Monday, January 12, 2009

SICP Section 2.2 Hierarchical Data and the Closure Property - Part 2

Exercise 2.44. Define the procedure up-split used by corner-split. It is similar to right-split, except that it switches the roles of below and beside.

Exercise 2.45. Right-split and up-split can be expressed as instances of a general splitting operation. Define a procedure split with the property that evaluating

produces procedures right-split and up-split with the same behaviors as the ones already defined.


Exercise 2.46. A two-dimensional vector v running from the origin to a point can be represented as a pair consisting of an x-coordinate and a y-coordinate. Implement a data abstraction for vectors by giving a constructor make-vect and corresponding selectors xcor-vect and ycor-vect. In terms of your selectors and constructor, implement procedures add-vect, sub-vect, and scale-vect that perform the operations vector addition, vector subtraction, and multiplying a vector by a scalar:


Exercise 2.47. Here are two possible constructors for frames:

For each constructor supply the appropriate selectors to produce an implementation for frames.


Exercise 2.48. A directed line segment in the plane can be represented as a pair of vectors -- the vector running from the origin to the start-point of the segment, and the vector running from the origin to the end-point of the segment. Use your vector representation from exercise 2.46 to define a representation for segments with a constructor make-segment and selectors start-segment and end-segment.


Exercise 2.49. Use segments->painter to define the following primitive painters:

a. The painter that draws the outline of the designated frame.

b. The painter that draws an ``X'' by connecting opposite corners of the frame.

c. The painter that draws a diamond shape by connecting the midpoints of the sides of the frame.

d. The wave painter.

Answer: a. The painter that draws the outline of the designated frame. This is done by connecting the four corners of the frame. Translated to the unit frame the corners are the points (0, 0), (1, 0), (0, 1) and (1, 1).

b. Painting an x is accomplished by connecting opposite corners of the frame. This means drawing a line connecting (0, 0) to (1, 1) and (0, 1) to (1, 0) respectively.

c. A diamond shape is created by connecting the midpoints of the sides of the unit square.

d. I'll skip the wave painter. Too many line segments!

Exercise 2.50. Define the transformation flip-horiz, which flips painters horizontally, and transformations that rotate painters counterclockwise by 180 degrees and 270 degrees.


Exercise 2.51. Define the below operation for painters. Below takes two painters as arguments. The resulting painter, given a frame, draws with the first painter in the bottom of the frame and with the second painter in the top. Define below in two different ways -- first by writing a procedure that is analogous to the beside procedure given above, and again in terms of beside and suitable rotation operations (from exercise 2.50).


Exercise 2.52. Make changes to the square limit of wave shown in figure 2.9 by working at each of the levels described above. In particular:

a. Add some segments to the primitive wave painter of exercise 2.49 (to add a smile, for example).

b. Change the pattern constructed by corner-split (for example, by using only one copy of the up-split and right-split images instead of two).

c. Modify the version of square-limit that uses square-of-four so as to assemble the corners in a different pattern. (For example, you might make the big Mr. Rogers look outward from each corner of the square.)

Answer: I am skipping the smiley part.

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