---
title: "Interpolation versus approximation spline"
subject: "Computer Graphics"
chapter: 5
key: "semester_5/computer_graphics:interpolation-vs-approximation-spline"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/interpolation-vs-approximation-spline
site: BCT Engineering
---

# Interpolation versus approximation spline

Computer Graphics · Chapter 5: Curve Modeling

- Asked in: 2070 Asar, 2 marks; 2076 Chaitra, 3 marks (asked 2 times)
- Video: [Interpolation and Approximation technique in computer graphics](https://www.youtube.com/watch?v=zoJQJkl-J_o) — Rashmi Tundalwar
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/interpolation-vs-approximation-spline
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-5

## Question

What is the difference between an interpolation spline and an approximation spline curve?

## Short answer

Interpolation spline passes through all control points, used for digitizing paths. Approximation spline follows shape but only endpoints are guaranteed, used for design. Interpolation can overshoot; approximation gives smoother, predictable shape. Examples: Hermite, cardinal are interpolation; Bezier, B-spline are approximation, with B-spline offering local control.

## Answer

An **interpolation spline** passes through all given control points. An **approximation spline** follows the general shape of the control points but need not pass through them (only some, like the end points).

| Point | Interpolation spline | Approximation spline |
|---|---|---|
| Passes through control points | Yes, all | No (usually only end points) |
| Used for | Digitizing drawings, animation paths | Designing shapes and surfaces |
| Control of shape | Less intuitive, may overshoot | Smooth, predictable |
| Control points known as | Data points | Control points forming a control graph |
| Examples | Hermite, cardinal, Catmull-Rom, natural cubic spline | Bezier, B-spline |
| Local change | Changing a point may disturb the curve widely | B-spline gives local control |

## Check yourself

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

1. Which statement correctly separates an interpolation spline from an approximation spline?
   A. An approximation spline passes through all control points; an interpolation spline does not
   B. Both pass through all points but differ in degree
   C. An interpolation spline passes through all control points; an approximation spline only follows their general shape
   D. An interpolation spline passes only through the end points
   Answer: C. Interpolation splines pass through every given point, while approximation splines need not (often only the end points). (Key point: Defining difference)

2. Which pair lists only approximation splines?
   A. Hermite and Bezier
   B. Catmull-Rom and B-spline
   C. Bezier and B-spline
   D. Cardinal and Hermite
   Answer: C. Bezier and B-spline are approximation splines; Hermite, cardinal and Catmull-Rom are interpolation splines. (Key point: Examples)

3. Which use best fits an interpolation spline?
   A. Digitizing drawings or animation paths through given points
   B. Designing free-form surfaces from a control graph
   C. Local shape editing of a car body
   D. Clipping polygons
   Answer: A. Interpolation splines are used where the curve must go through known data points, such as digitizing and animation paths. (Key point: Typical use)

## Related in Computer Graphics

- [Define spline curve](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Adefine-spline-curve) — Computer Graphics, chapter 5
- [Curve modeling using splines](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Acurve-modeling-using-splines) — Computer Graphics, chapter 5, asked 3×
- [Draw Bezier curve through 4 control points](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Abezier-four-points-p0-0-0) — Computer Graphics, chapter 5
- [Hermite curve and blending functions](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Ahermite-curve-blending-functions) — Computer Graphics, chapter 5, asked 2×

## Related in other subjects

- [B-spline curve versus Bezier curve](https://www.bctengineer.com/question.md?key=semester_4%2Fcomputer_aided_design%3Abspline-vs-bezier) — Computer Aided Design, chapter 3
- [Natural cubic spline: y(6.5)](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Aspline-5-7-9-11) — Numerical Method, chapter 4, asked 3×
- [Natural cubic spline: y(4.5)](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Aspline-4-5) — Numerical Method, chapter 4, asked 3×
- [Natural cubic spline: y(0.5)](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Aspline-y-0-5) — Numerical Method, chapter 4, asked 3×