---
title: "Wire-frame model and polygon table"
subject: "Computer Graphics"
chapter: 6
key: "semester_5/computer_graphics:wireframe-model-polygon-table"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/wireframe-model-polygon-table
site: BCT Engineering
---

# Wire-frame model and polygon table

Computer Graphics · Chapter 6: Surface Modeling

- Asked in: 2078 Bhadra, 5 marks
- Video: [3D Object | 3D Object Representation | Polygon | Computer Graphics | Indra PC | #cg](https://www.youtube.com/watch?v=TKJfFdZkJlU) — Indra PC
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/wireframe-model-polygon-table
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-6

## Question

What is Wire-frame model and why do we need polygon data table? Explain with examples.

## Short answer

A wireframe model represents a 3D object only by its edges and vertices, with no surface information, causing ambiguity. Polygon data tables add vertex, edge, and surface connectivity, enabling solid rendering, hidden surface removal, shading, texture mapping, and consistency checks.

## Answer

A **wireframe model** represents a 3D object only by its edges (lines) and vertices, like a skeleton made of wire, with no surface information.

```text
   +-------+
  /|      /|
 +-------+ |
 | +-----|-+
 |/      |/
 +-------+      cube wireframe
```

Features:
- Very fast to draw and to transform: only vertices need to be transformed.
- Ambiguous: a hidden line cannot be distinguished from a front line, and the object can be read in more than one way (the Necker cube effect).
- No surface, volume, colour or shading information.

#### Why a polygon data table is needed
A wireframe only stores which vertices are joined, not which edges form a face. To render solid surfaces (hidden surface removal, shading, texture), the faces must be known. A **polygon data table** (vertex, edge and surface tables) adds this connectivity and the attribute data.

Example: a triangular face

```text
Vertex table: V1 (0,0,0)  V2 (1,0,0)  V3 (0,1,0)
Edge table:   E1 V1V2  E2 V2V3  E3 V3V1
Surface table: S1 = E1 E2 E3 (colour = red, normal = (0,0,1))
```

With the tables, we can find the surface normal for shading, test visibility, check for errors, and fill the polygon.

## Check yourself

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

1. A wireframe model represents an object by:
   A. Filled surfaces
   B. Volume cells
   C. Its edges and vertices only
   D. Textures
   Answer: C. Like a skeleton of wire. (Key point: Wireframe)

2. A drawback of wireframe models is:
   A. Slow transformation
   B. Excess surface data
   C. Hidden lines cannot be distinguished from front lines
   D. Loss of vertices
   Answer: C. This gives the Necker cube ambiguity. (Key point: Ambiguity)

3. Why is a polygon data table needed?
   A. It records which edges form faces, plus attributes, for hidden surface removal and shading
   B. To make lines thicker
   C. To reduce the number of vertices
   D. To remove edges
   Answer: A. A wireframe has no face information. (Key point: Why tables)

4. Why are wireframes fast to transform?
   A. Faces are filled first
   B. They use textures
   C. Only vertices need to be transformed
   D. They use ray tracing
   Answer: C. Lines are redrawn between transformed vertices. (Key point: Speed)

## Related in Computer Graphics

- [Polygon tables to model Dharahara](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Apolygon-vertex-edge-table-dharahara) — Computer Graphics, chapter 6
- [Conditions for error-free polygon table](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aerror-free-polygon-table-conditions) — Computer Graphics, chapter 6, asked 3×
- [Polygon table and normal of S1](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Apolygon-table-surface-normal-s1) — Computer Graphics, chapter 6
- [Model curved surface using polygons](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Acurved-surface-polygons-tables) — Computer Graphics, chapter 6
- [Need of perspective projection](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Awhy-perspective-projection-world-to-viewing) — Computer Graphics, chapter 4
- [Model cone or cylinder surfaces](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aboundary-rep-cone-cylinder) — Computer Graphics, chapter 6

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