---
title: "Geometric tables for 3D object"
subject: "Computer Graphics"
chapter: 6
key: "semester_5/computer_graphics:geometric-tables-3d-error-free"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/geometric-tables-3d-error-free
site: BCT Engineering
---

# Geometric tables for 3D object

Computer Graphics · Chapter 6: Surface Modeling

- Asked in: 2074 Asoj, 8 marks
- Video: [Polygon Surfaces: 3D Object Representations](https://www.youtube.com/watch?v=NY53ihpQ2HM) — Prof. Brinal Colaco
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/geometric-tables-3d-error-free
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-6

## Question

How are geometric tables used to represent a 3D object? Explain with example. Give conditions to generate error free table.

## Short answer

Geometric tables (vertex, edge, surface) define object shape. Example: pyramid (5 vertices, 8 edges, 5 faces). Conditions: vertex in ≥2 edges, edge in ≥1 polygon, closed polygons, shared edges, consistent pointers, planar polygons, CCW ordering.

## Answer

**Geometric tables** are the data tables that describe the shape of a polygon-mesh object: a **vertex table** (coordinates), an **edge table** (end vertices of each edge) and a **polygon/surface table** (edges of each face). A 3D object is the collection of its surfaces, so the three tables together define the whole object; extra tables store attributes (colour, transparency).

**Example:** a square pyramid has 5 vertices, 8 edges and 5 faces.

```text
Vertex table        Edge table          Surface table
V1 (0,0,0)          E1: V1 V2           S1: E1 E2 E3 E4 (base)
V2 (2,0,0)          E2: V2 V3           S2: E1 E6 E5
V3 (2,2,0)          E3: V3 V4           S3: E2 E7 E6
V4 (0,2,0)          E4: V4 V1           S4: E3 E8 E7
V5 (1,1,2)          E5: V1 V5           S5: E4 E5 E8
                    E6: V2 V5
                    E7: V3 V5
                    E8: V4 V5
```

For fast processing, the edge table may also hold the faces that share each edge (E1: S1, S2), and the vertex table the edges meeting at each vertex.

**Conditions for an error-free table**
1. Every vertex belongs to at least two edges.
2. Every edge belongs to at least one polygon (exactly two in a closed solid).
3. Every polygon is a closed loop of edges.
4. Every polygon shares at least one edge with another polygon.
5. Pointers are consistent: if a polygon lists an edge, that edge points back to the polygon.
6. Polygons are planar and listed in a consistent (counter-clockwise) vertex order.

## Check yourself

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

1. The geometric tables of a mesh are:
   A. Colour, texture and light tables
   B. Pixel, line and circle tables
   C. Vertex, edge and polygon/surface tables
   D. Input, output and buffer tables
   Answer: C. They together define the shape. (Key point: Three tables)

2. In the pyramid example the base surface S1 consists of edges:
   A. E5 E6 E7 E8
   B. E1 E6 E5
   C. E1 E2
   D. E1 E2 E3 E4
   Answer: D. The base uses the four base edges. (Key point: Pyramid example)

3. Why store the faces sharing each edge in the edge table?
   A. For fast processing and consistency checks
   B. To reduce vertices
   C. To store colour
   D. To remove edges
   Answer: A. Pointers speed traversal. (Key point: Extra pointers)

4. Which is a condition for error-free tables?
   A. Every edge is unused
   B. Polygons are non-planar
   C. Vertices are unordered
   D. Every edge belongs to at least one polygon
   Answer: D. Edges must be used by polygons. (Key point: Condition)

## Related in Computer Graphics

- [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×
- [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
- [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×

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