## Invitation to Computer Science 8th Edition

Published by Cengage Learning

# Chapter 16 - 16.2 - Computer-Generated Imagery (CGI) - Practice Problem - Page 772: 1

#### Answer

\begin{array}{l}{\text { Because the motion takes place over a period of } 2 \text { seconds, we need to }} \\ {\text { produce a total of } 60 \text { frames, given that } 30 \text { frames is the standard }} \\ {\text { frame rate for video. These } 6 \text { frames represent } 59 \text { time intervals. So in each }} \\ {\text { of the } 58 \text { in-between frames, we must move the triangle } 1 / 55 \text { th of the total }} \\ {\text { distance from its position in the first move to its position in the last frame. }} \\ {\text { This information allows us to compute the translation matrix. }}\end{array} \begin{array}{l}{\text { Total x-distance moved }=4 \text { units }} \\ {\mathrm{a}=1 / 59 \times 4=0.067796} \\ {\text { Total y-distance moved = } 2 \text { units }} \\ {\mathrm{b}=1 / 59 \times 2=0.033898} \\ {\text { Total z-distance moved = 0 units }} \\ {\mathrm{c}=1 / 59 \times 0=0}\end{array} \begin{array}{l}{\text { Now, using the model shown in Figure } 16.6, \text { we can say that the translation }} \\ {\text { matrix required to perform the desired motion is as follows: }}\end{array} \begin{array}{cccc}{1} & {0} & {0} & {0.067796} \\ {0} & {1} & {0} & {0.033898} \\ {0} & {0} & {0} & {0} \\ {0} & {0} & {0} & {1}\end{array}

#### Work Step by Step

\begin{array}{l}{\text { Because the motion takes place over a period of } 2 \text { seconds, we need to }} \\ {\text { produce a total of } 60 \text { frames, given that } 30 \text { frames is the standard }} \\ {\text { frame rate for video. These } 6 \text { frames represent } 59 \text { time intervals. So in each }} \\ {\text { of the } 58 \text { in-between frames, we must move the triangle } 1 / 55 \text { th of the total }} \\ {\text { distance from its position in the first move to its position in the last frame. }} \\ {\text { This information allows us to compute the translation matrix. }}\end{array} \begin{array}{l}{\text { Total x-distance moved }=4 \text { units }} \\ {\mathrm{a}=1 / 59 \times 4=0.067796} \\ {\text { Total y-distance moved = } 2 \text { units }} \\ {\mathrm{b}=1 / 59 \times 2=0.033898} \\ {\text { Total z-distance moved = 0 units }} \\ {\mathrm{c}=1 / 59 \times 0=0}\end{array} \begin{array}{l}{\text { Now, using the model shown in Figure } 16.6, \text { we can say that the translation }} \\ {\text { matrix required to perform the desired motion is as follows: }}\end{array} \begin{array}{cccc}{1} & {0} & {0} & {0.067796} \\ {0} & {1} & {0} & {0.033898} \\ {0} & {0} & {0} & {0} \\ {0} & {0} & {0} & {1}\end{array}

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