# Linear Bezier curve projection

• I
• bobtedbob

#### bobtedbob

TL;DR Summary
Rational linear parametric curve and its implicit
form that is a projected image of the algebraic curve
I'm looking at the following web page which looks at rendering bezier curves.

GPU Gems 3 - Chapter 25
Paper on same topic

The mathematics is quite interesting, I was interested to know what the F matrix would look like for for a linear bezier equation. The maths for the quadratic case is in the paper (2nd link) section 3 claim 1. I understand how the M matrix is calculated (and its inverse) but I don't understand how the F matrix was created.

Can someone help explain the F matrix creation process and how it would apply to the linear bezier case?

[Moderator's note: approved.]

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In paper (2nd link) section 3 claim 1, the matrix F is a permutation matrix. This matrix F has the given form because the vector ##v=[1\,\, t\,\, t^2]## was rewritten as ##u=[t \,\,t^2\,\, 1]##. This is represented by the matrix F, which is the identity matrix, rewritten with colluns in different order.

It is not clear to me what you mean with the linear bezier case. Is this case? You can find some results on Bézier curves on SearchOnMath that can helps you.

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