---
title: "Model cone or cylinder surfaces"
subject: "Computer Graphics"
chapter: 6
key: "semester_5/computer_graphics:boundary-rep-cone-cylinder"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/boundary-rep-cone-cylinder
site: BCT Engineering
---

# Model cone or cylinder surfaces

Computer Graphics · Chapter 6: Surface Modeling

- Asked in: 2076 Chaitra, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/boundary-rep-cone-cylinder
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-6

## Question

How can we model cone or cylindrical like surfaces using boundary representation technique?

## Short answer

A cylinder is modeled by dividing top and bottom circles into n points, forming n side quadrilaterals and two n-gon caps. A cone uses n base points and one apex to form n side triangles and an n-gon base. Polygon tables store the vertices, edges (circular and vertical), and surfaces; increasing n gives a smoother approximation.

## Answer

In boundary representation (B-rep), a curved solid is modelled by its bounding surface, which is approximated by a polygon mesh; the vertices, edges and faces are stored in polygon tables.

#### Cylinder
Take the circle of radius r at the bottom (z = 0) and at the top (z = h), and divide each into n equal arcs (n = 8, say). Bottom vertices: (r cos θk, r sin θk, 0); top vertices: (r cos θk, r sin θk, h), with θk = 360°·k/n.

- The side is made of n rectangles (quadrilaterals), each using two adjacent bottom vertices and the two top vertices above them.
- The top and bottom are n-sided polygons (or n triangles from a centre point).

```text
 top    V9--V10--V11 ...
        |    |    |
 bottom V1--V2---V3  ...
```

Tables: 2n vertices; 3n edges (n bottom, n top, n vertical); n + 2 faces.

#### Cone
The circular base is divided into n points, and one extra vertex is the apex (0, 0, h).
- The side is made of n triangles, each joining the apex to two adjacent base vertices.
- The base is an n-sided polygon.

Tables: n + 1 vertices; 2n edges; n + 1 faces.

```text
Cone vertex table: V0 apex (0,0,h); V1..Vn base points
Edge table: E1..En base edges (Vk Vk+1); En+1..E2n apex edges (V0 Vk)
Surface table: S_k = apex edge, base edge, apex edge (k = 1..n); S_base = E1..En
```

A larger n gives a smoother approximation, and the flat look can be hidden by Gouraud or Phong shading. Alternatively, the curved side can be defined by a parametric surface patch.

## Check yourself

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

1. The side of an n-gon cylinder consists of:
   A. n triangles
   B. n rectangles (quadrilaterals)
   C. One curved face
   D. 2n triangles meeting at apex
   Answer: B. Each rectangle uses two adjacent bottom and top vertices. (Key point: Cylinder side)

2. A cylinder with n points per circle has how many vertices?
   A. n
   B. n + 1
   C. 2n
   D. 3n
   Answer: C. n on bottom and n on top. (Key point: Cylinder count)

3. A cone's side is made of:
   A. n rectangles
   B. One polygon
   C. n triangles joining the apex to adjacent base vertices
   D. n pentagons
   Answer: C. Apex plus two base vertices form each triangle. (Key point: Cone)

4. A cone with n base points has how many vertices and faces?
   A. n vertices and n faces
   B. n + 1 vertices and n + 1 faces
   C. 2n vertices and n faces
   D. n + 1 vertices and 2n faces
   Answer: B. Base points plus apex; n side triangles plus the base. (Key point: Cone count)

## Related in Computer Graphics

- [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×
- [Model curved surface using polygons](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Acurved-surface-polygons-tables) — 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

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