From 3D Models to 2D Pictures

Unit IV closes the course: how do we view a 3D scene on a 2D display? We classify projections, derive their matrices, and remove hidden surfaces so only visible polygons are drawn.

Why Projections Matter

A pinhole camera is the world's simplest perspective projection. Architecture and engineering, however, often want parallel projection so that measurements remain proportional regardless of depth. The choice depends on the audience:

• Cinema, games, AR/VR: perspective for realism.
• Engineering blueprints: orthographic so depth does not distort dimensions.

Why Hidden Surface Removal Matters

With no HSR, far surfaces would overwrite near ones (or vice versa) and the scene would look chaotic. Z-buffer is universal in modern GPUs because it is simple, parallel-friendly, and handles arbitrary geometry. Painter's algorithm is conceptually simpler but breaks on intersecting polygons.

Pipeline Position

Modeling -> View -> Projection -> Clipping -> Perspective Divide -> Viewport -> Rasterize -> Depth test (z-buffer) -> Fragment shading -> Framebuffer.

Goals

• Compare parallel vs perspective projections.
• Distinguish orthographic, axonometric (iso/di/trimetric), and oblique (cavalier, cabinet).
• Identify 1-, 2-, 3-point perspective by vanishing points.
• Implement z-buffer and painter's algorithm and explain failure modes.