---
title: "3D viewing pipeline"
subject: "Computer Graphics"
chapter: 4
key: "semester_5/computer_graphics:viewing-pipeline-3d"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/viewing-pipeline-3d
site: BCT Engineering
---

# 3D viewing pipeline

Computer Graphics · Chapter 4: Three-Dimensional Graphics

- Asked in: 2074 Chaitra, 6 marks; 2073 Shrawan, 4 marks; 2075 Chaitra, 4 marks; 2078 Kartik, 3 marks; 2082 Kartik (new course), 2 marks (asked 5 times)
- Video: [3D Viewing Introduction and 3D Viewing Pipeline](https://www.youtube.com/watch?v=1uCIUjk_vho) — Prof. Brinal Colaco
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/viewing-pipeline-3d
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-4

## Question

Describe the 3-D viewing pipeline (draw its block diagram).

## Short answer

The 3D viewing pipeline transforms object coordinates to device coordinates through modeling, viewing (camera), projection (parallel or perspective), normalization & clipping, and workstation (viewport) transforms. Each stage successively changes the coordinate system, ending in a 2D display image.

## Answer

The **3D viewing pipeline** is the sequence of transformations that converts a 3D scene described in object coordinates into a 2D image on the display device.

```text
 Modeling        Modeling
 Coordinates --> Transform --> World Coordinates
                                     |
                              Viewing Transform
                                     v
                             Viewing Coordinates
                                     |
                             Projection Transform
                                     v
                            Projection Coordinates
                                     |
                         Normalization + Clipping
                                     v
                           Normalized Coordinates
                                     |
                           Workstation Transform
                                     v
                             Device Coordinates
```

Stages:
1. **Modeling transformation:** each object is built in its own local (modeling) coordinates and placed into the common world coordinate system using translation, rotation and scaling.
2. **Viewing transformation:** the world is re-expressed in a coordinate system attached to the camera (view reference point, view-plane normal N and view-up vector V). It is done by translating the view reference point to the origin and rotating so that N lies along the z-axis.
3. **Projection transformation:** 3D viewing coordinates are projected onto the view plane, by parallel or perspective projection, giving 2D coordinates.
4. **Normalization and clipping:** coordinates are mapped to a normalized view volume (0 to 1 or −1 to 1) and parts of the scene outside the view volume are clipped away.
5. **Workstation (viewport) transformation:** the normalized coordinates are mapped to the viewport of the display device, giving device (pixel) coordinates for scan conversion.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which order is correct?
   A. Projection, modeling, viewing, workstation
   B. Modeling, viewing, projection, normalization/clipping, workstation
   C. Viewing, modeling, clipping, projection
   D. Workstation, projection, viewing, modeling
   Answer: B. Modeling -> world -> viewing -> projection -> normalized -> device. (Key point: Order)

2. What does the viewing transformation do?
   A. Projects 3D to 2D
   B. Clips the scene
   C. Re-expresses the world in camera coordinates by translating the view reference point to the origin and aligning N with z
   D. Maps to pixels
   Answer: C. It builds the camera coordinate system. (Key point: Viewing transformation)

3. What does the projection stage produce?
   A. Device pixels
   B. World coordinates
   C. Normalized volume
   D. 2D coordinates on the view plane
   Answer: D. Parallel or perspective projection gives 2D coordinates. (Key point: Projection)

4. What is the last step?
   A. Mapping normalized coordinates to the viewport giving device coordinates
   B. Clipping
   C. Modeling
   D. Projection
   Answer: A. The workstation transform produces pixel coordinates. (Key point: Workstation)

## Related in Computer Graphics

- [2D viewing pipeline with matrices](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aviewing-pipeline-2d-matrices) — Computer Graphics, chapter 3, asked 5×
- [Short note: 2D viewing pipeline](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Ashort-note-2d-viewing-pipeline) — Computer Graphics, chapter 3, asked 2×
- [3D world to viewing coordinate matrix](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aworld-to-viewing-3d-matrix) — Computer Graphics, chapter 4, asked 2×
- [Why 3D graphics is more complex than 2D](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Awhy-3d-more-complex-viewing-pipeline) — Computer Graphics, chapter 4

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