---
title: "General illumination model"
subject: "Computer Graphics"
chapter: 8
key: "semester_5/computer_graphics:general-illumination-model"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/general-illumination-model
site: BCT Engineering
---

# General illumination model

Computer Graphics · Chapter 8: Illumination and Surface Rendering methods

- Asked in: 2072 Kartik, 7 marks
- Video: [Illumination Model: Ambient Illumination| Diffused Reflection| Specular Reflection in just 15 min!](https://www.youtube.com/watch?v=hS1VowQ2es0) — Vinay Mishra
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/general-illumination-model
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-8

## Question

Explain the general illumination model.

## Short answer

The general illumination model combines local lighting (ambient, diffuse, specular with distance attenuation from all sources) and global effects of reflection and refraction: I = I_local + kr·I_reflected + kt·I_transmitted. It accounts for light-source and surface properties, geometry, and attenuation.

## Answer

An **illumination model** gives the intensity of light seen at a surface point. The general model for a surface point includes the local contributions (ambient, diffuse, specular from every light source) and the effects of light from other objects (reflection and transparency).

**Local illumination (Phong model with multiple sources and attenuation)**

I_local = ka·Ia + Σ_l f(d_l) · IL_l · [ kd (N·L_l) + ks (N·H_l)^n ]

- ka·Ia: ambient term; kd (N·L): diffuse; ks (N·H)^n: specular
- f(d) = min(1/(a0 + a1d + a2d²), 1): distance attenuation
- IL_l: intensity of light source l; n: shininess exponent

**Global effects.** For shiny and transparent objects, the intensity includes light arriving from the reflected and refracted directions:

I = I_local + kr · I_reflected + kt · I_transmitted

- kr = reflection coefficient, I_reflected = intensity coming from the mirror direction R
- kt = transmission (transparency) coefficient, I_transmitted = intensity coming through the object
This is evaluated recursively in ray tracing.

**Factors used in the model**
1. Light source properties: type, position, intensity, colour, direction (spotlight).
2. Surface properties: colour, reflection coefficients (ka, kd, ks), shininess, transparency, texture.
3. Geometry: normal N, light vector L, view vector V, reflection vector R.
4. Distance of the light source.

```text
 Light --> L      N
        \    |    / R
         \   |   /
          \  |  /   --> V (eye)
  ----------------
```

The model is used with a surface-rendering method (flat, Gouraud, Phong) to produce the pixel colours. Colour images use the model separately for the R, G and B components.

## Check yourself

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

1. The local part of the general illumination model is a sum of which terms?
   A. Ambient, plus diffuse and specular from each light source
   B. Ambient and transparency only
   C. Diffuse and reflection only
   D. Specular and refraction only
   Answer: A. I_local = ka*Ia + sum of f(d)*IL*[kd(N.L) + ks(N.H)^n] over the lights. (Key point: Local terms)

2. Which equation adds the effect of light from other objects for shiny and transparent surfaces?
   A. I = I_local * kr * kt
   B. I = I_local + kr*I_reflected + kt*I_transmitted
   C. I = ka*Ia + kd*IL
   D. I = I_local - kr*I_reflected
   Answer: B. Reflected light from direction R and light transmitted through the object are added to the local intensity. (Key point: Global effects)

3. What is the role of f(d) = min(1/(a0 + a1d + a2d^2), 1)?
   A. It sets the shininess of the surface
   B. It selects the colour of the light
   C. It reduces the light intensity with distance from the source
   D. It scales the ambient term only
   Answer: C. f(d) is the distance attenuation factor applied to each source's diffuse and specular contribution. (Key point: Attenuation)

4. In which technique is the reflected and transmitted intensity evaluated recursively?
   A. Flat shading
   B. Gouraud shading
   C. Scan-line polygon filling
   D. Ray tracing
   Answer: D. Ray tracing follows reflected and refracted rays recursively to get I_reflected and I_transmitted. (Key point: Recursive evaluation)

## Related in Computer Graphics

- [Phong illumination model expression](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aphong-illumination-model-derive) — Computer Graphics, chapter 8, asked 8×
- [Define illumination and surface rendering](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Adefine-illumination-rendering) — Computer Graphics, chapter 8, asked 3×

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