A First Course in Linear Algebra
A First Course in Linear Algebra (UNSW). Taught by Professor N. J. Wildberger, this course presents a geometrical view to Linear Algebra, with special orientation to applications and understanding of key concepts. The subject naturally sits inside affine geometry, which is the natural setting for vectors. Flexibility in choosing coordinate frameworks is important for understanding the subject. Determinants also play a key role, and these are introduced in the context of multi-vectors in the sense of Grassmann. The course features a careful treatment of polynomial spaces, with applications to Stirling numbers and cubic splines.
| Lecture 24 - Cubic Splines (Bezier Curves) Using Linear Algebra |
We introduce de Casteljau Bezier curves by combining linked convex/affine motions along line segments. This way of describing and specifying curves was introduced around 1960 by these two engineers, aiming to find a better way to capture curves for design work (originally for automobiles, but now these are used everywhere in design work).
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