► |  | How to Design Programs Teachpacks

1 | Ht DP Teachpacks
2 | Ht DP/ 2e Teachpacks

▼ | 2 | Ht DP/ 2e Teachpacks

2.1 | Batch Input/ Output: "batch-io.ss"
2.2 | Images: "image.ss"
2.3 | Image Guide
2.4 | Worlds and the Universe: "universe.ss"
2.5 | Planet Cute Images
2.6 | Porting World Programs to Universe

► | 2.2 | Images: "image.ss"

2.2.1 | Basic Images
2.2.2 | Polygons
2.2.3 | Overlaying Images
2.2.4 | Placing Images & Scenes
2.2.5 | Rotating, Scaling, Flipping, Cropping, and Framing Images
2.2.6 | Bitmaps
2.2.7 | Image Properties
2.2.8 | Image Predicates
2.2.9 | Equality Testing of Images
2.2.10 | Pinholes
2.2.11 | Exporting Images to Disk

On this page:

2.2.1`` Basic Images
circle
ellipse
line
add-line
add-curve
text
text/ font
empty-image
2.2.2`` Polygons
triangle
right-triangle
isosceles-triangle
triangle/ sss
triangle/ ass
triangle/ sas
triangle/ ssa
triangle/ aas
triangle/ asa
triangle/ saa
square
rectangle
rhombus
star
star-polygon
radial-star
regular-polygon
polygon
2.2.3`` Overlaying Images
overlay
overlay/ align
overlay/ offset
overlay/ align/ offset
overlay/ xy
underlay
underlay/ align
underlay/ offset
underlay/ align/ offset
underlay/ xy
beside
beside/ align
above
above/ align
2.2.4`` Placing Images & Scenes
empty-scene
place-image
place-image/ align
scene+ line
scene+ curve
2.2.5`` Rotating, Scaling, Flipping, Cropping, and Framing Images
rotate
scale
scale/ xy
flip-horizontal
flip-vertical
crop
frame
2.2.6`` Bitmaps
bitmap
bitmap/ url
bitmap/ file
image->color-list
color-list->bitmap
freeze
2.2.7`` Image Properties
image-width
image-height
image-baseline
2.2.8`` Image Predicates
image?
mode?
image-color?
color
y-place?
x-place?
angle?
side-count?
step-count?
real-valued-posn?
pen
pen-style?
pen-cap?
pen-join?
2.2.9`` Equality Testing of Images
2.2.10`` Pinholes
center-pinhole
put-pinhole
pinhole-x
pinhole-y
clear-pinhole
overlay/ pinhole
underlay/ pinhole
2.2.11`` Exporting Images to Disk
save-image
save-svg-image

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#### 2.2`` Images: "image.ss"

( require 2htdp/image )

The image teachpack provides a number of basic image construction functions, along with combinators for building more complex images out of existing images. Basic images include various polygons, ellipses and circles, and text, as well as bitmaps (typically bitmaps come about via the Insert Image... menu item in DrRacket). Existing images can be rotated, scaled, flipped, and overlaid on top of each other.

##### 2.2.1`` Basic Images

> > procedure

> > ( circle radius mode color) → image?

> radius : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?
> ( circle radius outline-mode pen-or-color) → image?
> radius : ( and/c real? ( not/c negative? ))
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Constructs a circle with the given radius, height, mode, and color.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( circle 30 "outline" "red")
> > ( circle 20 "solid" "blue")
> > ( circle 20 100 "blue")

> > procedure

> > ( ellipse width height mode color) → image?

> width : ( and/c real? ( not/c negative? ))
> height : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?
> ( ellipse width height mode pen-or-color) → image?
> width : ( and/c real? ( not/c negative? ))
> height : ( and/c real? ( not/c negative? ))
> mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c image-color? pen? )

Constructs an ellipse with the given width, height, mode, and color.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( ellipse 60 30 "outline" "black")
> > ( ellipse 30 60 "solid" "blue")
> > ( ellipse 30 60 100 "blue")

> > procedure

> > ( line x1 y1 pen-or-color) → image?

> x1 : real?
> y1 : real?
> pen-or-color : ( or/c pen? image-color? )

Constructs an image representing a line segment that connects the points (0,0) to (x1,y1).

Examples:

> > ( line 30 30 "black")
> > ( line -30 20 "red")
> > ( line 30 -20 "red")

> > procedure

> > ( add-line image x1 y1 x2 y2 pen-or-color) → image?

> image : image?
> x1 : real?
> y1 : real?
> x2 : real?
> y2 : real?
> pen-or-color : ( or/c pen? image-color? )

Adds a line to the image image, starting from the point (x1,y1) and going to the point (x2,y2). Unlike scene+line, if the line passes outside of image, the image gets larger to accommodate the line.

Examples:

> > ( add-line ( ellipse 40 40 "outline" "maroon")
> 0 40 40 0 "maroon")

> > ( add-line ( rectangle 40 40 "solid" "gray")
> -10 50 50 -10 "maroon")

> > ( add-line
> ( rectangle 100 100 "solid" "darkolivegreen")
> 25 25 75 75
> ( make-pen "goldenrod" 30 "solid" "round" "round"))

> > procedure

> > ( add-curve |  | image |  |  |  |
> > |  | x1 |  |  |  |
> > |  | y1 |  |  |  |
> > |  | angle1 |  |  |  |
> > |  | pull1 |  |  |  |
> > |  | x2 |  |  |  |
> > |  | y2 |  |  |  |
> > |  | angle2 |  |  |  |
> > |  | pull2 |  |  |  |
> > |  | pen-or-color) |  | → |  | image?

> image : image?
> x1 : real?
> y1 : real?
> angle1 : angle?
> pull1 : real?
> x2 : real?
> y2 : real?
> angle2 : angle?
> pull2 : real?
> pen-or-color : ( or/c pen? image-color? )

Adds a curve to image, starting at the point (x1,y1), and ending at the point (x2,y2).

The angle1 and angle2 arguments specify the angle that the curve has as it leaves the initial point and as it reaches the final point, respectively.

The pull1 and pull2 arguments control how long the curve tries to stay with that angle. Larger numbers mean that the curve stays with the angle longer.

Unlike scene+curve, if the line passes outside of image, the image gets larger to accommodate the curve.

Examples:

> > ( add-curve ( rectangle 100 100 "solid" "black")
> 20 20 0 1/3
> 80 80 0 1/3
> "white")

> > ( add-curve ( rectangle 100 100 "solid" "black")
> 20 20 0 1
> 80 80 0 1
> "white")

> > ( add-curve
> ( add-curve
> ( rectangle 40 100 "solid" "black")
> 20 10 180 1/2
> 20 90 180 1/2
> ( make-pen "white" 4 "solid" "round" "round"))
> 20 10 0 1/2
> 20 90 0 1/2
> ( make-pen "white" 4 "solid" "round" "round"))

> > ( add-curve ( rectangle 100 100 "solid" "black")
> -20 -20 0 1
> 120 120 0 1
> "red")

> > procedure

> > ( text string font-size color) → image?

> string : string?
> font-size : ( and/c integer? (<=/c 1 255))
> color : image-color?

Constructs an image that draws the given string, using the font size and color.

Examples:

> > ( text "Hello" 24 "olive")
> > ( text "Goodbye" 36 "indigo")

> > procedure

> > ( text/font |  | string |  |  |  |
> > |  | font-size |  |  |  |
> > |  | color |  |  |  |
> > |  | face |  |  |  |
> > |  | family |  |  |  |
> > |  | style |  |  |  |
> > |  | weight |  |  |  |
> > |  | underline?) |  | → |  | image?

> string : string?
> font-size : ( and/c integer? (<=/c 1 255))
> color : image-color?
> face : ( or/c string? #f)
> family : ( or/c 'default 'decorative 'roman 'script 'swiss 'modern 'symbol 'system)
> style : ( or/c 'normal 'italic 'slant)
> weight : ( or/c 'normal 'bold 'light)
> underline? : any/c

Constructs an image that draws the given string, using a complete font specification.

