---
title: "Classification of CAD surface entities"
subject: "Computer Aided Design"
chapter: 4
key: "semester_4/computer_aided_design:surface-entities-classification"
source: https://www.bctengineer.com/q/semester_4/computer_aided_design/surface-entities-classification
site: BCT Engineering
---

# Classification of CAD surface entities

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

- Asked in: year not given, 5 marks
- Video: [L 33 Types of Analytical and Synthetic Surfaces | Computer Aided Design | Mechanical](https://www.youtube.com/watch?v=3L1xs82uCbc) — MECHANICAL & AUTOMOBILE ENGINEERING_LJIET
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/computer_aided_design/surface-entities-classification
- Whole chapter: https://www.bctengineer.com/md/semester_4/computer_aided_design/chapter-4

## Question

List and classify the surface entities used in CAD systems. Briefly describe the plane, ruled, tabulated cylinder and surface of revolution, and state where synthetic surfaces are used.

## Short answer

CAD surface entities are divided into analytic (plane, ruled, tabulated cylinder, surface of revolution) and synthetic (Bezier, B-spline, Coons patch) surfaces. Synthetic surfaces model free-form shapes such as car bodies and aircraft wings.

## Answer

CAD surface entities are divided into **analytic** and **synthetic** surfaces.

| Class | Surfaces | Defined by |
|---|---|---|
| Analytic | Plane, ruled surface, surface of revolution, tabulated cylinder | Standard equations, few parameters |
| Synthetic | Bezier, B-spline (NURBS), Coons patch, Hermite bicubic | Control points / boundary curves |
| Derived | Fillet surface, offset surface, blend surface | Built from other surfaces |

#### Analytic surfaces
- **Plane surface:** defined by three non-collinear points, or a point and a normal. Equation $ax+by+cz=d$.
- **Ruled (lofted) surface:** generated by joining corresponding points of two boundary curves with straight lines: $\mathbf P(u,w)=(1-w)\mathbf P_1(u)+w\mathbf P_2(u)$. Example: a cone or a twisted turbine-blade strip.
- **Tabulated cylinder:** a planar curve (directrix) translated along a straight line of fixed direction and length: $\mathbf P(u,w)=\mathbf C(u)+w\mathbf L$. Example: an extruded profile.
- **Surface of revolution:** a plane curve (generatrix) rotated through an angle about an axis: $\mathbf P(u,\phi)$ with the radius from the curve. Examples: bottles, vases, pulleys, domes.

#### Synthetic surfaces
These are free-form surfaces for shapes with no simple equation: car bodies, aircraft wings, ship hulls, helmets and plastic housings. They are built from a net of control points (Bezier, B-spline) or from four boundary curves (Coons patch).

Surfaces are stored in parametric form $\mathbf P(u,w)$, $0\le u,w\le1$, so normals, tangents and boundaries are easy to compute for display and machining.

## Check yourself

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

1. Which is a synthetic surface?
   A. Plane
   B. Coons patch
   C. Tabulated cylinder
   D. Surface of revolution
   Answer: B. Bezier, B-spline, Coons and Hermite bicubic are synthetic; plane, ruled, revolution, tabulated cylinder are analytic. (Key point: Classification)

2. How is a ruled surface formed?
   A. Rotating a curve about an axis
   B. Translating a curve along a line
   C. Straight lines joining corresponding points of two boundary curves
   D. Four boundary curves
   Answer: C. P(u,w) = (1-w)P1(u) + wP2(u). (Key point: Ruled surface)

3. Where are synthetic surfaces used?
   A. Simple flat plates
   B. Only for cylinders
   C. Only for drafting
   D. Free-form shapes like car bodies and aircraft wings
   Answer: D. Synthetic surfaces model shapes with no simple equation. (Key point: Synthetic use)

4. What defines a tabulated cylinder?
   A. Translating a planar curve along a straight line
   B. Rotating a curve
   C. Joining two curves
   D. A net of control points
   Answer: A. P(u,w) = C(u) + wL; like an extrude. (Key point: Tabulated cylinder)

## Related in Computer Aided Design

- [Tabulated cylinder surface](https://www.bctengineer.com/question.md?key=semester_4%2Fcomputer_aided_design%3Atabulated-cylinder-surface) — Computer Aided Design, chapter 4
- [Ruled surface between two lines: points](https://www.bctengineer.com/question.md?key=semester_4%2Fcomputer_aided_design%3Aruled-surface-numerical) — Computer Aided Design, chapter 4
- [Surface of revolution: equation, points, area](https://www.bctengineer.com/question.md?key=semester_4%2Fcomputer_aided_design%3Asurface-of-revolution-numerical) — Computer Aided Design, chapter 4
- [Selection, manipulation and editing of entities](https://www.bctengineer.com/question.md?key=semester_4%2Fcomputer_aided_design%3Aentity-selection-manipulation-editing) — Computer Aided Design, chapter 5

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