Mathematics
posted by Tanveer on .
Images on a computer can be stored many ways to account for quality and space issues. One of the factors we can adjust is colour depth. Colour depth determines the number of bits we use for each pixel of an image. The pixels are the small dots that make up an image. The higher the colour depth (or bit per pixel), the more distinct colours an image can have. Some standard colour depths include 2bit (CGA), 4bit (EGA), and 8 bit (VGA).
a) Given an image that is 1024x768 pixels determine the size (in bytes) of the image at CGA, EGA, and VGA resolutions. (2 marks)
b) An image with dimensions of 400x800 pixels is compressed to save space. The compressed file is reduced to 76% of the original size, and now measures 972800 bytes. Determine the colour depth of the original image, in bits. (3 marks)
c) A computer generated sphere is covered with a texture. A texture is single image that is repeated many times in order to save memory. Given the sphere has a diameter of 1000 pixels, how many time must a 64x64 pixel image be repeated to cover the entire sphere? (4 marks)

a) 1024x768 = 788736 pixels.
Just multiply by 2,4,8 to get # bits used
Divide by 8 to get bytes.
b) The compressed size is 972800 bytes, so the full expanded size is 972800/.76 = 1280000 bytes.
Multiply by 8 to get bits.
Divide by 400x800 to get depth
c) Area = pi d^2 = 3141593 px^2
Divide by 64x64 to get replication factor. Assuming the repetitions would exactly cover the sphere.