The face and the family combine to give the complete typeface. If face is available on the system, it is used, but if not then a default typeface based on the family is chosen. The style controls if the face is italic or not (on Windows and Mac OS X, 'slant and 'italic are the same), the weight controls if it is boldface (or light), and underline? determines if the face is underlined. For more details on these arguments, see font%, which ultimately is what this code uses to draw the font.

Examples:

> > ( text/font "Hello" 24 "olive"
> "Gill Sans" 'swiss 'normal 'bold #f)

> > ( text/font "Goodbye" 18 "indigo"
> #f 'modern 'italic 'normal #f)

> > ( text/font "not really a link" 18 "blue"
> #f 'roman 'normal 'normal #t)

> > value

> > empty-image : image?

The empty image. Its width and height are both zero and it does not draw at all.

Examples:

> > ( image-width empty-image )
> 0

> > ( equal? ( above empty-image
> ( rectangle 10 10 "solid" "red"))
> ( beside empty-image
> ( rectangle 10 10 "solid" "red")))

> #t

In most cases, combining an image with empty-image produces the original image (as shown in the above example). In some situations, however, the combination can cause the resulting pict to have a different baseline (see image-baseline) and thus not be equal.

Examples:

> > ( image-baseline ( above ( text "Hello" 24 "olive") empty-image ))
> 28
> > ( image-baseline ( text "Hello" 24 "olive"))
> 22

> > ( equal? ( above ( text "Hello" 24 "olive") empty-image )
> ( text "Hello" 24 "olive"))

> #f

##### 2.2.2`` Polygons

> > procedure

> > ( triangle side-length mode color) → image?

> side-length : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?

> ( triangle |  | side-length |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> side-length : ( and/c real? ( not/c negative? ))
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Constructs a upward-pointing equilateral triangle. The side-length argument determines the length of the side of the triangle.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Example:

> > ( triangle 40 "solid" "tan")

> > procedure

> > ( right-triangle |  | side-length1 |  |  |  |
> > |  | side-length2 |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> side-length1 : ( and/c real? ( not/c negative? ))
> side-length2 : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?

> ( right-triangle |  | side-length1 |  |  |  |
> |  | side-length2 |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> side-length1 : ( and/c real? ( not/c negative? ))
> side-length2 : ( and/c real? ( not/c negative? ))
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Constructs a triangle with a right angle where the two sides adjacent to the right angle have lengths side-length1 and side-length2.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Example:

> > ( right-triangle 36 48 "solid" "black")

> > procedure

> > ( isosceles-triangle |  | side-length |  |  |  |
> > |  | angle |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> side-length : ( and/c real? ( not/c negative? ))
> angle : angle?
> mode : mode?
> color : image-color?

> ( isosceles-triangle |  | side-length |  |  |  |
> |  | angle |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> side-length : ( and/c real? ( not/c negative? ))
> angle : angle?
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Creates a triangle with two equal-length sides, of length side-length where the angle between those sides is angle. The third leg is straight, horizontally. If the angle is less than 180, then the triangle will point up and if the angle is more, then the triangle will point down.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( isosceles-triangle 200 170 "solid" "seagreen")
> > ( isosceles-triangle 60 30 "solid" "aquamarine")
> > ( isosceles-triangle 60 330 "solid" "lightseagreen")

To create a triangle given known sides and angles, the following family of functions are useful:

- triangle/sss, if all three sides are known

- triangle/ass, triangle/sas, or triangle/ssa, if two sides and their included angle are known

- triangle/aas, triangle/asa, or triangle/saa, if two angles and their shared side are known.

They all construct a triangle oriented as follows:

> > procedure

> > ( triangle/sss |  | side-length-a |  |  |  |
> > |  | side-length-b |  |  |  |
> > |  | side-length-c |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> side-length-a : ( and/c real? ( not/c negative? ))
> side-length-b : ( and/c real? ( not/c negative? ))
> side-length-c : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?

> ( triangle/sss |  | side-length-a |  |  |  |
> |  | side-length-b |  |  |  |
> |  | side-length-c |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> side-length-a : ( and/c real? ( not/c negative? ))
> side-length-b : ( and/c real? ( not/c negative? ))
> side-length-c : ( and/c real? ( not/c negative? ))
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Creates a triangle where the side lengths a, b, and, c are given by side-length-a, side-length-b, and, side-length-c respectively.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( triangle/sss 40 60 80 "solid" "seagreen")
> > ( triangle/sss 80 40 60 "solid" "aquamarine")
> > ( triangle/sss 80 80 40 "solid" "lightseagreen")

> > procedure

> > ( triangle/ass |  | angle-a |  |  |  |
> > |  | side-length-b |  |  |  |
> > |  | side-length-c |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> angle-a : angle?
> side-length-b : ( and/c real? ( not/c negative? ))
> side-length-c : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?

> ( triangle/ass |  | angle-a |  |  |  |
> |  | side-length-b |  |  |  |
> |  | side-length-c |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> angle-a : angle?
> side-length-b : ( and/c real? ( not/c negative? ))
> side-length-c : ( and/c real? ( not/c negative? ))
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Creates a triangle where the angle A and side length a and b, are given by angle-a, side-length-b, and, side-length-c respectively. See above for a diagram showing where which sides and which angles are which.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( triangle/ass 10 60 100 "solid" "seagreen")
> > ( triangle/ass 90 60 100 "solid" "aquamarine")
> > ( triangle/ass 130 60 100 "solid" "lightseagreen")

> > procedure

> > ( triangle/sas |  | side-length-a |  |  |  |
> > |  | angle-b |  |  |  |
> > |  | side-length-c |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> side-length-a : ( and/c real? ( not/c negative? ))
> angle-b : angle?
> side-length-c : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?

> ( triangle/sas |  | side-length-a |  |  |  |
> |  | angle-b |  |  |  |
> |  | side-length-c |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> side-length-a : ( and/c real? ( not/c negative? ))
> angle-b : angle?
> side-length-c : ( and/c real? ( not/c negative? ))
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Creates a triangle where the side length a, angle B, and, side length c given by side-length-a, angle-b, and, side-length-c respectively. See above for a diagram showing where which sides and which angles are which.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( triangle/sas 60 10 100 "solid" "seagreen")
> > ( triangle/sas 60 90 100 "solid" "aquamarine")
> > ( triangle/sas 60 130 100 "solid" "lightseagreen")

> > procedure

> > ( triangle/ssa |  | side-length-a |  |  |  |
> > |  | side-length-b |  |  |  |
> > |  | angle-c |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> side-length-a : ( and/c real? ( not/c negative? ))
> side-length-b : ( and/c real? ( not/c negative? ))
> angle-c : angle?
> mode : mode?
> color : image-color?

> ( triangle/ssa |  | side-length-a |  |  |  |
> |  | side-length-b |  |  |  |
> |  | angle-c |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> side-length-a : ( and/c real? ( not/c negative? ))
> side-length-b : ( and/c real? ( not/c negative? ))
> angle-c : angle?
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Creates a triangle where the side length a, side length b, and, angle c given by side-length-a, side-length-b, and, angle-c respectively. See above for a diagram showing where which sides and which angles are which.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( triangle/ssa 60 100 10 "solid" "seagreen")
> > ( triangle/ssa 60 100 90 "solid" "aquamarine")
> > ( triangle/ssa 60 100 130 "solid" "lightseagreen")

> > procedure

> > ( triangle/aas |  | angle-a |  |  |  |
> > |  | angle-b |  |  |  |
> > |  | side-length-c |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> angle-a : angle?
> angle-b : angle?
> side-length-c : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?

