Memory is important when storing images $($textures$)$ on

a graphics card. Quite often GPU devices have limited memory. We will look at

this practical problem of storage space. Consider the following diagram showing a set of animation frames and an image that is scaled for higher resolution.

Assume h and w are the same in both examples.

Answer the following questions:

$($a$)$ What is the size needed to store one frame of the original w $\backslash$times h image in

memory? These images are RGBA values, which mean red, green, blue,

and alpha components. Each of these RGBA components is stored as one

byte of data $(0-255).$

$($b$)$ What would be the size in memory for $100$ animation frames of the original

image, assuming the original image was $512\backslash$times $256.($Remember that $1$ kb

$=1024$ bytes, $1$ mb $=1024$ kb$,$ and $1$ gb $=1024$ mb$.)$

$($c$)$ What would be the size in memory for an image scaled by $4,$ assuming

the original image was $512\backslash$times $256?$

$($d$)$ Which operation scales better in terms of memory space efficency? Is

more memory needed for adding animation frames or for scaling to a

higher resolution image? Analyze this using the Big Theta notation. Part B: Problem $1$: Memory is important when storing images $($textures$)$ on

a graphics card. Quite often GPU devices have limited memory. We will look at

this practical problem of storage space. Consider the following diagram show$-$

ing a set of animation frames and an image that is scaled for higher resolution.

Assume h and w are the same in both examples.

Answer the following questions:

$($a$)$ What is the size needed to store one frame of the original $wh$ image in

memory? These images are RGBA values, which mean red, green, blue,

and alpha components. Each of these RGBA components is stored as one

byte of data $(0-255).$

$($b$)$ What would be the size in memory for $100$ animation frames of the original

image, assuming the original image was $512256.($Remember that $1$ kb

$=1024$ bytes, $1mb=1024kb,$ and $1gb=1024mb.)$

$($c$)$ What would be the size in memory for an image scaled by $4,$ assuming

the original image was $512256?$

$($d$)$ Which operation scales better in terms of memory space efficency? Is

more memory needed for adding animation frames or for scaling to a

higher resolution image? Analyze this using the Big Theta notation.