Today’s start-of-class procedure
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Approximate optimistic overview
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I saw many of you doing something like this.
(define ccc
(lambda (c1 c2 c3)
(overlay (solid-circle 20 c1)
(solid-circle 40 c2)
(solid-circle 60 c3))))
(define red-blue-mix
(overlay (solid-circle 20 (rgb 255 0 0))
(solid-circle 40 (rgb 255 0 255))
(solid-circle 60 (rgb 0 0 255))))
Why might I object to that definition of red-blue-mix? (TPS)
Now that you’ve defined
ccc, it’s much more concise to use(ccc (rgb 255 0 0) (rgb 255 0 255) (rgb 0 0 255)).
How does the describe-image procedure work?
When you make an image (using almost any image-making procedure), you can specify a description of the image.
describe-imagethen grabs that description. If you don’t provide a description, it does the best job it can. (We’ll do an example in class.)
> (solid-isosceles-triangle 50 20 "blue")
.
> (describe-image (solid-isosceles-triangle 50 20 "blue"))
"a solid blue 50-by-20 isosceles triangle"
> (describe-image (above (solid-isosceles-triangle 50 20 "red")
(solid-square 40 "brown")))
"a center-aligned stack of images (a solid red 50-by-20 isosceles triangle above a solid brown square with side length 40)"
> (above (solid-isosceles-triangle 50 20 "red")
(solid-square 40 "brown"))
.
> (define house (above (solid-isosceles-triangle 50 20 "red")
(solid-square 40 "brown")
"a mediocre image of a house"))
> house
.
> (describe-image house)
"a mediocre image of a house"
> (define triangle (solid-polygon (list (pt 0 0) (pt 25 75) (pt 0 100))))
. . solid-polygon: arity mismatch;
the expected number of arguments does not match the given number
given: 1
> (define triangle (solid-polygon (list (pt 0 0) (pt 25 75) (pt 0 100)) "red"))
> triangle
.
> (describe-image triangle)
"a solid red polygon built from the points (list (pt 0 0) (pt 25 75) (pt 0 100))"
Can you provide more clarification on this part of the assignment: “You should use outlined-polygon for this part of the assignment. Note that outlined-polygon only works correctly if you create the points in clockwise order. Otherwise, the outline goes on the “inside” rather than the “outside”.”
I’ll try drawing pictures in class
> (define triangle (solid-polygon (list (pt 0 0) (pt 25 75) (pt 0 100)) "red"
"the best red triangle you've ever encountered"))
> triangle
.
> (describe-image triangle)
"the best red triangle you've ever encountered"
> (define triangle (solid-polygon (list (pt 0 0) (pt 0 100) (pt 25 75)) "red"
"the best red triangle you've ever encountered"))
> triangle
.
> (describe-image triangle)
"the best red triangle you've ever encountered"
> (define triangle (outlined-polygon (list (pt 0 0) (pt 25 75) (pt 0 100)) "red" 20
"the best red triangle you've ever encountered, now outlined"))
> triangle
.
> (describe-image triangle)
"the best red triangle you've ever encountered, now outlined"
> (define triangle (outlined-polygon (list (pt 0 0) (pt 0 100) (pt 25 75)) "red" 20
"the best red triangle you've ever encountered, now outlined"))
> (describe-image triangle)
"the best red triangle you've ever encountered, now outlined"
> triangle
.
What is meant by “Code has been reformatted with Ctrl-I before submitting.”
If you hit Ctrl-I, the code is re-indented for readability. You’re now at the stage where you should be striving for moderately well organized code..
What does the “arity mismatch” error message mean and how can we fix the error?
It usually means that you’ve provided the wrong number of arguments in calling a procedure. You fix it by providing the correct number of arguments. You may have to look at the documentation to figure out what arguments you are missing.
> (outlined-polygon (list (pt 0 0) (pt 25 75) (pt 0 100)))
. . outlined-polygon: arity mismatch;
the expected number of arguments does not match the given number
given: 1
> (outlined-polygon (list (pt 0 0) (pt 25 75) (pt 0 100)) "red")
. . outlined-polygon: arity mismatch;
the expected number of arguments does not match the given number
given: 2
> (outlined-polygon (list (pt 0 0) (pt 25 75) (pt 0 100)) "red" 10)
.
> (outlined-polygon (list (pt 0 0) (pt 25 75) (pt 0 100) "red" 10))
. . outlined-polygon: arity mismatch;
the expected number of arguments does not match the given number
given: 1
Will you please discribe DrRacket’s understanding of the coordinate system? A visual representation would be useful.
