Linear Algebra › Section H · The geometry of vector spaces › Topic H.6
Curves and surfaces
The letters of most digital fonts and many car-body panels are drawn with Bézier curves, built from a few control points by convex combinations. This topic shows how those curves are defined, why they behave so predictably, how pieces join smoothly, and how the same idea makes surfaces.
In this topic
- Curves from control points
- Quadratic Bézier curves
- Cubic Bézier curves
- Worked example: points on a cubic
- The matrix form
- Joining curves smoothly
- Worked example: a smooth join
- Subdivision by repeated midpoints
- Bézier surfaces
- Common mistakes to avoid
- Key takeaways
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