> ( triangle/aas |  | angle-a |  |  |  |
> |  | angle-b |  |  |  |
> |  | side-length-c |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> angle-a : angle?
> angle-b : angle?
> side-length-c : ( and/c real? ( not/c negative? ))
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Creates a triangle where the angle A, angle B, and, side length c given by angle-a, angle-b, and, side-length-c respectively. See above for a diagram showing where which sides and which angles are which.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( triangle/aas 10 40 200 "solid" "seagreen")
> > ( triangle/aas 90 40 200 "solid" "aquamarine")
> > ( triangle/aas 130 40 40 "solid" "lightseagreen")

> > procedure

> > ( triangle/asa |  | angle-a |  |  |  |
> > |  | side-length-b |  |  |  |
> > |  | angle-c |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> angle-a : angle?
> side-length-b : ( and/c real? ( not/c negative? ))
> angle-c : angle?
> mode : mode?
> color : image-color?

> ( triangle/asa |  | angle-a |  |  |  |
> |  | side-length-b |  |  |  |
> |  | angle-c |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> angle-a : angle?
> side-length-b : ( and/c real? ( not/c negative? ))
> angle-c : angle?
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Creates a triangle where the angle A, side length b, and, angle C given by angle-a, side-length-b, and, angle-c respectively. See above for a diagram showing where which sides and which angles are which.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( triangle/asa 10 200 40 "solid" "seagreen")
> > ( triangle/asa 90 200 40 "solid" "aquamarine")
> > ( triangle/asa 130 40 40 "solid" "lightseagreen")

> > procedure

> > ( triangle/saa |  | side-length-a |  |  |  |
> > |  | angle-b |  |  |  |
> > |  | angle-c |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> side-length-a : ( and/c real? ( not/c negative? ))
> angle-b : angle?
> angle-c : angle?
> mode : mode?
> color : image-color?

> ( triangle/saa |  | side-length-a |  |  |  |
> |  | angle-b |  |  |  |
> |  | angle-c |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> side-length-a : ( and/c real? ( not/c negative? ))
> angle-b : angle?
> angle-c : angle?
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Creates a triangle where the side length a, angle B, and, angle C given by side-length-a, angle-b, and, angle-c respectively. See above for a diagram showing where which sides and which angles are which.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( triangle/saa 200 10 40 "solid" "seagreen")
> > ( triangle/saa 200 90 40 "solid" "aquamarine")
> > ( triangle/saa 40 130 40 "solid" "lightseagreen")

> > procedure

> > ( square side-len mode color) → image?

> side-len : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?
> ( square side-len outline-mode pen-or-color) → image?
> side-len : ( and/c real? ( not/c negative? ))
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Constructs a square.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( square 40 "solid" "slateblue")
> > ( square 50 "outline" "darkmagenta")

> > procedure

> > ( rectangle width height mode color) → image?

> width : real?
> height : real?
> mode : mode?
> color : image-color?

> ( rectangle |  | width |  |  |  |
> |  | height |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> width : real?
> height : real?
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Constructs a rectangle with the given width, height, mode, and color.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( rectangle 40 20 "outline" "black")
> > ( rectangle 20 40 "solid" "blue")

> > procedure

> > ( rhombus side-length angle mode color) → image?

> side-length : ( and/c real? ( not/c negative? ))
> angle : angle?
> mode : mode?
> color : image-color?

> ( rhombus |  | side-length |  |  |  |
> |  | angle |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> side-length : ( and/c real? ( not/c negative? ))
> angle : angle?
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Constructs a four sided polygon with all equal sides and thus where opposite angles are equal to each other. The top and bottom pair of angles is angle and the left and right are ( - 180 angle).

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( rhombus 40 45 "solid" "magenta")
> > ( rhombus 80 150 "solid" "mediumpurple")

> > procedure

> > ( star side-length mode color) → image?

> side-length : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?
> ( star side-length outline-mode color) → image?
> side-length : ( and/c real? ( not/c negative? ))
> outline-mode : ( or/c 'outline "outline")
> color : ( or/c pen? image-color? )

Constructs a star with five points. The side-length argument determines the side length of the enclosing pentagon.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Example:

> > ( star 40 "solid" "gray")

> > procedure

> > ( star-polygon |  | side-length |  |  |  |
> > |  | side-count |  |  |  |
> > |  | step-count |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> side-length : ( and/c real? ( not/c negative? ))
> side-count : side-count?
> step-count : step-count?
> mode : mode?
> color : image-color?

> ( star-polygon |  | side-length |  |  |  |
> |  | side-count |  |  |  |
> |  | step-count |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> side-length : ( and/c real? ( not/c negative? ))
> side-count : side-count?
> step-count : step-count?
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Constructs an arbitrary regular star polygon (a generalization of the regular polygons). The polygon is enclosed by a regular polygon with side-count sides each side-length long. The polygon is actually constructed by going from vertex to vertex around the regular polgon, but connecting every step-count-th vertex (i.e., skipping every ( - step-count 1) verticies).

For example, if side-count is 5 and step-count is 2, then this function produces a shape just like star.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( star-polygon 40 5 2 "solid" "seagreen")
> > ( star-polygon 40 7 3 "outline" "darkred")
> > ( star-polygon 20 10 3 "solid" "cornflowerblue")

> > procedure

> > ( radial-star |  | point-count |  |  |  |
> > |  | inner-radius |  |  |  |
> > |  | outer-radius |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> point-count : ( and/c integer? (>=/c 2))
> inner-radius : ( and/c real? ( not/c negative? ))
> outer-radius : ( and/c real? ( not/c negative? ))
> mode : mode?
> color : image-color?

> ( radial-star |  | point-count |  |  |  |
> |  | inner-radius |  |  |  |
> |  | outer-radius |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> point-count : ( and/c integer? (>=/c 2))
> inner-radius : ( and/c real? ( not/c negative? ))
> outer-radius : ( and/c real? ( not/c negative? ))
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Constructs a star-like polygon where the star is specified by two radii and a number of points. The first radius determines where the points begin, the second determines where they end, and the point-count argument determines how many points the star has.

Examples:

> > ( radial-star 8 8 64 "solid" "darkslategray")
> > ( radial-star 32 30 40 "outline" "black")

> > procedure

> > ( regular-polygon |  | side-length |  |  |  |
> > |  | side-count |  |  |  |
> > |  | mode |  |  |  |
> > |  | color) |  | → |  | image?

> side-length : ( and/c real? ( not/c negative? ))
> side-count : side-count?
> mode : mode?
> color : image-color?

> ( regular-polygon |  | side-length |  |  |  |
> |  | side-count |  |  |  |
> |  | outline-mode |  |  |  |
> |  | pen-or-color) |  | → |  | image?

> side-length : ( and/c real? ( not/c negative? ))
> side-count : side-count?
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Constructs a regular polygon with side-count sides.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( regular-polygon 50 3 "outline" "red")
> > ( regular-polygon 40 4 "outline" "blue")
> > ( regular-polygon 20 8 "solid" "red")

> > procedure

> > ( polygon vertices mode color) → image?

> vertices : (listof real-valued-posn? )
> mode : mode?
> color : image-color?
> ( polygon vertices outline-mode pen-or-color) → image?
> vertices : (listof real-valued-posn? )
> outline-mode : ( or/c 'outline "outline")
> pen-or-color : ( or/c pen? image-color? )

Constructs a polygon connecting the given vertices.

If the mode is 'outline or "outline", then the last argument can be a pen struct or an image-color?, but if the mode is 'solid or "solid", then the last argument must be an image-color?.

