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. Animation (k time frames) h Scaling (resolution increased by factor of s T₁ T₂ SW Answer the following questions: (a) What is the size needed to store one frame of the original w× 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 × 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 × 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. Animation (k time frames) h Scaling (resolution increased by factor of s T₁ T₂ SW Answer the following questions: (a) What is the size needed to store one frame of the original w× 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 × 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 × 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.