Held: Tuesday, 27 January 2015

Back to Outline 04 - Computing with Symbols and Numbers. On to Outline 06 - Writing Your Own Procedures.

Summary

We explore a special kind of values, values that represent images. We call this the "drawings as values" model, and describe images by transforming and composing very simple shapes.

Related Pages

• Reading: Drawings as Values
• Lab: Drawings as Values
• Morning EBoard 5 (Source a.m. 5)
• Afternoon EBoard 5 (Source p.m. 5)

Overview

• Representing images.
• Thinking about drawings through composition/decomposition.
• The underlying representation.
• Pure approaches vs impure approaches.

Administrivia

• Continue partners!
• Office Hours:
  • Normally: 10:00-11:00 MTWF, 3:15-4:00 M (may change)
  • Currently booked: Tu 10:15-10:30, 10:45-11:00, F 10:00-11:00
  • Reserve a slot at https://rebelsky.youcanbook.me/.
  • Also feel free to try to visit during unbooked times or open times http://www.grinnell.edu/~rebelsky/schedule.html. Note that I may be busy with other things during open times.

Upcoming Work

• Assignment 2.
  • Due TONIGHT at 10:30 p.m.
• Assignment 3 to be distributed tomorrow.
  • Plan: Wednesday/Friday partners will also be your HW partner.
• Lab writeup for lab 4, due Wednesday at 10:30 p.m.: Problem 2, parts d,e,f. http://bitly.com/151-2015S-lab04
• Lab writeup for lab 5, due Thursday at 10:30 p.m., Problem 4:, parts a, c, e. http://bitly.com/151-2015S-lab05
• Readings for Wednesday: [Writing Your Own Procedures] (../readings/procedures-reading.html) and How Scheme Evaluates Expressions (Take 2)

Extra Credit Opportunities

Academic

• Friday, 12:10 p.m., JRC 224A (Day PDR), CS Table, To be determined.

Peer Support (Morning Section)

• Swimming, Friday, January 30, 6:30 p.m., Osgood Natatorium
• Swimming, Saturday, January 31, noon, Osgood Natatorium
• Julia's radio show, "The Hot Box". Wednesday night/Thursday morning 1:00-2:00 a.m.

Peer Support (Afternoon Section)

• Men's Baskeball, Tuesday, 7 p.m., New Darby
• Meditation group, Saturday, 4 p.m., CRSSJ
• Meditation group, Wednesday, 9:00 p.m., CRSSJ
• Swimming, Friday, January 30, 6:30 p.m., Osgood Natatorium
• Swimming, Saturday, January 31, noon, Osgood Natatorium
• Men's Tennis, Saturday, January 31, Field House

Recommended Events (no EC unless mentioned above)

• Women's Basketball, Tuesday, 5pm, New Darby
• Belly Dance Club, to be scheduled
• Salsa Club, Tuesdays at 7pm and Saturdays at 2pm
• Meditation group, Wednesdays at 9:00 and Sundays at 4:00 in CRSSJ
• #OneGrinnell, Wednesday, February 4 at 4:15 p.m.

Representing Images

• One of the themes of this course is that there is more than one way to represent an image.
• In this course, we will also consider multiple computational ways to think about images.
• Today we explore our first one, based on simple shapes. We call this model drawings as values.

Drawings

• Your questions about a new type should be
  • What kinds of values do I have?
  • How do I represent those values?
  • What operations do I have?
• We start with a few basic values (the unit square and the unit circle).
  • We represent these as drawing-unit-square and drawing-unit-circle
  • These are values, not procedures.
• We add a few operations (procedures)
  • Scaling
    • If d is a drawing, (scale-drawing amt d) is a drawing
  • Shifting
    • If d is a drawing, (hshift-drawing amt d) is a drawing
  • Recoloring
    • If d is a drawing, (recolor-drawing color d) is a drawing
  • Grouping
    • If d1 and d2 are drawings, so is (drawing-group d1 d2)
• Once we've described a drawing, we can view it with (image-show (drawing->image d width height))
• We will explore what benefits (and obstacles) this approach gives us.
• This model of images models one of the ways we sometimes think about images: Every image can be thought of as a composition of simpler components.
  • We just take that idea to the extreme.

Representing Drawings

• There is an underlying representation.
• You shouldn't need to know it.
• But it can be helpful to look.

Lab

• Do The lab.
• Be prepared to reflect.

Purity (Optional)

• Note that the definition of drawings uses induction, in much the same way that the definition of whole numbers uses induction.
• For whole numbers:
  • 0 is a whole number
  • If w is a whole number, 1+w is a whole number
• For drawings
  • The unit circle is a drawing.
  • The unit square is a drawing.
  • If d is a drawing, then a shifted version of d is a drawing.
  • If d is a drawing, then a scaled version of d is a drawing.
  • If d1 and d2 are drawings, the grouping of d1 and d2 is a drawing.
• When we build a new whole number from a previous whole number (by adding 1), we don't affect the previous whole number.
• Similarly, when we build a new drawing from a previous drawing, we don't affect the previous drawing.
• Contrast this with the GIMP tools, in which each command changes (sometimes irrevocably) the underlying image.
• When operations do not affect the underlying data structure, we call them pure operations.