Examples:

> > ( polygon ( list ( make-posn 0 0)
> ( make-posn -10 20)
> ( make-posn 60 0)
> ( make-posn -10 -20))
> "solid"
> "burlywood")

> > ( polygon ( list ( make-posn 0 0)
> ( make-posn 0 40)
> ( make-posn 20 40)
> ( make-posn 20 60)
> ( make-posn 40 60)
> ( make-posn 40 20)
> ( make-posn 20 20)
> ( make-posn 20 0))
> "solid"
> "plum")

> > ( underlay
> ( rectangle 80 80 "solid" "mediumseagreen")
> ( polygon
> ( list ( make-posn 0 0)
> ( make-posn 50 0)
> ( make-posn 0 50)
> ( make-posn 50 50))
> "outline"
> ( make-pen "darkslategray" 10 "solid" "round" "round")))

> > ( underlay
> ( rectangle 90 80 "solid" "mediumseagreen")
> ( polygon
> ( list ( make-posn 0 0)
> ( make-posn 50 0)
> ( make-posn 0 50)
> ( make-posn 50 50))
> "outline"
> ( make-pen "darkslategray" 10 "solid" "projecting" "miter")))

##### 2.2.3`` Overlaying Images

> > procedure

> > ( overlay i1 i2 is ...) → image?

> i1 : image?
> i2 : image?
> is : image?

Overlays all of its arguments building a single image. The first argument goes on top of the second argument, which goes on top of the third argument, etc. The images are all lined up on their centers.

Examples:

> > ( overlay ( rectangle 30 60 "solid" "orange")
> ( ellipse 60 30 "solid" "purple"))

> > ( overlay ( ellipse 10 10 "solid" "red")
> ( ellipse 20 20 "solid" "black")
> ( ellipse 30 30 "solid" "red")
> ( ellipse 40 40 "solid" "black")
> ( ellipse 50 50 "solid" "red")
> ( ellipse 60 60 "solid" "black"))

> > ( overlay ( regular-polygon 20 5 "solid" ( make-color 50 50 255))
> ( regular-polygon 26 5 "solid" ( make-color 100 100 255))
> ( regular-polygon 32 5 "solid" ( make-color 150 150 255))
> ( regular-polygon 38 5 "solid" ( make-color 200 200 255))
> ( regular-polygon 44 5 "solid" ( make-color 250 250 255)))

> > procedure

> > ( overlay/align x-place y-place i1 i2 is ...) → image?

> x-place : x-place?
> y-place : y-place?
> i1 : image?
> i2 : image?
> is : image?

Overlays all of its image arguments, much like the overlay function, but using x-place and y-place to determine where the images are lined up. For example, if x-place and y-place are both "middle", then the images are lined up on their centers.

Examples:

> > ( overlay/align "left" "middle"
> ( rectangle 30 60 "solid" "orange")
> ( ellipse 60 30 "solid" "purple"))

> > ( overlay/align "right" "bottom"
> ( rectangle 20 20 "solid" "silver")
> ( rectangle 30 30 "solid" "seagreen")
> ( rectangle 40 40 "solid" "silver")
> ( rectangle 50 50 "solid" "seagreen"))

> > procedure

> > ( overlay/offset i1 x y i2) → image?

> i1 : image?
> x : real?
> y : real?
> i2 : image?

Just like overlay, this function lines up its image arguments on top of each other. Unlike overlay, it moves i2 by x pixels to the right and y down before overlaying them.

Examples:

> > ( overlay/offset ( circle 40 "solid" "red")
> 10 10
> ( circle 40 "solid" "blue"))

> > ( overlay/offset ( overlay/offset ( rectangle 60 20 "solid" "black")
> -50 0
> ( circle 20 "solid" "darkorange"))
> 70 0
> ( circle 20 "solid" "darkorange"))

> > ( overlay/offset
> ( overlay/offset ( circle 30 'solid ( color 0 150 0 127))
> 26 0
> ( circle 30 'solid ( color 0 0 255 127)))
> 0 26
> ( circle 30 'solid ( color 200 0 0 127)))

> > procedure

> > ( overlay/align/offset |  | x-place |  |  |  |
> > |  | y-place |  |  |  |
> > |  | i1 |  |  |  |
> > |  | x |  |  |  |
> > |  | y |  |  |  |
> > |  | i2) |  | → |  | image?

> x-place : x-place?
> y-place : y-place?
> i1 : image?
> x : real?
> y : real?
> i2 : image?

Overlays image i1 on top of i2, using x-place and y-place as the starting points for the overlaying, and then adjusts i2 by x to the right and y pixels down.

This function combines the capabilities of overlay/align and overlay/offset.

Examples:

> > ( overlay/align/offset
> "right" "bottom"
> ( star-polygon 20 20 3 "solid" "navy")
> 10 10
> ( circle 30 "solid" "cornflowerblue"))

> > ( overlay/align/offset
> "left" "bottom"
> ( star-polygon 20 20 3 "solid" "navy")
> -10 10
> ( circle 30 "solid" "cornflowerblue"))

> > procedure

> > ( overlay/xy i1 x y i2) → image?

> i1 : image?
> x : real?
> y : real?
> i2 : image?

Constructs an image by overlaying i1 on top of i2. The images are initially lined up on their upper-left corners and then i2 is shifted to the right by x pixels to and down by y pixels.

This is the same as ( underlay/xy i2 ( - x) ( - y) i1).

See also overlay/offset and underlay/offset.

Examples:

> > ( overlay/xy ( rectangle 20 20 "outline" "black")
> 20 0
> ( rectangle 20 20 "outline" "black"))

> > ( overlay/xy ( rectangle 20 20 "solid" "red")
> 10 10
> ( rectangle 20 20 "solid" "black"))

> > ( overlay/xy ( rectangle 20 20 "solid" "red")
> -10 -10
> ( rectangle 20 20 "solid" "black"))

> > ( overlay/xy
> ( overlay/xy ( ellipse 40 40 "outline" "black")
> 10
> 15
> ( ellipse 10 10 "solid" "forestgreen"))
> 20
> 15
> ( ellipse 10 10 "solid" "forestgreen"))

> > procedure

> > ( underlay i1 i2 is ...) → image?

> i1 : image?
> i2 : image?
> is : image?

Underlays all of its arguments building a single image.

It behaves like overlay, but with the arguments in the reverse order. That is, the first argument goes underneath of the second argument, which goes underneath the third argument, etc. The images are all lined up on their centers.

Examples:

> > ( underlay ( rectangle 30 60 "solid" "orange")
> ( ellipse 60 30 "solid" "purple"))

> > ( underlay ( ellipse 10 60 "solid" "red")
> ( ellipse 20 50 "solid" "black")
> ( ellipse 30 40 "solid" "red")
> ( ellipse 40 30 "solid" "black")
> ( ellipse 50 20 "solid" "red")
> ( ellipse 60 10 "solid" "black"))

> > ( underlay ( ellipse 10 60 40 "red")
> ( ellipse 20 50 40 "red")
> ( ellipse 30 40 40 "red")
> ( ellipse 40 30 40 "red")
> ( ellipse 50 20 40 "red")
> ( ellipse 60 10 40 "red"))

> > procedure

> > ( underlay/align x-place y-place i1 i2 is ...) → image?

> x-place : x-place?
> y-place : y-place?
> i1 : image?
> i2 : image?
> is : image?

Underlays all of its image arguments, much like the underlay function, but using x-place and y-place to determine where the images are lined up. For example, if x-place and y-place are both "middle", then the images are lined up on their centers.

Examples:

> > ( underlay/align "left" "middle"
> ( rectangle 30 60 "solid" "orange")
> ( ellipse 60 30 "solid" "purple"))

> > ( underlay/align "right" "top"
> ( rectangle 50 50 "solid" "seagreen")
> ( rectangle 40 40 "solid" "silver")
> ( rectangle 30 30 "solid" "seagreen")
> ( rectangle 20 20 "solid" "silver"))

> > ( underlay/align "left" "middle"
> ( rectangle 50 50 50 "seagreen")
> ( rectangle 40 40 50 "seagreen")
> ( rectangle 30 30 50 "seagreen")
> ( rectangle 20 20 50 "seagreen"))

> > procedure

> > ( underlay/offset i1 x y i2) → image?

