---
title: "Fillet surface and offset surface"
subject: "Computer Aided Design"
chapter: 4
key: "semester_4/computer_aided_design:fillet-offset-surface"
source: https://www.bctengineer.com/q/semester_4/computer_aided_design/fillet-offset-surface
site: BCT Engineering
---

# Fillet surface and offset surface

Computer Aided Design · Chapter 4: Representation of Surfaces and Solids

- Asked in: year not given, 5 marks
- Video: [AutoCAD 3D Surfaces | Planar | Network | Blend | Patch | Offset | Fillet](https://www.youtube.com/watch?v=OeeZGIIr7iA) — Techhub Solutions Official
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/computer_aided_design/fillet-offset-surface
- Whole chapter: https://www.bctengineer.com/md/semester_4/computer_aided_design/chapter-4

## Question

Write short notes on (a) fillet surface and (b) offset surface, with their uses in CAD/CAM.

## Short answer

Fillet surface smoothly rounds the intersection of two surfaces with constant or variable radius to remove sharp edges; used for stress reduction, mouldability, safety and appearance. Offset surface is P_o=P+d n-hat, a constant-distance surface; used for cutter paths, shelling, clearance and mould cavities. Offsets can self-intersect when d exceeds the concave radius of curvature.

## Answer

#### (a) Fillet surface
A **fillet surface** is a smooth blending surface that joins two intersecting surfaces (or a surface and a plane) with a rounded transition. It removes sharp edges.

- **Constant-radius fillet:** the surface is the envelope of a ball of radius $r$ rolling in contact with both surfaces; the ball centre follows the curve that lies at distance $r$ from both. The section is a circular arc tangent to both surfaces.
- **Variable-radius fillet:** the radius changes along the edge.
- A **chamfer** is the flat version.
- For a given radius, the arc length of the fillet depends on the angle at which the two faces meet.

```text
   before            after fillet
   |                 |
   |____             |__
                        `--.____   (rounded corner)
```

Uses: reduces stress concentration in machine parts, makes castings and moulds easier to manufacture (draft and flow), improves appearance and safety, and avoids sharp edges in sheet-metal and plastic parts.

#### (b) Offset surface
An **offset surface** is a surface at a constant distance $d$ along the normal from a given surface:

$$
\mathbf P_o(u,w)=\mathbf P(u,w)+d\,\hat{\mathbf n}(u,w)
$$

Examples: offsetting a cylinder of radius 20 by $d=3$ gives radius 23 (outward) or 17 (inward); a plane offset is a parallel plane.

- Limitation: if $d$ is larger than the smallest radius of curvature on the concave side, the offset self-intersects (a cusp or loop appears).
- Uses: **cutter-path generation** (offset the part surface by the tool radius so the tool centre follows it), shelling and wall thickness (hollow parts, plastic housings), clearance and tolerance zones, mould cavities made from a part with shrinkage allowance, and sheet-metal thickness.

## Check yourself

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

1. What is a constant-radius fillet surface?
   A. A flat cut across a sharp edge
   B. A rounded blend that is the envelope of a ball of radius r rolling in contact with both surfaces
   C. A surface at constant distance along the normal from another surface
   D. A surface made by rotating a profile about an axis
   Answer: B. The fillet section is a circular arc tangent to both faces; the flat version is a chamfer. (Key point: Fillet surface)

2. Which equation gives an offset surface at distance d?
   A. P_o = P + d n (unit normal)
   B. P_o = P + d (constant vector)
   C. P_o = (1-d) P
   D. P_o = P x n
   Answer: A. The offset moves each point a distance d along the unit surface normal. (Key point: Offset surface equation)

3. When does an offset surface self-intersect, and what is a key use?
   A. When d is smaller than the radius; used only for drawing
   B. When d exceeds the smallest radius of curvature on the concave side; used for cutter-path generation
   C. Never; used for fillets only
   D. When d is zero; used for chamfers
   Answer: B. A large offset causes cusps or loops; offsetting by the tool radius gives the cutter-centre path. (Key point: Offset limit and use)

## Related in Computer Aided Design

- [Define CAD, CAM and CAE](https://www.bctengineer.com/question.md?key=semester_4%2Fcomputer_aided_design%3Acad-cam-cae-definitions) — Computer Aided Design, chapter 1
- [Integration of CAD and CAM](https://www.bctengineer.com/question.md?key=semester_4%2Fcomputer_aided_design%3Acad-cam-integration) — Computer Aided Design, chapter 6
- [Classification of CAD surface entities](https://www.bctengineer.com/question.md?key=semester_4%2Fcomputer_aided_design%3Asurface-entities-classification) — Computer Aided Design, chapter 4

## Related in other subjects

- [Drawing cam profile for offset roller follower](https://www.bctengineer.com/question.md?key=semester_6%2Ftheory_of_mechanism_and_machine_i%3Aoffset-roller-follower-cam-profile) — Theory of Mechanism and Machine I, chapter 3