I’ll draw one in class.
I still don’t quite understand what the program does when it shifts the image. “As the documentation for solid-polygon suggests, no matter what coordinates you use for the vertices, the polygon gets shifted so that the leftmost point is at the left edge of the image and the topmost point is at the top edge of the image. You can likely use this feature to your advantage. For example, if you’re making a somewhat symmetrical image, you can use (0,0) as the center.”
I’ll try to go over that in class.
> (solid-polygon (list (pt 75 75) (pt 50 100) (pt 100 100)) "orange")
.
> (above (solid-polygon (list (pt 0 0) (pt 25 75) (pt 0 100)) "green")
(solid-polygon (list (pt 75 75) (pt 50 100) (pt 100 100)) "orange"))
.
> (above (solid-polygon (list (pt 0 0) (pt 25 75) (pt 0 100)) "green")
(hshift (solid-polygon (list (pt 75 75) (pt 50 100) (pt 100 100)) "orange") 50))
.
> (above/align "left" (solid-polygon (list (pt 0 0) (pt 25 75) (pt 0 100)) "green")
(hshift (solid-polygon (list (pt 75 75) (pt 50 100) (pt 100 100)) "orange") 50))
.
> (above/align "left" (solid-polygon (list (pt 0 0) (pt 25 75) (pt 0 100)) "green")
(hshift (solid-polygon (list (pt 75 75) (pt 50 100) (pt 100 100)) "orange") 50))
.
Can we make a pentagon “by hand” so that I understand all of the steps?
Certainly.
; With an incorrect definition of radius
> (define radius (* 50 (sin (* 2/10 pi))))
> (define angle (* 2/5 pi))
> (make-polar radius angle)
9.081781600067012+27.95084971874737i
> (define pt1-x (real-part (make-polar radius angle)))
> pt1-x
9.081781600067012
> (define pt1-y (imaginary-part (make-polar radius angle)))
. . imaginary-part: undefined;
cannot reference an identifier before its definition
> (define pt1-y (imag-part (make-polar radius angle)))
> (define pt2-x (real-part (make-polar radius (* 2 angle))))
> (define pt2-y (imag-part (make-polar radius (* 2 angle))))
> (define pt3-x (real-part (make-polar radius (* 3 angle))))
> (define pt3-y (imag-part (make-polar radius (* 3 angle))))
> (define pt4-x (real-part (make-polar radius (* 4 angle))))
> (define pt4-y (imag-part (make-polar radius (* 4 angle))))
> (solid-polygon (list (pt radius 0)
(pt pt1-x pt1-y)
(pt pt2-x pt2-y)
(pt pt3-x pt3-y)
(pt pt4-x pt4-y))
"purple")
.
> (beside (solid-square 100 "black")
(solid-polygon (list (pt radius 0)
(pt pt1-x pt1-y)
(pt pt2-x pt2-y)
(pt pt3-x pt3-y)
(pt pt4-x pt4-y))
"purple"))
.
; Whoops!
; correct radius
> (define radius (/ 50 (sin (* 2/10 pi))))
> (define pt1-x (real-part (make-polar radius angle)))
> (define pt1-y (imag-part (make-polar radius angle)))
> (define pt2-x (real-part (make-polar radius (* 2 angle))))
> (define pt2-y (imag-part (make-polar radius (* 2 angle))))
> (define pt3-x (real-part (make-polar radius (* 3 angle))))
> (define pt3-y (imag-part (make-polar radius (* 3 angle))))
> (define pt4-x (real-part (make-polar radius (* 4 angle))))
> (define pt4-y (imag-part (make-polar radius (* 4 angle))))
> (beside (solid-square 100 "black")
(solid-polygon (list (pt radius 0)
(pt pt1-x pt1-y)
(pt pt2-x pt2-y)
(pt pt3-x pt3-y)
(pt pt4-x pt4-y))
"purple"))
.
What does “non-trivial” mean?
“Trivial” means “as simple as possible”. Non-trivial means “not trivial”. In Scheme, if it needs to be further evaluated, it’s non-trivial.
In the example: (add-3 (* 2 3) (+ 8 3) (/ 1 2)), do we start with solving
(/ 1 2) first? Or (* 2 3) first? Or all together?
We usually go left to right on the subexpressions. (The official Scheme standard says that we can do them in any order.)
Today’s lab is on paper! Grab a sheet of paper and a pen.