Provide an Appropriate Response $\mathbf { p } _ { 0 } , \mathbf { p } _ { 1 }$

question 31

Multiple Choice

Provide an appropriate response.
-A quadratic Bézier curve is determined by 3 control points $\mathbf { p } _ { 0 } , \mathbf { p } _ { 1 }$ , and $\mathbf { p } _ { 2 }$ . The equation is $\mathbf { x } ( \mathrm { t } ) =$ $( 1 - t ) ^ { 2 } \mathbf { p } _ { 0 } + 2 t ( 1 - t ) \mathbf { p } _ { 1 } + \mathrm { t } ^ { 2 } \mathbf { p } _ { 2 }$ . Construct the quadratic Bézier basis matrix $\mathrm { M } _ { \mathrm { B } }$ for $\mathbf { x } ( \mathrm { t } )$ .

• A) \(\left[ \begin{array} { r r r } 1 & 0 & 1 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{array} \right]\)
• B) \(\left[ \begin{array} { r r r } 1 & - 2 & 1 \\ 0 & 2 & - 2 \\ 0 & 0 & 1 \end{array} \right]\)
• C) \(\left[ \begin{array} { r r } 1 & 1 \\ 2 & - 2 \\ 0 & 1 \end{array} \right]\)
• D) \(\left[ \begin{array} { r r r } 1 & 2 & 2 \\ 0 & 2 & - 2 \\ 0 & 0 & 1 \end{array} \right]\)

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