---
title: "Polygon meshes for 3D objects"
subject: "Computer Graphics"
chapter: 6
key: "semester_5/computer_graphics:polygon-meshes-3d-objects"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/polygon-meshes-3d-objects
site: BCT Engineering
---

# Polygon meshes for 3D objects

Computer Graphics · Chapter 6: Surface Modeling

- Asked in: 2082 Kartik (new course), 3 marks
- Video: [Introduction to Polygon Meshes in Computer Graphics ~xRay Pixy](https://www.youtube.com/watch?v=Yt0uULat1YU) — Ritika xRay Pixy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/polygon-meshes-3d-objects
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-6

## Question

How do polygon meshes support representing a 3D object? Explain with relevant figures.

## Short answer

Polygon meshes represent a 3D object as a collection of vertices, edges, and polygonal faces that approximate its surface. Vertices are shared, transformations apply only to vertices, and triangles are always planar, making rendering simple and efficient.

## Answer

A **polygon mesh** is a collection of vertices, edges and faces (polygons) that share vertices and edges and together approximate the surface of a 3D object. Because graphics hardware works with polygons, the mesh is the most common way to represent 3D objects.

Common forms:
- **Triangle strip:** a series of connected triangles where each new vertex adds one triangle. n vertices give n − 2 triangles.
- **Quadrilateral mesh:** an n × m array of vertices gives (n − 1)(m − 1) quadrilaterals.
- **Triangle fan:** triangles sharing one common vertex.

```text
Triangle strip:         Quad mesh:
 V1--V3--V5--V7        +--+--+--+
  \ / \ / \ /          |  |  |  |
   V2--V4--V6          +--+--+--+
                       |  |  |  |
                       +--+--+--+
```

How the mesh supports 3D objects:
1. Planar and curved surfaces are approximated; finer meshes give a smoother surface.
2. Vertices are shared, saving storage and keeping the surface connected.
3. Transformations are applied to vertices only.
4. Face normals and vertex normals support shading, and each polygon can be filled with colour or texture.
5. Triangles are always planar, which makes rendering simple.

The mesh is stored in vertex, edge and surface tables.

## Check yourself

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

1. A triangle strip has n vertices. How many triangles does it contain?
   A. n - 2
   B. n - 1
   C. n
   D. n / 3
   Answer: A. Each new vertex after the first two adds one triangle, so n vertices give n - 2 triangles. (Key point: Triangle strip count)

2. An n x m array of vertices forms a quadrilateral mesh. How many quadrilaterals result?
   A. n x m
   B. (n + 1)(m + 1)
   C. (n - 1)(m - 1)
   D. n x m / 4
   Answer: C. Each quad needs a 2 x 2 block of vertices, giving (n-1)(m-1) quads. (Key point: Quad mesh count)

3. What is the benefit of vertices being shared between polygons in a mesh?
   A. It makes each polygon curved
   B. It saves storage and keeps the surface connected
   C. It removes the need for shading
   D. It stops transformations being needed
   Answer: B. Shared vertices are stored once and tie neighbouring faces together. (Key point: Shared vertices)

4. How does a finer mesh affect the approximation of a curved surface?
   A. The surface becomes flat
   B. Fewer vertices are needed
   C. Shading becomes impossible
   D. The surface looks smoother
   Answer: D. More, smaller polygons follow the curve more closely. (Key point: Finer mesh)

## Related in Computer Graphics

- [Polygon as standard graphics object](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Apolygon-standard-graphics-object) — Computer Graphics, chapter 6
- [Geometric tables for 3D object](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Ageometric-tables-3d-error-free) — Computer Graphics, chapter 6
- [Boundary representation of 3D objects](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aboundary-representation-technique) — Computer Graphics, chapter 6, asked 4×
- [3D rotation about arbitrary axis](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Arotate-3d-arbitrary-axis-steps) — Computer Graphics, chapter 4, asked 2×
- [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 rotation about axis (1,2,3)-(10,20,30)](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Arotate-3d-axis-1-2-3) — Computer Graphics, chapter 4

## Related in other subjects

- [Add objects of two different classes](https://www.bctengineer.com/question.md?key=semester_3%2Fobject_oriented_programming%3Afriend-add-two-class-objects) — Object Oriented Programming, chapter 4, asked 2×
- [Time class: add two objects](https://www.bctengineer.com/question.md?key=semester_3%2Fobject_oriented_programming%3Atime-class-add-objects) — Object Oriented Programming, chapter 1
- [Rental car system candidate objects](https://www.bctengineer.com/question.md?key=semester_6%2Fobject_oriented_analysis_and_design%3Arental-car-system-candidate-objects) — Object Oriented Analysis and Design, chapter 2
- [Polygon abstract class with Area()](https://www.bctengineer.com/question.md?key=semester_3%2Fobject_oriented_programming%3Apolygon-abstract-area) — Object Oriented Programming, chapter 7