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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Definitions:

Cause and Effect

A relationship where one event (the cause) directly leads to the occurrence of another event (the effect).

Real Objects

In psychoanalytic theory, refers to tangible, physical objects as opposed to imagined or conceptual ones.

Reasoning

The method of using reason and logic to examine something to make a decision or verdict.

Dynamic Systems

Dynamic systems are systems characterized by constant change, activity, or progress, where interactions and relationships within the system can lead to varying outcomes over time.