3D Viewing Pipeline

Theory of Computation & Computer Graphics — Three-Dimensional Transformation, NEC licence examination syllabus (Nepal Engineering Council).

3D Viewing Pipeline

The multi-stage journey from a 3D world to a flat 2D image on your screen.

🎬 The Pipeline Stages

1. Modeling transformationPosition objects within the 3D world (translate/rotate/scale each object into place).

2. Viewing transformationConvert world coordinates into "camera/eye" coordinates, based on where the virtual viewer is looking from.

3. ProjectionFlatten the 3D scene down into 2D (covered fully in the next topic).

4. Viewport mappingMap the projected 2D coordinates onto actual screen pixels — same idea as the 2D window-to-viewport mapping, one more time.

💡 One-liner: list the 4 stages of the 3D viewing pipeline in the correct order — a common short-answer question testing whether you understand the overall flow, not just individual formulas.

What each stage is actually for

The four stages answer four different questions, and naming them in order is a standard short-answer question.

🎬 The pipeline, as four questions

ModelingWhere does each object sit in the world? Each model is built at its own origin, then placed.

ViewingWhere is the camera, and which way is it pointing? Re-expresses the world relative to the viewer.

ProjectionHow does a 3D scene become flat? Parallel or perspective — the next topic.

ViewportWhich pixels? The same window-to-viewport mapping as in 2D.

The viewing stage is the one worth understanding rather than reciting. Moving the camera right is equivalent to moving the entire world left — there is no camera in the mathematics, only a transformation that re-expresses every coordinate relative to the viewer. That equivalence is what lets one matrix do the job.

💡 Note that stages 1, 2 and 4 are all transformations you already know from this section — placement, change of reference, and window-to-viewport mapping. Only stage 3 introduces anything genuinely new, which is why projection gets a topic of its own.

Syllabus points

Stages of the 3D viewing pipeline

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