Transformation pipeline
To create 2D images form 3D scenes, OpenGL requires a series of transforms. Each transform changes the coordinate space that is being used.These are common operations and the transforms and coordinate spaces used.
- Move the models around to prepare the world
Object transforms
World coordinate space - Adjust for the camera position and orientation
Camera/Inverse camera/modelview transform
Eye coordinates - Reshape the viewable scene to fit OpenGL's view
Projection transform
Clip coordinate space - Adjust for perspective
Perspective divide
Normalized device coordinate space - Reshape OpenGL's view to fit the image resolution
Viewport/image transform
Window/image coordinate space
Object transforms
The individual models of the virtual world need to composed into a coherent scene. Since each model has a different origin and orientation, many transforms are needed to build a scene from individual models.
Camera transform
The OpenGL camera is fixed at the origin, looking down the -z axis, with its up being along +y. This camera is not useful for general scenes, so a camera transform must be applied. This transform adjust the OpenGL view, so the scene will render from a specified camera view. A camera matrix can be formed using the camera position and its basis vectors. However, this matrix transforms points into the camera's reference frame and not into OpenGL's. Once we form the camera matrix, its inverse is used to move world coordinates into OpenGL's view coordinates.
Projection transform
OpenGL can only render objects in the range \( (-1, -1, -1) - (1, 1, 1) \). This space is called Normalized Device Coordinates. Our view of the world is often a pyramid shaped frustum and thus must be reshaped to fit OpenGL's renderable region. The projection matrix warps the viewable scene into this space. After this transform, all objects outside the viewable region are discarded.
There are two main projection transforms: orthographic and perspective. Orthographic preserves parallel lines and relative object sizes, however far away objects do not appear smaller. Orthographic projection is often used in design tools. Perspective projection makes far away objects appear smaller and matches what humans perceive, however it is difficult to compare object size in perspective projection. Perspective projection is often used when viewing realistic 3D scenes.
Higher res orthographic image
Higher res perspective image
Perspective divide
Perspective transforms are non-linear and require adjustment of the homogeneous coordinates. This step scales all the vertices by their distance from the camera to adjust for perspective warping. After this operation, The scene is confined to the \( (-1, -1, -1) - (1, 1, 1) \) range.