---
title: "Short note: 2D viewing pipeline"
subject: "Computer Graphics"
chapter: 3
key: "semester_5/computer_graphics:short-note-2d-viewing-pipeline"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/short-note-2d-viewing-pipeline
site: BCT Engineering
---

# Short note: 2D viewing pipeline

Computer Graphics · Chapter 3: Two –Dimensional Transformations

- Asked in: 2069 Asar, 4 marks; 2068 Bhadra (old course), 5 marks (asked 2 times)
- Video: [Computer Graphics:- 2D Viewing: 2D Viewing Pipeline](https://www.youtube.com/watch?v=2fw-Akpy0Kc) — Priyanka Pujari
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/short-note-2d-viewing-pipeline
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-3

## Question

Write a short note on the two-dimensional viewing pipeline.

## Short answer

The 2D viewing pipeline converts world-coordinate scenes to device coordinates: choose a window, transform to viewing coordinates by translating and rotating it to align axes, map to normalised coordinates and clip, then map the window to the viewport using xv=xvmin+(xw-xwmin)sx, yv=yvmin+(yw-ywmin)sy with sx=(xvmax-xvmin)/(xwmax-xwmin), sy=(yvmax-yvmin)/(ywmax-ywmin).

## Answer

The **2D viewing pipeline** is the series of steps that maps a picture from the world coordinate system to the device coordinate system.

```text
World coords -> Viewing coords -> Normalised -> Viewport
 (modelling)   (window rotate     coords      (device
                & translate)    + clipping     coords)
```

1. Objects are made in modelling coordinates and placed into **world coordinates**.
2. A **window** is chosen in the world. It is converted to **viewing coordinates** (translate to the origin, rotate to align with the axes if the window is tilted).
3. The scene is mapped to **normalised coordinates** (0 to 1, device independent) and **clipped** against the window, so that parts outside are discarded.
4. The window is mapped to the **viewport** on the screen using

```text
xv = xvmin + (xw − xwmin)·sx,   yv = yvmin + (yw − ywmin)·sy
sx = (xvmax − xvmin)/(xwmax − xwmin),  sy = (yvmax − yvmin)/(ywmax − ywmin)
```

As a matrix: M = T(xvmin, yvmin) · S(sx, sy) · T(−xwmin, −ywmin).
The pipeline lets the same scene be shown at different sizes, positions and parts (zoom, pan) on different devices.

## Check yourself

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

1. The 2D viewing pipeline maps a picture from:
   A. world coordinates to device coordinates
   B. device to world coordinates
   C. modelling to polar coordinates
   D. pixel to frame buffer coordinates only
   Answer: A. It is a series of steps from WC to device. (Key point: Purpose)

2. The x mapping from window to viewport is:
   A. xv = xwmin + (xw − xvmin)·sx
   B. xv = xvmin + (xw − xwmin)·sx
   C. xv = xw·sx
   D. xv = xvmin − (xw − xwmin)·sx
   Answer: B. Offset from window edge, scaled, added to the viewport edge. (Key point: Mapping equation)

3. A benefit of the pipeline is:
   A. it removes the need for clipping
   B. it makes all pictures the same size
   C. the same scene can be shown at different sizes, positions or parts on different devices (zoom, pan)
   D. it converts to 3D
   Answer: C. Changing the window or viewport changes the display. (Key point: Benefit)

## 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×
- [3D viewing pipeline](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aviewing-pipeline-3d) — Computer Graphics, chapter 4, asked 5×
- [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
- [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×

## Related in other subjects

- [Derive two-dimensional heat equation](https://www.bctengineer.com/question.md?key=semester_4%2Fapplied_mathematics%3Aheat-eq-2d-derive) — Applied Mathematics, chapter 3, asked 2×
- [Two dimensional arrays in FORTRAN](https://www.bctengineer.com/question.md?key=semester_1%2Fcomputer_programming%3Afortran-2d-array-syntax) — Computer Programming, chapter 11