> i1 : image?
> x : real?
> y : real?
> i2 : image?

Just like underlay, this function lines up its first image argument underneath the second. Unlike underlay, it moves i2 by x pixels to the right and y down before underlaying them.

Examples:

> > ( underlay/offset ( circle 40 "solid" "red")
> 10 10
> ( circle 40 "solid" "blue"))

> > ( underlay/offset ( circle 40 "solid" "gray")
> 0 -10
> ( underlay/offset ( circle 10 "solid" "navy")
> -30 0
> ( circle 10 "solid" "navy")))

> > procedure

> > ( underlay/align/offset |  | x-place |  |  |  |
> > |  | y-place |  |  |  |
> > |  | i1 |  |  |  |
> > |  | x |  |  |  |
> > |  | y |  |  |  |
> > |  | i2) |  | → |  | image?

> x-place : x-place?
> y-place : y-place?
> i1 : image?
> x : real?
> y : real?
> i2 : image?

Underlays image i1 underneath i2, using x-place and y-place as the starting points for the combination, and then adjusts i2 by x to the right and y pixels down.

This function combines the capabilities of underlay/align and underlay/offset.

Examples:

> > ( underlay/align/offset
> "right" "bottom"
> ( star-polygon 20 20 3 "solid" "navy")
> 10 10
> ( circle 30 "solid" "cornflowerblue"))

> > ( underlay/align/offset
> "right" "bottom"
> ( underlay/align/offset
> "left" "bottom"
> ( underlay/align/offset
> "right" "top"
> ( underlay/align/offset
> "left" "top"
> ( rhombus 120 90 "solid" "navy")
> 16 16
> ( star-polygon 20 11 3 "solid" "cornflowerblue"))
> -16 16
> ( star-polygon 20 11 3 "solid" "cornflowerblue"))
> 16 -16
> ( star-polygon 20 11 3 "solid" "cornflowerblue"))
> -16 -16
> ( star-polygon 20 11 3 "solid" "cornflowerblue"))

> > procedure

> > ( underlay/xy i1 x y i2) → image?

> i1 : image?
> x : real?
> y : real?
> i2 : image?

Constructs an image by underlaying i1 underneath i2. The images are initially lined up on their upper-left corners and then i2 is shifted to the right by x pixels to and down by y pixels.

This is the same as ( overlay/xy i2 ( - x) ( - y) i1).

See also underlay/offset and overlay/offset.

Examples:

> > ( underlay/xy ( rectangle 20 20 "outline" "black")
> 20 0
> ( rectangle 20 20 "outline" "black"))

> > ( underlay/xy ( rectangle 20 20 "solid" "red")
> 10 10
> ( rectangle 20 20 "solid" "black"))

> > ( underlay/xy ( rectangle 20 20 "solid" "red")
> -10 -10
> ( rectangle 20 20 "solid" "black"))

> > ( underlay/xy
> ( underlay/xy ( ellipse 40 40 "solid" "gray")
> 10
> 15
> ( ellipse 10 10 "solid" "forestgreen"))
> 20
> 15
> ( ellipse 10 10 "solid" "forestgreen"))

> > procedure

> > ( beside i1 i2 is ...) → image?

> i1 : image?
> i2 : image?
> is : image?

Constructs an image by placing all of the argument images in a horizontal row, aligned along their centers.

Example:

> > ( beside ( ellipse 20 70 "solid" "gray")
> ( ellipse 20 50 "solid" "darkgray")
> ( ellipse 20 30 "solid" "dimgray")
> ( ellipse 20 10 "solid" "black"))

> > procedure

> > ( beside/align y-place i1 i2 is ...) → image?

> y-place : y-place?
> i1 : image?
> i2 : image?
> is : image?

Constructs an image by placing all of the argument images in a horizontal row, lined up as indicated by the y-place argument. For example, if y-place is "middle", then the images are placed side by side with their centers lined up with each other.

Examples:

> > ( beside/align "bottom"
> ( ellipse 20 70 "solid" "lightsteelblue")
> ( ellipse 20 50 "solid" "mediumslateblue")
> ( ellipse 20 30 "solid" "slateblue")
> ( ellipse 20 10 "solid" "navy"))

> > ( beside/align "top"
> ( ellipse 20 70 "solid" "mediumorchid")
> ( ellipse 20 50 "solid" "darkorchid")
> ( ellipse 20 30 "solid" "purple")
> ( ellipse 20 10 "solid" "indigo"))

> > ( beside/align "baseline"
> ( text "ijy" 18 "black")
> ( text "ijy" 24 "black"))

> > procedure

> > ( above i1 i2 is ...) → image?

> i1 : image?
> i2 : image?
> is : image?

Constructs an image by placing all of the argument images in a vertical row, aligned along their centers.

Example:

> > ( above ( ellipse 70 20 "solid" "gray")
> ( ellipse 50 20 "solid" "darkgray")
> ( ellipse 30 20 "solid" "dimgray")
> ( ellipse 10 20 "solid" "black"))

> > procedure

> > ( above/align x-place i1 i2 is ...) → image?

> x-place : x-place?
> i1 : image?
> i2 : image?
> is : image?

Constructs an image by placing all of the argument images in a vertical row, lined up as indicated by the x-place argument. For example, if x-place is "middle", then the images are placed above each other with their centers lined up.

Examples:

> > ( above/align "right"
> ( ellipse 70 20 "solid" "gold")
> ( ellipse 50 20 "solid" "goldenrod")
> ( ellipse 30 20 "solid" "darkgoldenrod")
> ( ellipse 10 20 "solid" "sienna"))

> > ( above/align "left"
> ( ellipse 70 20 "solid" "yellowgreen")
> ( ellipse 50 20 "solid" "olivedrab")
> ( ellipse 30 20 "solid" "darkolivegreen")
> ( ellipse 10 20 "solid" "darkgreen"))

##### 2.2.4`` Placing Images & Scenes

Placing images into scenes is particularly useful when building worlds and universes using 2htdp/universe.

> > procedure

> > ( empty-scene width height) → image?

> width : ( and/c real? ( not/c negative? ))
> height : ( and/c real? ( not/c negative? ))
> ( empty-scene width height color) → image?
> width : ( and/c real? ( not/c negative? ))
> height : ( and/c real? ( not/c negative? ))
> color : image-color?

Creates an empty scene, i.e., a white rectangle with a black outline.

Example:

> > ( empty-scene 160 90)

The three-argument version creates a rectangle of the specified color with a black outline.

> > procedure

> > ( place-image image x y scene) → image?

> image : image?
> x : real?
> y : real?
> scene : image?

Places image onto scene with its center at the coordinates (x,y) and crops the resulting image so that it has the same size as scene. The coordinates are relative to the top-left of scene.

Examples:

> > ( place-image
> ( triangle 32 "solid" "red")
> 24 24
> ( rectangle 48 48 "solid" "gray"))

> > ( place-image
> ( triangle 64 "solid" "red")
> 24 24
> ( rectangle 48 48 "solid" "gray"))

> > ( place-image
> ( circle 4 "solid" "white")
> 18 20
> ( place-image
> ( circle 4 "solid" "white")
> 0 6
> ( place-image
> ( circle 4 "solid" "white")
> 14 2
> ( place-image
> ( circle 4 "solid" "white")
> 8 14
> ( rectangle 24 24 "solid" "goldenrod")))))

> > procedure

> > ( place-image/align |  | image |  |  |  |
> > |  | x |  |  |  |
> > |  | y |  |  |  |
> > |  | x-place |  |  |  |
> > |  | y-place |  |  |  |
> > |  | scene) |  | → |  | image?

> image : image?
> x : real?
> y : real?
> x-place : x-place?
> y-place : y-place?
> scene : image?

