Transformations and 3D

This article describes the 3D math functions bundled with OOGL and how they can be used for view transformation and perspective projection.

Basic transformations

To rotate the triangle in the sample from the previous article, we can use a rotation matrix. Because we're going to use 3D coordinates soon enough, let's use the Mat4 class, which supports 3D transformations.

GL::Mat4 trans;
trans.RotateZ( GL::Rad( 10 ) );

The constructor of the matrix class initializes it as a 4-by-4 identity matrix. The RotateZ member function multiplies it by a rotation matrix around the Z axis. All trigonometry functions in OOGL take radians. The Rad utility function is used here to convert degrees to radians.

To apply this transformation to the vertices, it can be uploaded to the graphics card as a uniform. The vertex shader will now look like this:

in vec2 position;
uniform mat4 trans;
void main() {
	gl_Position = trans * vec4( position, 0.0, 1.0 );
}

The uniform can be set with the overloaded SetUniform member function:

program.SetUniform( program.GetUniform( "trans" ), trans );

If you run your program now, the triangle will be rotated by 10 degrees around the origin.

View transformation and perspective projection

Recall that 3D requires transforming the world to the camera coordinate system, perspective projection and perspective division. The latter is performed by OpenGL based on the w coordinate but the view transformation and projection matrix have to be supplied by you.

The Mat4 class contains implementations of gluLookAt and glPerspective for your convenience. Setting up the complete transformation is easy.

GL::Mat4 model;
model.RotateZ( GL::Rad( 10 ) );
GL::Mat4 view = GL::Mat4::LookAt( GL::Vec3( 1, 1, 1 ), GL::Vec3( 0, 0, 0 ), GL::Vec3( 0, 0, 1 ) );
GL::Mat4 proj = GL::Mat4::Perspective( GL::Rad( 60 ), 800.0f / 600.0f, 0.1f, 10.0f );

program.SetUniform( program.GetUniform( "trans" ), proj * view * model );

You can also do the transformations in software using the Mat4::Project and Mat4::UnProject functions or multiplying a Vec3 by the transformation matrix yourself and performing perspective division.