1. high-level operations on pictures
fifteen
high-level operations on pictures

2. Recap: vector graphics constructors
[box width height] Creates a picture with a box
[group pictures …] Makes a compound picture from existing pictures
[translate point pictures …] A new picture with all pictures shifted by point
[scale size-or-point pictures …] A new picture with all pictures grown/shrunk/stretched
If size-or-point is an integer, picture is uniformly grown/shrunk
If size-or-point is a point, the pictures are stretched horizontally by the point’s X coordinate, and vertically by its Y coordinate
[paint color pictures …] Renders pictures filled with color
[ink brush pictures …] Renders pictures outlined with brush

3. New: vector graphics accessors
The bounding box of a picture is the smallest (unrotated) box that completely encloses the picture
[left-edge picture] [right-edge picture] [top-edge picture] [bottom-edge picture]
Returns the X coordinate of the left/right edge of picture’s bounding box
Returns the Y coordinate of the top/bottom edge of picture’s bounding box
[width picture] [height picture]
The width/height in pixels of picture’s bounding box
[center picture]
The center point of picture’s bounding box
objects in picture
bounding box

4. Stacking boxes
How do we write a procedure to stack one picture on top of another? [stack-top [box 40 40] [box ]
[define stack-top
[top base →
[group base
[translate [point 0
[− [top-edge base]
[bottom-edge top]]]
top]]]]

5. Stacking boxes
How do we do the reverse [stack-bottom [box 40 40] [box ]
[define stack-bottom
[bottom base →
[group base
[translate [point 0
[− [bottom-edge base]
[top-edge bottom]]]
top]]]]

6. Handling variable numbers of objects
How do we make it handle more than two arguments? [stack [box 10 10] [box 20 20] [box 30 30]]
[define stack [??? → ???]]

7. New feature: Procedures with variable numbers of arguments
[name … → exp]
The “…” after the argument name means the procedure can accept a variable number of arguments
All of the arguments get packaged as a list and named name.
If the procedure is called with no arguments, then name is a list with 0 elements.
[name1 name2 … → exp]
This means the procedure requires at least 1 argument, which is named name1.
Any other arguments are packaged as a list named name2.
[name1 name2 name3 … → exp]
Same, but the first two arguments are named name1, name2.
Can have any number of extra names
But only the last name can have the “…” on it.

8. Handling variable numbers of objects
How do we make it handle more than two arguments? [stack [box 10 10] [box 20 20] [box 30 30]]
[define stack [pictures … → ???]]

9. Recap: lists [map proc list]
Runs proc on each element of list and returns a new list of the results
[fold proc list] [fold proc start-value list]
Runs proc on successive elements of list to reduce it to a single value (e.g. [fold + list] returns the sum of all elements of the list.
[apply proc list]
Runs proc with the elements of list as its arguments.
[list item1 item2 … itemn]
Makes a new list with items.

10. Handling variable numbers of objects
How do we make it handle more than two arguments? [stack [box 10 10] [box 20 20] [box 30 30]]
[define stack [pictures … → [fold stack-top pictures]]]

11. Esoteric point: Handling empty argument lists
The two-argument version of fold breaks when we call it with a list with no arguments.
So stack will break if we just say [stack]
What if we say this instead:
[define stack
[pictures … → [fold stack-top [group] «an empty group» pictures]]]

12. Stacking horizontally
[define stack-right
[base right →
[group base
[translate [point [− [right-edge base]
[left-edge right]] ]
right]]]]
[define splay
[pictures … → [fold stack-right [group] pictures]]]

13. Fixing the position of an object
Stack-top, etc. all leave base in its original position …
… and stack everything else off the end of it
So unlike box, they don’t return a picture centered around the origin
How do we recenter an existing picture around the origin?
[define recenter
[picture →
[translate [− [center picture]] picture]]]

14. Prairie School stained glass patterns
Frank Lloyd Wright
Designs emphasized strong horizontals and verticals
Common motifs
Deformed grids
Symmetry (vertical and horizontal)
Repeated patterns

15. Making deformed grids
We’d like to be able to express this picture simply and clearly
Without having to write 35 calls to box
We’ll start by just trying to get the leading (the black lines) right, without worrying about color

16. Making the leading
The design consists of almost identical rows of boxes
Each row is a fixed design
But the height varies from row to row
Start by writing code to make one row

17. Making the top row of boxes
[define top-row
[splay [box 10 10] [box 10 10] [box 15 10] [box 60 10] [box 15 10] [box 10 10] [box 10 10]]]

18. Making an arbitrary row
[define row [height →
[splay [box 10 height] [box 10 height] [box 15 height] [box 60 height] [box 15 height] [box 10 height] [box 10 height]]]]

19. Making the leading
[stack [row 10]
[row 15]
[row 190]
[row 10]]

20. What’s wrong with this? [stack [row 10] [row 15] [row 190] [row 10]]
If we want to change the design we have to redefine row
We’d like to have a procedure that
Takes the widths and heights of the rows and columns as arguments
And makes the picture

21. Making the heights be a parameter
How do we change:
[stack [row 10]
[row 15]
[row 190]
[row 10]]
into just:
[leading [list ]] ?

22. Making the heights be a parameter
[define leading
[heights →
[stack [map row heights]]]]
Well, almost:
Generates ArgumentTypeException
What’s wrong?
Splay wants to take several pictures as arguments …
… not a (single) list of pictures

23. Fixing the bug How do we fix it? [define leading [heights →
[apply stack
[map row heights]]]]

24. Making the heights be a parameter
Okay, what should we change next?
We still need to redefine row any time we want to change the design
How do we change it so we can just say:
[leading [list ] [list ]] i.e. so we can pass it both the widths and the heights as arguments?

25. Making the widths be a parameter
Now the widths need to be an argument to row
[define leading
[widths heights →
[apply stack
[map [height →
[row widths height]]
heights]]]]

26. Fixing the row procedure
This time, row will take as arguments
A list of widths
A single height
It needs to make a box for each width
And splay all the boxen together
[define row
[widths height →
[apply splay
[map [width →
[box width height]]
widths]]]]

27. Live hacking exercise Okay, now we have the leading
But no color
How do we specify the colors for each of the boxes?
Big list of colors
Procedure to compute color for each box
But what are the arguments to the procedure?
Width and height?
But what if we have identically sized boxes with different colors?
Position?
In x, y coordinates?
Or in grid position?