Like place-image, but uses image’s x-place and y-place to anchor the image. Also, like place-image, place-image/align crops the resulting image so that it has the same size as scene.

Examples:

> > ( place-image/align ( triangle 48 "solid" "yellowgreen")
> 64 64 "right" "bottom"
> ( rectangle 64 64 "solid" "mediumgoldenrod"))

> > ( beside
> ( place-image/align ( circle 8 "solid" "tomato")
> 0 0 "center" "center"
> ( rectangle 32 32 "outline" "black"))
> ( place-image/align ( circle 8 "solid" "tomato")
> 8 8 "center" "center"
> ( rectangle 32 32 "outline" "black"))
> ( place-image/align ( circle 8 "solid" "tomato")
> 16 16 "center" "center"
> ( rectangle 32 32 "outline" "black"))
> ( place-image/align ( circle 8 "solid" "tomato")
> 24 24 "center" "center"
> ( rectangle 32 32 "outline" "black"))
> ( place-image/align ( circle 8 "solid" "tomato")
> 32 32 "center" "center"
> ( rectangle 32 32 "outline" "black")))

> > procedure

> > ( scene+line image x1 y1 x2 y2 pen-or-color) → image?

> image : image?
> x1 : real?
> y1 : real?
> x2 : real?
> y2 : real?
> pen-or-color : ( or/c pen? image-color? )

Adds a line to the image scene, starting from the point (x1,y1) and going to the point (x2,y2); unlike add-line, this function crops the resulting image to the size of scene.

Examples:

> > ( scene+line ( ellipse 40 40 "outline" "maroon")
> 0 40 40 0 "maroon")

> > ( scene+line ( rectangle 40 40 "solid" "gray")
> -10 50 50 -10 "maroon")

> > ( scene+line
> ( rectangle 100 100 "solid" "darkolivegreen")
> 25 25 100 100
> ( make-pen "goldenrod" 30 "solid" "round" "round"))

> > procedure

> > ( scene+curve |  | scene |  |  |  |
> > |  | x1 |  |  |  |
> > |  | y1 |  |  |  |
> > |  | angle1 |  |  |  |
> > |  | pull1 |  |  |  |
> > |  | x2 |  |  |  |
> > |  | y2 |  |  |  |
> > |  | angle2 |  |  |  |
> > |  | pull2 |  |  |  |
> > |  | color) |  | → |  | image?

> scene : image?
> x1 : real?
> y1 : real?
> angle1 : angle?
> pull1 : real?
> x2 : real?
> y2 : real?
> angle2 : angle?
> pull2 : real?
> color : image-color?

Adds a curve to scene, starting at the point (x1,y1), and ending at the point (x2,y2).

The angle1 and angle2 arguments specify the angle that the curve has as it leaves the initial point and as it reaches the final point, respectively.

The pull1 and pull2 arguments control how long the curve tries to stay with that angle. Larger numbers mean that the curve stays with the angle longer.

Unlike add-curve, this function crops the curve, only showing the parts that fit onto scene.

Examples:

> > ( scene+curve ( rectangle 100 100 "solid" "black")
> 20 20 0 1/3
> 80 80 0 1/3
> "white")

> > ( scene+curve ( rectangle 100 100 "solid" "black")
> 20 20 0 1
> 80 80 0 1
> "white")

> > ( scene+curve
> ( add-curve
> ( rectangle 40 100 "solid" "black")
> 20 10 180 1/2
> 20 90 180 1/2
> "white")
> 20 10 0 1/2
> 20 90 0 1/2
> "white")

> > ( scene+curve ( rectangle 100 100 "solid" "black")
> -20 -20 0 1
> 120 120 0 1
> "red")

##### 2.2.5`` Rotating, Scaling, Flipping, Cropping, and Framing Images

> > procedure

> > ( rotate angle image) → image?

> angle : angle?
> image : image?

Rotates image by angle degrees in a counter-clockwise direction.

Examples:

> > ( rotate 45 ( ellipse 60 20 "solid" "olivedrab"))
> > ( rotate 5 ( rectangle 50 50 "outline" "black"))

> > ( rotate 45
> ( beside/align
> "center"
> ( rectangle 40 20 "solid" "darkseagreen")
> ( rectangle 20 100 "solid" "darkseagreen")))

> > procedure

> > ( scale factor image) → image?

> factor : ( and/c real? positive? )
> image : image?

Scales image by factor.

The pen sizes are also scaled and thus draw thicker (or thinner) lines than the original image, unless the pen was size 0. That pen size is treated specially to mean “the smallest available line” and thus it always draws a one pixel wide line; this is also the case for 'outline and "outline" shapes that are drawn with an image-color? instead of a pen.

Examples:

> > ( scale 2 ( ellipse 20 30 "solid" "blue"))
> > ( ellipse 40 60 "solid" "blue")

> > procedure

> > ( scale/xy x-factor y-factor image) → image?

> x-factor : ( and/c real? positive? )
> y-factor : ( and/c real? positive? )
> image : image?

Scales image by x-factor horizontally and by y-factor vertically.

Examples:

> > ( scale/xy 3
> 2
> ( ellipse 20 30 "solid" "blue"))

> > ( ellipse 60 60 "solid" "blue")

> > procedure

> > ( flip-horizontal image) → image?

> image : image?

Flips image left to right.

Flipping images with text is not supported (so passing flip-horizontal an image that contains a text or text/font image inside somewhere signals an error).

Example:

> > ( beside
> ( rotate 30 ( square 50 "solid" "red"))
> ( flip-horizontal
> ( rotate 30 ( square 50 "solid" "blue"))))

> > procedure

> > ( flip-vertical image) → image?

> image : image?

Flips image top to bottom.

Flipping images with text is not supported (so passing flip-vertical an image that contains a text or text/font image inside somewhere signals an error).

Example:

> > ( above
> ( star 40 "solid" "firebrick")
> ( scale/xy 1 1/2 ( flip-vertical ( star 40 "solid" "gray"))))

> > procedure

> > ( crop x y width height image) → image?

> x : real?
> y : real?
> width : ( and/c real? ( not/c negative? ))
> height : ( and/c real? ( not/c negative? ))
> image : image?

Crops image to the rectangle with the upper left at the point (x,y) and with width and height.

Examples:

> > ( crop 0 0 40 40 ( circle 40 "solid" "chocolate"))
> > ( crop 40 60 40 60 ( ellipse 80 120 "solid" "dodgerblue"))

> > ( above
> ( beside ( crop 40 40 40 40 ( circle 40 "solid" "palevioletred"))
> ( crop 0 40 40 40 ( circle 40 "solid" "lightcoral")))
> ( beside ( crop 40 0 40 40 ( circle 40 "solid" "lightcoral"))
> ( crop 0 0 40 40 ( circle 40 "solid" "palevioletred"))))

> > procedure

> > ( frame image) → image?

> image : image?

Returns an image just like image, except with a black, single pixel frame drawn around the bounding box of the image.

Example:

> > ( frame ( ellipse 40 40 "solid" "gray"))

Generally speaking, this function is useful to debug image constructions, i.e., to see where certain sub-images appear within some larger image.

Example:

> > ( beside
> ( ellipse 20 70 "solid" "lightsteelblue")
> ( frame ( ellipse 20 50 "solid" "mediumslateblue"))
> ( ellipse 20 30 "solid" "slateblue")
> ( ellipse 20 10 "solid" "navy"))

##### 2.2.6`` Bitmaps

DrRacket’s Insert Image ... menu item allows you to insert images into your program text, and those images are treated as images for this library.

Unlike all of the other images in this library, those images (and the other images created by functions in this section of the documentation) are represented as bitmaps, i.e., an array of colors (that can be quite large in some cases). This means that scaling and rotating them loses fidelity in the image and is significantly more expensive than with the other shapes.

See also the 2htdp/planetcute library.

