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Data Representation and Multimedia: Question 9

Syllabus 1.1, 1.2, 1.3

Structured AS 8 marks

A graphic design company is creating a company logo, which contains a single filled circle.

(a) State three properties, other than the fact that the object is a circle, that a vector graphics file would need to store in order to describe and redraw this circle. [3]

(b) The logo is stored as a vector image containing 250 separate objects (shapes). Each object requires 48 bytes to store its type and properties. Calculate the total uncompressed file size of the vector image, in bytes. Show your working. [2]

(c) A bitmap version of the same logo has a file size of 50 kilobytes (kB), where 1 kB = 1000 bytes. Using your answer to part (b), state which version of the logo file is smaller, and calculate how many times smaller it is than the other. Give your answer to 1 decimal place. [3]

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Worked solution

Part (a): Properties stored for a vector object

A vector graphics file does not store individual pixel colours. Instead, for each drawn object, it stores a set of properties that describe how to draw that object, which a program can use to redraw it at any size.

For a filled circle, three properties that would need to be stored (in addition to the fact that the object is a circle) are, for example:

  • The centre coordinates (x, y position) of the circle
  • The radius of the circle
  • The fill colour used to shade the inside of the circle

(Other valid properties include the outline or border colour, and the outline’s line thickness.)

[3 marks]: [1] each for up to three valid, distinct object properties (not including individual pixel colour data or the object type “circle” itself).

Part (b): Vector file size from stored objects

A vector file’s size depends on the number of objects it stores and how many bytes each object needs, not on a fixed pixel grid.

250 objects x 48 bytes per object = 12,000 bytes

[2 marks]: [1] for multiplying the number of objects by the bytes per object (rather than adding the two values or using only one of them), [1] for the correct result, 12,000 bytes.

Part (c): Comparing with the bitmap file size

The bitmap file size is given as 50 kB, using the decimal kilobyte (1 kB = 1000 bytes):

50 x 1000 = 50,000 bytes

Comparing the two file sizes: the vector file is 12,000 bytes, and the bitmap file is 50,000 bytes, so the vector file is smaller.

To find how many times smaller, divide the larger file size by the smaller one:

50,000 / 12,000 = 4.1666...

Rounded to 1 decimal place, the vector file is approximately 4.2 times smaller than the bitmap file.

[3 marks]: [1] for correctly converting 50 kB to 50,000 bytes, [1] for identifying the vector file as the smaller of the two, [1] for the correctly calculated and rounded ratio, 4.2.

Final answers

  • (a) Any three of: centre coordinates, radius, fill colour, outline colour, outline thickness
  • (b) 12,000 bytes
  • (c) The vector file (12,000 bytes) is smaller than the bitmap file (50,000 bytes), about 4.2 times smaller