Unit 2 - Transformations and Composition

In this unit, students learn about a new algebra of pictures, which has rules similar to those of numbers. The overlay operator combines two pictures by laying the first picture over the second one, and this operation is associative but not commutative. Other transformations, such as translations, can also be applied to pictures. Overlays and translations are the tools that allow us to decompose pictures into separate parts that we can process or synthesize separately.

Unit objectives

  • Describe how overlays and translations transform pictures
  • Demonstrate how a picture can be built out of of simple components
  • Create hierarchical decompositions of objects more than two levels deep
  • Use unevaluated expressions to indicate calculations to be performed by a computer
  • Design rules to calculate layouts that follow grid patterns
  • Explain how graphical objects can be reused to create different parts of a drawing