> > syntax

> > ( bitmap bitmap-spec)

> bitmap-spec |  | = |  | rel-string
> |  | | |  | id

Loads the bitmap specified by bitmap-spec. If bitmap-spec is a string, it is treated as a relative path. If it is an identifier, it is treated like a require spec and used to refer to a file in a collection.

Examples:

> > ( bitmap icons/stop-16x16.png)
> > ( bitmap icons/b-run.png)

> > procedure

> > ( bitmap/url url) → image?

> url : string?

Goes out on the web and downloads the image at url.

Downloading the image happens each time this function is called, so you may find it simpler to download the image once with a browser and then paste it into your program or download it and use bitmap.

> > procedure

> > ( bitmap/file ps) → image?

> ps : path-string?

Loads the image from ps.

If ps is a relative path, the file is relative to the current directory. (When running in DrRacket, the current directory is set to the place where the definitions window is saved, but in general this can be an arbitrary directory.)

> > procedure

> > ( image->color-list image) → (listof color? )

> image : image?

Returns a list of colors that correspond to the colors in the image, reading from left to right, top to bottom.

Examples:

> > ( image->color-list ( rectangle 2 2 "solid" "black"))
> (list (color 0 0 0 255) (color 0 0 0 255) (color 0 0 0 255) (color 0 0 0 255))

> > ( image->color-list
> ( above ( beside ( rectangle 1 1 "solid" ( make-color 1 1 1))
> ( rectangle 1 1 "solid" ( make-color 2 2 2)))
> ( beside ( rectangle 1 1 "solid" ( make-color 3 3 3))
> ( rectangle 1 1 "solid" ( make-color 4 4 4)))))

> (list (color 1 1 1 255) (color 2 2 2 255) (color 3 3 3 255) (color 4 4 4 255))

> > procedure

> > ( color-list->bitmap colors width height) → image?

> colors : (listof image-color? )
> width : ( and/c real? ( not/c negative? ))
> height : ( and/c real? ( not/c negative? ))

Constructs a bitmap from the given colors, with the given width and height.

Example:

> > ( scale
> 40
> ( color-list->bitmap
> ( list "red" "green" "blue")
> 3 1))

> > procedure

> > ( freeze image) → image?

> image : image?
> ( freeze width height image) → image?
> width : ( and/c real? ( not/c negative? ))
> height : ( and/c real? ( not/c negative? ))
> image : image?
> ( freeze x y width height image) → image?
> x : real?
> y : real?
> width : ( and/c real? ( not/c negative? ))
> height : ( and/c real? ( not/c negative? ))
> image : image?

Freezing an image internally builds a bitmap, crops the image, draws the cropped image into the bitmap and then uses the bitmap to draw that image afterwards. Typically this is used as a performance hint. When an image both contains many sub-images and is going to be drawn many times (but not scaled or rotated), using freeze on the image can substantially improve performance without changing how the image draws (assuming it draws only inside its bounding box; see also The nitty gritty of pixels, pens, and lines).

If freeze is passed only the image argument, then it crops the image to its bounding box. If it is given three arguments, the two numbers are used as the width and height and the five argument version fully specifies where to crop the image.

##### 2.2.7`` Image Properties

> > procedure

> > ( image-width i) → ( and/c integer? ( not/c negative? ) exact? )

> i : image?

Returns the width of i.

Examples:

> > ( image-width ( ellipse 30 40 "solid" "orange"))
> 30
> > ( image-width ( circle 30 "solid" "orange"))
> 60

> > ( image-width ( beside ( circle 20 "solid" "orange")
> ( circle 20 "solid" "purple")))

> 80
> > ( image-width ( rectangle 0 10 "solid" "purple"))
> 0

> > procedure

> > ( image-height i) → ( and/c integer? ( not/c negative? ) exact? )

> i : image?

Returns the height of i.

Examples:

> > ( image-height ( ellipse 30 40 "solid" "orange"))
> 40
> > ( image-height ( circle 30 "solid" "orange"))
> 60

> > ( image-height ( overlay ( circle 20 "solid" "orange")
> ( circle 30 "solid" "purple")))

> 60
> > ( image-height ( rectangle 10 0 "solid" "purple"))
> 0

> > procedure

> > ( image-baseline i) → ( and/c integer? ( not/c negative? ) exact? )

> i : image?

Returns the distance from the top of the image to its baseline. The baseline of an image is the place where the bottoms any letters line up, but without counting the descenders, e.g. the tail on “y” or “g” or “j”.

Unless the image was constructed with text, text/font or, in some cases, crop, this will be the same as its height.

Examples:

> > ( image-baseline ( text "Hello" 24 "black"))
> 22
> > ( image-height ( text "Hello" 24 "black"))
> 28
> > ( image-baseline ( rectangle 100 100 "solid" "black"))
> 100
> > ( image-height ( rectangle 100 100 "solid" "black"))
> 100

A cropped image’s baseline is the same as the image’s baseline, if the cropping stays within the original image’s bounding box. But if the cropping actually enlarges the image, then the baseline can end up being smaller.

Examples:

> > ( image-height ( rectangle 20 20 "solid" "black"))
> 20
> > ( image-baseline ( rectangle 20 20 "solid" "black"))
> 20
> > ( image-height ( crop 10 10 5 5 ( rectangle 20 20 "solid" "black")))
> 5
> > ( image-baseline ( crop 10 10 5 5 ( rectangle 20 20 "solid" "black")))
> 5
> > ( image-height ( crop 10 10 30 30 ( rectangle 20 20 "solid" "black")))
> 30
> > ( image-baseline ( crop 10 10 30 30 ( rectangle 20 20 "solid" "black")))
> 20

##### 2.2.8`` Image Predicates

This section lists predicates for the basic structures provided by the image library.

> > procedure

> > ( image? x) → boolean?

> x : any/c

Determines if x is an image. Images are returned by functions like ellipse and rectangle and accepted by functions like overlay and beside.

Additionally, images inserted into a DrRacket window are treated as bitmap images, as are instances of image-snip% and bitmap%.

> > procedure

> > ( mode? x) → boolean?

> x : any/c

Determines if x is a mode suitable for constructing images.

It can be one of 'solid, "solid", 'outline, or "outline", indicating if the shape is filled in or not.

It can also be an integer between 0 and 255 (inclusive) indicating the transparency of the image. The integer 255 is fully opaque, and is the same as "solid" (or 'solid). The integer 0 means fully transparent.

> > procedure

> > ( image-color? x) → boolean?

> x : any/c

Determines if x represents a color. Strings, symbols, and color structs are allowed as colors.

For example, "magenta", "black", 'orange, and 'purple are allowed. Colors are not case-sensitive, so "Magenta", "Black", 'Orange, and 'Purple are also allowed, and are the same colors as in the previous sentence. If a string or symbol color name is not recognized, black is used in its place.

The complete list of colors is available in the documentation for color-database<%>.

> > struct

> > ( struct |  | color (red green blue alpha)
> > |  | #:extra-constructor-name make-color )

> red : ( and/c natural-number/c (<=/c 255))
> green : ( and/c natural-number/c (<=/c 255))
> blue : ( and/c natural-number/c (<=/c 255))
> alpha : ( and/c natural-number/c (<=/c 255))

The color struct defines a color with red, green, blue, and alpha components that range from 0 to 255.

The red, green, and blue fields combine to make a color, with the higher values meaning more of the given color. For example, ( make-color 255 0 0) makes a bright red color and ( make-color 255 0 255) makes a bright purple.

The alpha field controls the transparency of the color. A value of 255 means that the color is opaque and 0 means the color is fully transparent.

The constructor, make-color, also accepts only three arguments, in which case the three arguments are used for the red, green, and blue fields, and the alpha field defaults to 255.

> > procedure

> > ( y-place? x) → boolean?

