Why 3D graphics is more complex than 2D

3D graphics is more complex because the scene has an extra dimension, but the display is still 2D. The 3D data must be converted into a 2D image, and this needs many extra steps that do not exist in 2D.

2D pipeline: world coordinates → window-to-viewport transformation (with clipping) → device coordinates.

3D pipeline:

Modeling coords
   | modeling transform
World coords
   | viewing transform (camera)
Viewing coords
   | projection (parallel/perspective)
Projection coords
   | normalization + 3D clipping
Normalized coords
   | hidden surface removal, shading
   | workstation transform
Device coords

Reasons for extra complexity:

1. Viewing specification: in 2D only a window is needed. In 3D we must choose a camera position, view direction, up vector, view plane and view volume (a viewing-coordinate transformation is required).
2. Projection: 3D points must be projected on a plane (parallel or perspective). This needs 4×4 matrices and a homogeneous divide.
3. Transformations: rotation can be about any axis (not only a point), so composite matrices are bigger (4×4) and order-dependent.
4. Clipping: done against a 3D view volume (a box or frustum) with six planes, not a 2D rectangle.
5. Visible-surface detection: objects hide each other, so back-face, z-buffer or scan-line methods are required.
6. Illumination and shading: realistic images need light models, surface normals and shading (Gouraud, Phong).
7. Object representation: surfaces, solids and curved patches need polygon tables, splines, etc., and more data.
8. Computation and memory: far more points, depth buffer and floating-point work.