\( \newcommand{\vecIII}[3]{\left[\begin{array}{c} #1\\#2\\#3 \end{array}\right]} \newcommand{\vecIV}[4]{\left[\begin{array}{c} #1\\#2\\#3\\#4 \end{array}\right]} \newcommand{\Choose}[2]{ { { #1 }\choose{ #2 } } } \newcommand{\vecII}[2]{\left[\begin{array}{c} #1\\#2 \end{array}\right]} \newcommand{\vecIII}[3]{\left[\begin{array}{c} #1\\#2\\#3 \end{array}\right]} \newcommand{\vecIV}[4]{\left[\begin{array}{c} #1\\#2\\#3\\#4 \end{array}\right]} \newcommand{\matIIxII}[4]{\left[ \begin{array}{cc} #1 & #2 \\ #3 & #4 \end{array}\right]} \newcommand{\matIIIxIII}[9]{\left[ \begin{array}{ccc} #1 & #2 & #3 \\ #4 & #5 & #6 \\ #7 & #8 & #9 \end{array}\right]} \)

Quiz

  1. For question 2 on this quiz, can you specify how option A and option B differ? 

    Match the curve specification with the description
1. interpolating
    The user specifies four points that are on the curve.
2. Hermite
    The user specifies two endpoints and
    the derivative at the each endpoints
3. Bezier
    The user specifies two endpoints and
    two points that suggest the direction at the endpoints.

    In an interpolating curve, we specify the curve by giving points is that the curve goes through.

    In a Hermite curve, we specify the curve by giving the endpoints and the direction (derivative) at each endpoint.

  2. I am still a little confused on blending functions and I was hoping that we could go over them?

    Glad to. I think of them as the amount of pull each control point has as a function of t

  3. I'm a little lost on how the Bezier curves apply to Bezier surfaces.

    It's a tricky transition, for sure.

    Each edge of the surface is a Bezier curve.

    The four interior points also pull the patch towards them.

    I once had students create a Pringle or saddle as an exercise.