> x : any/c

Determines if x is a placement option for the vertical direction. It can be one of "top", 'top, "bottom", 'bottom, "middle", 'middle, "center", 'center, "baseline", 'baseline, "pinhole", or 'pinhole.

Using "pinhole" or 'pinhole is only allowed when all of the image arguments have pinholes.

See also image-baseline for more discussion of baselines.

> > procedure

> > ( x-place? x) → boolean?

> x : any/c

Determines if x is a placement option for the horizontal direction. It can be one of "left", 'left, "right", 'right, "middle", 'middle, "center", 'center, "pinhole", or 'pinhole.

Using "pinhole" or 'pinhole is only allowed when all of the image arguments have pinholes.

> > procedure

> > ( angle? x) → boolean?

> x : any/c

Determines if x is an angle, namely a real number between 0 (inclusive) and 360 (exclusive).

> > procedure

> > ( side-count? x) → boolean?

> x : any/c

Determines if x is an integer greater than or equal to 3.

> > procedure

> > ( step-count? x) → boolean?

> x : any/c

Determines if x is an integer greater than or equal to 1.

> > procedure

> > ( real-valued-posn? x) → boolean?

> x : any/c

Determines if x is a posn whose x and y fields are both real? numbers.

> > struct

> > ( struct |  | pen (color width style cap join)
> > |  | #:extra-constructor-name make-pen )

> color : image-color?
> width : ( and/c real? (<=/c 0 255))
> style : pen-style?
> cap : pen-cap?
> join : pen-join?

The pen struct specifies how the drawing library draws lines.

A good default for style is "solid", and good default values for the cap and join fields are "round".

Using 0 as a width is special; it means to always draw the smallest possible, but visible, pen. This means that the pen will always be one pixel in size, no matter how the image is scaled.

> > procedure

> > ( pen-style? x) → boolean?

> x : any/c

Determines if x is a valid pen style. It can be one of "solid", 'solid, "dot", 'dot, "long-dash", 'long-dash, "short-dash", 'short-dash, "dot-dash", or 'dot-dash.

> > procedure

> > ( pen-cap? x) → boolean?

> x : any/c

Determines if x is a valid pen cap. It can be one of "round", 'round, "projecting", 'projecting, "butt", or 'butt.

> > procedure

> > ( pen-join? x) → boolean?

> x : any/c

Determines if x is a valid pen join. It can be one of "round", 'round, "bevel", 'bevel, "miter", or 'miter.

##### 2.2.9`` Equality Testing of Images

Two images are equal? if they draw exactly the same way at their current size (not necessarily at all sizes) and, if there are pinholes, the pinholes are in the same place.

##### 2.2.10`` Pinholes

A pinhole is an optional property of an image that identifies a point somewhere in the image. The pinhole can then be used to facilitate overlaying images by lining them up on the their pinholes.

When an image has a pinhole, the pinhole is drawn with crosshairs on the image. The crosshairs are drawn with a two one pixel wide black lines (one horizontal and one vertical) and two one pixel wide white lines, where the black lines is drawn .5 pixels to the left and above the pinhole, and the white lines are drawn .5 pixels to the right and below the pinhole. Accordingly, when the pixel is on an integral coordinate, then black and white lines all take up a single pixel and in the center of their intersections is the actual pinholes. See The nitty gritty of pixels, pens, and lines for more details about pixels.

When images are overlay’d, underlay’d (or the variants of those functions), placed beside, or above each other, the pinhole of the resulting image is the pinhole of the first image argument passed to the combining operation. When images are combined with place-image (or the variants of place-image), then the scene argument’s pinhole is preserved.

> > procedure

> > ( center-pinhole image) → image?

> image : image?

Creates a pinhole in image at its center.

Examples:

> > ( center-pinhole ( rectangle 40 20 "solid" "red"))
> > ( rotate 30 ( center-pinhole ( rectangle 40 20 "solid" "orange")))

> > procedure

> > ( put-pinhole x y image) → image?

> x : integer?
> y : integer?
> image : image?

Creates a pinhole in image at the point (x,y).

Example:

> > ( put-pinhole 2 18 ( rectangle 40 20 "solid" "forestgreen"))

> > procedure

> > ( pinhole-x image) → ( or/c integer? #f)

> image : image?

Returns the x coordinate of image’s pinhole.

Example:

> > ( pinhole-x ( center-pinhole ( rectangle 10 10 "solid" "red")))
> 5

> > procedure

> > ( pinhole-y image) → ( or/c integer? #f)

> image : image?

Returns the y coordinate of image’s pinhole.

Example:

> > ( pinhole-y ( center-pinhole ( rectangle 10 10 "solid" "red")))
> 5

> > procedure

> > ( clear-pinhole image) → image?

> image : image?

Removes a pinhole from image (if the image has a pinhole).

> > procedure

> > ( overlay/pinhole i1 i2 is ...) → image?

> i1 : image?
> i2 : image?
> is : image?

Overlays all of the image arguments on their pinholes. If any of the arguments do not have pinholes, then the center of the image is used instead.

Examples:

> > ( overlay/pinhole
> ( put-pinhole 25 10 ( ellipse 100 50 "solid" "red"))
> ( put-pinhole 75 40 ( ellipse 100 50 "solid" "blue")))

> > (let ([petal ( put-pinhole
> 20 20
> ( ellipse 100 40 "solid" "purple"))])
> ( clear-pinhole
> ( overlay/pinhole
> ( circle 30 "solid" "yellow")
> ( rotate ( * 60 0) petal)
> ( rotate ( * 60 1) petal)
> ( rotate ( * 60 2) petal)
> ( rotate ( * 60 3) petal)
> ( rotate ( * 60 4) petal)
> ( rotate ( * 60 5) petal))))

> > procedure

> > ( underlay/pinhole i1 i2 is ...) → image?

> i1 : image?
> i2 : image?
> is : image?

Underlays all of the image arguments on their pinholes. If any of the arguments do not have pinholes, then the center of the image is used instead.

Examples:

> > ( underlay/pinhole
> ( put-pinhole 25 10 ( ellipse 100 50 "solid" "red"))
> ( put-pinhole 75 40 ( ellipse 100 50 "solid" "blue")))

> > (let* ([t ( triangle 40 "solid" "orange")]
> [w ( image-width t)]
> [h ( image-height t)])
> ( clear-pinhole
> ( overlay/pinhole
> ( put-pinhole ( / w 2) 0 t)
> ( put-pinhole w h t)
> ( put-pinhole 0 h t))))

##### 2.2.11`` Exporting Images to Disk

In order to use an image as an input to another program (e.g., Photoshop or a web browser), it is necessary to represent it in a format that these programs can understand.

The save-image function provides this functionality, writing an image to disk using the PNG format. Since this format represents an image using a set of pixel values, an image written to disk generally contains less information than the image that was written, and cannot be scaled or manipulated as cleanly (by any image program).

The save-svg-image function writes an SVG file format representation of the file to the disk that, unlike save-image produces an image that can still be scaled arbitrarily look as good as scaling the image directly via scale.

> > procedure

> > ( save-image image filename [width height]) → boolean?

> image : image?
> filename : path-string?
> width : ( and/c real? ( not/c negative? )) = ( image-width image)

> | height |  | : |  | ( and/c real? ( not/c negative? ))
> |  |  | = |  | ( image-height image)

Writes an image to the path specified by filename, using the PNG format.

The last two arguments are optional. If present, they determine the width and height of the save image file. If absent, the width and height of the image is used.

> > procedure

> > ( save-svg-image image filename [width height]) → void?

> image : image?
> filename : path-string?
> width : ( and/c real? ( not/c negative? )) = ( image-width image)

> | height |  | : |  | ( and/c real? ( not/c negative? ))
> |  |  | = |  | ( image-height image)

Writes an image to the path specified by filename, using the SVG format.

The last two arguments are optional. If present, they determine the width and height of the save image file. If absent, the width and height of the image is used.

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