---
title: "Gouraud shading for polygon rendering"
subject: "Computer Graphics"
chapter: 8
key: "semester_5/computer_graphics:gouraud-shading-intensity-interpolation"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/gouraud-shading-intensity-interpolation
site: BCT Engineering
---

# Gouraud shading for polygon rendering

Computer Graphics · Chapter 8: Illumination and Surface Rendering methods

- Asked in: 2069 Chaitra, 7 marks; 2075 Chaitra, 7 marks; 2069 Asar, 6 marks; 2068 Chaitra, 8 marks; 2072 Kartik, 7 marks; 2072 Chaitra, 5 marks (asked 6 times)
- Video: [Shading Models : Flat and Gouraud Shading Explained in Hindi | Computer Graphics Course](https://www.youtube.com/watch?v=nAZ1SzoI64o) — 5 Minutes Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/gouraud-shading-intensity-interpolation
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-8

## Question

Explain the Gouraud shading (intensity-interpolation scheme) for polygon rendering, with its pros and cons.

## Short answer

Gouraud shading calculates vertex intensities using averaged normals and the illumination model, then linearly interpolates them along edges and scanlines. It is fast and removes the faceted look, but highlights inside polygons can be missed, Mach bands may appear, and silhouettes remain polygonal.

## Answer

**Gouraud shading** (intensity-interpolation scheme) renders a polygon mesh by computing the intensity at each vertex with an illumination model and then linearly interpolating these intensities over the polygon surface.

**Steps**
1. **Vertex normal:** find the normal at each vertex by averaging the normals of all polygons meeting at that vertex.

   N_v = (Σ N_k) / |Σ N_k|

2. **Vertex intensity:** apply the illumination model at each vertex using N_v.
3. **Edge interpolation:** for a scan line y_s crossing an edge from vertex 1 (y1) to vertex 2 (y2):

   I_a = ((y_s − y2)/(y1 − y2))·I1 + ((y1 − y_s)/(y1 − y2))·I2

   (Incremental form: moving down one scan line, I' = I + (I2 − I1)/(y1 − y2).)
4. **Scan-line interpolation:** between the left (a) and right (b) intersection points, for pixel x_p:

   I_p = ((x_b − x_p)/(x_b − x_a))·I_a + ((x_p − x_a)/(x_b − x_a))·I_b

   (Incremental form along the scan line: I_{p+1} = I_p + (I_b − I_a)/(x_b − x_a).)
5. Fill each pixel with I_p.

```text
 I1 o
    |\
  Ia o--o Ib    I_p interpolated between Ia and Ib
    |    \
 I2 o-----o I3
```

**Advantages**
- Removes the faceted look and gives smooth shading.
- Much faster than Phong shading, since the illumination model is applied only at the vertices and the interpolation is linear and incremental.

**Disadvantages**
- Specular highlights inside a polygon may be missed or appear wrong, because only vertex intensities are used.
- The Mach-band effect (visible bright or dark bands) can appear at polygon boundaries.
- The silhouette still looks polygonal.
- Results depend on the orientation of the polygon on the screen.

## Check yourself

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

1. What does Gouraud shading do?
   A. Computes intensities at vertices and interpolates them linearly
   B. Interpolates normals per pixel
   C. Gives one intensity per polygon
   D. Casts rays through each pixel
   Answer: A. The model is applied only at vertices. (Key point: Basic idea)

2. How is the vertex normal obtained?
   A. Using one polygon's normal
   B. Averaging normals of polygons meeting at the vertex
   C. Using depth
   D. Using light direction
   Answer: B. N_v = sum(N_k)/|sum(N_k)|. (Key point: Vertex normal)

3. What is the order of interpolation?
   A. Pixel by pixel from the centre
   B. Between vertices diagonally only
   C. Along edges to scan-line ends, then along the scan line
   D. Per polygon once
   Answer: C. I_a, I_b on edges, then I_p between them. (Key point: Order of interpolation)

4. Which is a disadvantage of Gouraud shading?
   A. Slow speed
   B. Facetted look
   C. Needs per-pixel normals
   D. Missed highlights and Mach bands
   Answer: D. Vertex-only lighting gives such artefacts. (Key point: Disadvantage)

## Related in Computer Graphics

- [Gouraud intensity at midpoint P](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Agouraud-intensity-midpoint-scan-line) — Computer Graphics, chapter 8
- [Compare Gouraud and Phong shading](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Acompare-gouraud-phong) — Computer Graphics, chapter 8, asked 7×
- [Flat (constant intensity) shading](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aflat-shading-accurate-condition) — Computer Graphics, chapter 8, asked 2×
- [Phong shading method](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aphong-shading-method) — Computer Graphics, chapter 8, asked 9×
- [Disadvantage of intensity interpolation](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aintensity-interpolation-disadvantage) — Computer Graphics, chapter 8

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