Bézier Curve Coefficient Matrix
- Author:
- Ryan Hirst
- Topic:
- Matrices, Parametric Curves
Tool (.ggt): http://www.geogebratube.org/material/show/id/83831
Command: BezierCf[n]
Output: (n+1)×(n+1) matrix
Given a list of Points
and a variable of motion, t
In GGB,t can be used as a scalar parameter, with the Locus[] command.
For a Curve[], trade t for x:
τ = Sequence[x^k, k, 0, n]
The x- and y- components of the curve are then
βx = Sum[Zip[a b, a, Join[{x(Pts)} C], b, τ]]
βy = Sum[Zip[a b, a, Join[{y(Pts)} C], b, τ]]
From which the Bézier curve is
β = Curve[βx(a), βy(a), a, 0, 1]
What? GGBScript is not math. In math, the product
β = Pts C τ(t), 0≤t≤1
is immediate and unambiguous.
It's cute that math people wonder why students have a hard time with math at the computer.
?
When did we make it possible for them to do math at the computer?
________
Bézier Curves: 2. High Order Curves
- Standard Curve: → Coefficient Matrix(+TOOL) Bézier Curve of Order n (+TOOL): http://www.geogebratube.org/material/show/id/83844
- Curve from Path: http://www.geogebratube.org/material/show/id/84017 Coefficient Matrix (+TOOL): http://www.geogebratube.org/material/show/id/84218 Bézier Path of Order n (+TOOL): http://www.geogebratube.org/material/show/id/84231