---
title: "Polygon tables to model Dharahara"
subject: "Computer Graphics"
chapter: 6
key: "semester_5/computer_graphics:polygon-vertex-edge-table-dharahara"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/polygon-vertex-edge-table-dharahara
site: BCT Engineering
---

# Polygon tables to model Dharahara

Computer Graphics · Chapter 6: Surface Modeling

- Asked in: 2079 Baisakh, 2+2+2+2 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/polygon-vertex-edge-table-dharahara
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-6

## Question

Describe polygon, vertex and edge table. How can these terms be used to construct a model of Dharahara?

## Short answer

A polygon is a closed plane figure bounded by straight edges. The vertex table stores (x,y,z) coordinates of each vertex; the edge table stores pairs of vertex identifiers. To model Dharahara, define vertices for a tapered shaft frustum and spire tip, create edges connecting them, and define surfaces as edge loops (e.g., side quadrilaterals and spire triangles) using these tables.

## Answer

#### Polygon
A **polygon** is a closed plane figure bounded by straight line segments (edges). Polygons (usually triangles and quadrilaterals) are the basic surface elements used to describe 3D objects.

#### Vertex table
Stores the coordinates (x, y, z) of each vertex of the object once, with an identifier V1, V2, ...

#### Edge table
Stores each edge as a pair of vertex identifiers (and optionally the polygons sharing it), e.g. E1: V1 V2.

(The surface/polygon table stores each face as a list of its edges, e.g. S1: E1 E2 E3 E4.)

#### Modelling Dharahara
Dharahara (Bhimsen Tower) is a tall, tapering tower with a base shaft, a balcony and a pointed top. A simple model: a tapered square shaft (a frustum) with a pyramid-shaped spire on top.

Assumed vertices (units are arbitrary):
- Base square (z = 0): V1 (−2,−2,0), V2 (2,−2,0), V3 (2,2,0), V4 (−2,2,0)
- Shaft top (z = 8): V5 (−1,−1,8), V6 (1,−1,8), V7 (1,1,8), V8 (−1,1,8)
- Spire tip: V9 (0,0,10)

```text
Vertex: V1..V9 with coordinates above
Edge table:
 base:   E1 V1V2   E2 V2V3   E3 V3V4   E4 V4V1
 top:    E5 V5V6   E6 V6V7   E7 V7V8   E8 V8V5
 shaft:  E9 V1V5   E10 V2V6  E11 V3V7  E12 V4V8
 spire:  E13 V5V9  E14 V6V9  E15 V7V9  E16 V8V9
Surface table:
 S1 side:  E1 E10 E5 E9
 S2 side:  E2 E11 E6 E10
 S3 side:  E3 E12 E7 E11
 S4 side:  E4 E9 E8 E12
 S5 spire: E5 E14 E13     S6: E6 E15 E14
 S7 spire: E7 E16 E15     S8: E8 E13 E16
 S9 base:  E1 E2 E3 E4
```

More detail (balconies, windows, the round dome) is added by more vertices and polygons. The real tower can be refined by adding extra stacked frusta for each storey, and an octagonal or circular cross-section for a better approximation.

## Check yourself

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

1. A polygon is:
   A. A curve with no corners
   B. A single point
   C. A closed plane figure bounded by straight line segments
   D. An open chain of lines
   Answer: C. Polygons are basic surface elements. (Key point: Polygon)

2. The vertex table stores:
   A. Pairs of vertices
   B. Faces' edges
   C. Colours only
   D. The (x,y,z) coordinates of each vertex once
   Answer: D. Each vertex has an identifier and coordinates. (Key point: Vertex table)

3. The edge table stores:
   A. Each edge as a pair of vertex identifiers
   B. Coordinates of edges
   C. Face colours
   D. Light positions
   Answer: A. E1: V1 V2. (Key point: Edge table)

## Related in Computer Graphics

- [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
- [Spatial orientation and polygon tables](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aspatial-orientation-surface-significance) — 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
- [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
- [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×
- [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

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