---
title: "Need of perspective projection"
subject: "Computer Graphics"
chapter: 4
key: "semester_5/computer_graphics:why-perspective-projection-world-to-viewing"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/why-perspective-projection-world-to-viewing
site: BCT Engineering
---

# Need of perspective projection

Computer Graphics · Chapter 4: Three-Dimensional Graphics

- Asked in: 2082 Kartik (new course), 2+3 marks
- Video: [Perspective projection in 5 minutes](https://www.youtube.com/watch?v=F5WA26W4JaM) — Graphics in 5 Minutes
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/why-perspective-projection-world-to-viewing
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-4

## Question

Why do we need perspective projection in 3D environment? Explain transformation from world to viewing coordinates.

## Short answer

Perspective projection gives realistic depth by making distant objects smaller and creating vanishing points. World-to-viewing transformation: define camera axes n, u, v; translate camera to origin; rotate to align axes with world axes using matrix M = R·T with rows u, v, n and translation -(u·R0, v·R0, n·R0).

## Answer

#### Need for perspective projection
Parallel projection keeps sizes equal whatever the distance, so the picture looks unnatural. **Perspective projection** projects points along lines meeting at the centre of projection (the eye), so:
- distant objects look smaller (perspective foreshortening), as seen by the human eye or a camera;
- parallel lines meet at vanishing points, giving depth;
- it gives realistic images, needed in games, animation, architecture and flight simulators.

Its drawbacks are that true sizes and angles are not preserved.

#### World to viewing coordinates
The scene is given in world coordinates, but projection is easier in a coordinate system fixed to the viewer.

1. Choose the view reference point R0, the view-plane normal N and the view-up vector V.
2. Compute unit vectors: n = N/|N|, u = (V × N)/|V × N|, v = n × u.
3. Translate R0 to the origin with T(−x0, −y0, −z0).
4. Rotate so that u, v, n become the x, y, z axes.

```text
M = R · T = | u1 u2 u3 -(u·R0) |
            | v1 v2 v3 -(v·R0) |
            | n1 n2 n3 -(n·R0) |
            | 0  0  0   1      |
```

P_viewing = M · P_world. The projection then works on P_viewing.

## Check yourself

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

1. Why use perspective projection?
   A. Distant objects look smaller, giving realism
   B. It preserves true sizes
   C. It is faster than parallel
   D. It removes hidden surfaces
   Answer: A. Perspective foreshortening and vanishing points mimic the eye. (Key point: Need)

2. A drawback of perspective is:
   A. No depth
   B. True sizes and angles are not preserved
   C. Lines never converge
   D. It needs no matrix
   Answer: B. Hence not used for measurements. (Key point: Drawback)

3. The world-to-viewing transformation is done by:
   A. Scaling by N
   B. Shearing along V
   C. Translating R0 to the origin and rotating u, v, n to x, y, z
   D. Projecting along u
   Answer: C. M = R·T. (Key point: Viewing transform)

4. The viewing x-axis u is:
   A. N/|N|
   B. n × u
   C. V/|V|
   D. (V × N)/|V × N|
   Answer: D. u is perpendicular to both V and N. (Key point: Unit vector u)

## Related in Computer Graphics

- [3D rotation steps and perspective projection](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Arotate-3d-arbitrary-axis-perspective) — 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×
- [Derive perspective projection matrix](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aperspective-projection-matrix-derive) — Computer Graphics, chapter 4, asked 3×
- [Perspective projection of pyramid](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aperspective-pyramid-zprp-20) — Computer Graphics, chapter 4, asked 2×
- [Short note: Two-point perspective projection](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Ashort-note-two-point-perspective) — Computer Graphics, chapter 4
- [3D viewing pipeline](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aviewing-pipeline-3d) — Computer Graphics, chapter 4, asked 5×

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- [Why do we need FFT](https://www.bctengineer.com/question.md?key=semester_7%2Fdigital_signal_analysis_and_processing%3Awhy-need-fft) — Digital Signal Analysis and Processing, chapter 7, asked 2×