Bézier curves and B-splines
Free-form curves let a planner describe a fibre path with a handful of numbers: control points. Those numbers become design variables an optimiser can move. A quadratic Bézier fixes the start and end angles exactly, and one parameter, β₁, decides where the turn happens, and so how tight it gets.
Predict · at 1:50 in the video
Zero to forty-five degrees over half a metre. Beta one of zero point three, zero point five, or zero point seven. Which is easiest to steer?
Zero point five. Its tightest radius is five hundred millimetres. At zero point three, the turn is crammed near the start: a hundred and twenty-nine.
Automated Fiber Placement: Status, Challenges, and Evolution, Ramy Harik & Alex Brasington.
- Chapter 5, section 2.3.4.1
- Chapter 5, section 2.3.4.1.A
- Chapter 5, section 2.3.4.1.B
Simulations in this lesson are our own. Where the numbers are invented to show a mechanism, the video says so on screen.
