---
title: "Flat (constant intensity) shading"
subject: "Computer Graphics"
chapter: 8
key: "semester_5/computer_graphics:flat-shading-accurate-condition"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/flat-shading-accurate-condition
site: BCT Engineering
---

# Flat (constant intensity) shading

Computer Graphics · Chapter 8: Illumination and Surface Rendering methods

- Asked in: 2068 Bhadra (old course), 7 marks; 2071 Shrawan, 3 marks (asked 2 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/flat-shading-accurate-condition
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-8

## Question

Discuss the constant intensity (flat) shading method. Under what condition(s) does flat shading give accurate rendering?

## Short answer

Flat shading fills a polygon with a constant intensity computed from the polygon normal. It is accurate when the polygon truly is a flat face of a polyhedron, and both light source and viewer are at infinity, so N·L and V (or N·H) are constant across the polygon.

## Answer

**Constant-intensity (flat) shading** is the simplest polygon rendering method. A single intensity is calculated for each polygon (using one normal, usually the polygon normal, and one point on the polygon) and the whole polygon is filled with it.

**Steps**
1. Find the unit normal N of the polygon (from the plane equation, N = (A, B, C)/|N|).
2. Calculate the intensity of one point of the polygon using the illumination model: I = ka·Ia + IL [kd (N·L) + ks (N·H)^n].
3. Fill all pixels of the polygon with this intensity.

**Advantages**
- Fast and simple, with few calculations (one per polygon).
- Good for quick previews.

**Disadvantages**
- Faceted appearance: adjacent polygons have different intensities, so edges are clearly visible, even on a curved surface approximated by a mesh.
- Mach-band effect appears at the edges.
- Highlights are inaccurate.

**Conditions for accurate rendering**

Flat shading is accurate when the intensity is really the same over the whole polygon, i.e.:
1. The object is a true polyhedron, and each polygon is a real flat face (not an approximation of a curved surface).
2. The light source is at infinity (or far away), so N·L is the same for every point on the polygon.
3. The viewer is at infinity (or far away), so V (and hence N·H or R·V) is constant across the polygon.

Then the diffuse and specular terms do not change over the polygon. Using smaller polygons in the mesh also improves accuracy.

## Check yourself

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

1. In flat (constant-intensity) shading, how many intensity calculations are made for each polygon?
   A. One, and the whole polygon is filled with it
   B. One per vertex, then interpolated across the polygon
   C. One per pixel using an interpolated normal
   D. One per edge, then averaged
   Answer: A. A single intensity is computed for the polygon and all its pixels get that value. (Key point: What flat shading does)

2. Why does flat shading give a faceted look on a mesh approximating a curved surface?
   A. Normals are interpolated too smoothly across edges
   B. Adjacent polygons get different intensities, so their edges are clearly visible
   C. Specular highlights are over-brightened at all vertices
   D. The depth buffer fails at polygon borders
   Answer: B. Each polygon has its own constant intensity, so jumps appear at edges (also causing Mach bands). (Key point: Visible drawback)

3. Which light-source condition makes N.L the same for every point of a flat polygon?
   A. The light source is very close to the polygon
   B. The light is a spotlight with a narrow cone
   C. The light source is at infinity (or far away)
   D. The light source is ambient only and placed at the viewer
   Answer: C. A distant source gives parallel rays, so L (and N.L) is constant over a flat face. (Key point: Light-source condition)

4. Which set of conditions makes flat shading accurate?
   A. A smooth curved surface with a nearby light and viewer
   B. Any mesh as long as the polygons are triangles
   C. A polyhedron with the viewer close to the surface so V changes quickly
   D. A true polyhedron with flat faces, with light and viewer both at (or near) infinity
   Answer: D. Intensity is truly constant only when each face is really flat and L and V do not vary over it. (Key point: Viewer and object conditions)

## Related in Computer Graphics

- [Gouraud shading for polygon rendering](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Agouraud-shading-intensity-interpolation) — Computer Graphics, chapter 8, asked 6×
- [Phong shading method](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aphong-shading-method) — Computer Graphics, chapter 8, asked 9×
- [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

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