screen projection and obtain the X and Y screen coordinates of a vector, use the projectVectorX(...) and projectVectorY(...) functions, respectively.

- Function Format -

Arguments:

• vectorID: The ID of the vector to project.
• rendererID: The ID of the renderer.

Example Program

Let's get the screen coordinates corresponding to the origin of the world coordinate system. Try writing and running the following code:

import graphics3d.Graphics3DFramework ;
import Graphics3D ;

// Function called at the start of the program
void onStart ( int rendererID ) {

	// Create a vector at the origin
	int vector = newVector( 0.0, 0.0, 0.0 ) ;

	// Place the vector in the world coordinate system
	mountVector( vector, rendererID ) ;

	// Project the vector onto the screen
	int x = projectVectorX( vector, rendererID );
	int y = projectVectorY( vector, rendererID );


	// Output the result
	println( "X=" + x + ", " + "Y=" + y ) ;
}

When you run this program, the VCSSL console will display something like:

This indicates the coordinates near the center of the rendering area.
(The exact values may vary depending on your environment or software version.)

Note: In the Graphics3DFramework, the component ID of the GUI element representing the rendering area can be obtained using the getImageLabel() function.