- Asked 2/25
- 2070 Asar · 2 marks
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Interpolation versus approximation spline
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.
What is the difference between an interpolation spline and an approximation spline curve?
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 |
✓ Answer checked by Claude Opus 5.5 (high effort)
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