---
title: "Conditions for error-free polygon table"
subject: "Computer Graphics"
chapter: 6
key: "semester_5/computer_graphics:error-free-polygon-table-conditions"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/error-free-polygon-table-conditions
site: BCT Engineering
---

# Conditions for error-free polygon table

Computer Graphics · Chapter 6: Surface Modeling

- Asked in: 2072 Chaitra, 4 marks; 2068 Chaitra, 3 marks; 2073 Chaitra, 5 marks (asked 3 times)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/error-free-polygon-table-conditions
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-6

## Question

What are the conditions (guidelines) for error-free generation of a polygon (geometric) table?

## Short answer

Every vertex in ≥2 edges; every edge in ≥1 polygon (2 for closed solid); polygons closed loops; each polygon shares an edge; consistent back-pointers; polygons planar; vertices listed CCW; no duplicate vertices/edges; no zero-length edges.

## Answer

When the geometric tables are produced, they should be checked for consistency. The usual conditions are:

1. **Every vertex is listed as an end point of at least two edges.**
2. **Every edge is part of at least one polygon** (for a closed solid, exactly two polygons).
3. **Every polygon is closed:** its edges form a closed loop, so the last vertex joins back to the first.
4. **Every polygon has at least one shared edge,** so polygons are connected.
5. **If the edge table contains pointers to polygons, every edge referenced by a polygon must point back to that polygon** (consistent back-pointers).
6. **Each polygon is planar,** with its vertices lying in one plane; triangles are always planar.
7. **No duplicate vertices or edges,** and no zero-length edges.
8. **Vertices are listed in a consistent order** (all counter-clockwise when viewed from outside) so that normals point outwards.

Checking these rules helps to find missing or repeated data before the model is rendered, which would otherwise cause holes or wrong shading.

## Check yourself

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

1. In an error-free table, every vertex must be:
   A. An end point of at least two edges
   B. Used by exactly one edge
   C. Isolated
   D. Shared by all polygons
   Answer: A. A vertex with fewer edges signals a missing edge. (Key point: Vertex rule)

2. Every edge must belong to:
   A. No polygon
   B. Exactly three polygons
   C. At least one polygon (two in a closed solid)
   D. All polygons
   Answer: C. Edges not in any polygon indicate error. (Key point: Edge rule)

3. Every polygon must be:
   A. An open chain
   B. A single edge
   C. Non-planar
   D. A closed loop of edges
   Answer: D. The last vertex joins the first. (Key point: Polygon closure)

4. Why list vertices in a consistent counter-clockwise order?
   A. So normals consistently point outwards
   B. To reduce the number of vertices
   C. To make edges longer
   D. To avoid planar polygons
   Answer: A. Consistent order gives consistent normals for visibility and shading. (Key point: Orientation)

5. If a polygon lists an edge, the edge table must:
   A. Not mention the polygon
   B. Delete the edge
   C. Store its colour
   D. Point back to that polygon
   Answer: D. Consistent pointers prevent mismatches. (Key point: Back-pointers)

## Related in Computer Graphics

- [Construct geometric table, 6 vertices](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Ageometric-table-construct-6-vertices) — Computer Graphics, chapter 6
- [Wire-frame model and polygon table](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Awireframe-model-polygon-table) — Computer Graphics, chapter 6
- [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
- [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
- [Storing geometric and attribute information](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Ageometric-attribute-info-storage) — Computer Graphics, chapter 6, asked 8×
- [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

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