<br>Data definition: 
<pre>
<code>
;; <em>{(idx Mode)}</em> is one of the following two symbols or strings: 
;; -- 'solid 
;; -- 'outline 
;; -- "solid"
;; -- "outline"

;; Interpretation: <code>'solid</code> is used for creating solid basic
;; shapes; <code>'outline</code> is used for creating outlines of basic
;; shapes. Strings are used in an analogous manner. 
</code></pre>

Data definition: 
<pre>
<code>
(define-struct color (red blue green))
;; A CS is a structure: (make-color N N N)
;; where N is between 0 and 255. 

;; <em>{(idx Color)}</em> is one of:
;; -- a color symbol, e.g., 'blue
;; -- a color string, e.g., "blue"
;; -- a CS, e.g., (make-color 0 0 255), which also denotes blue. 

;; Interpretation: <code>Color</code> arguments are used to paint the shapes
;; or their outlines. See below for more information about color structs.
</code>
</pre>

The following predicate precisely specifies what a valid image color is: 
<menu>
<li><code>{(idx image-color?)} :  anything -> boolean </code><br>
 to determine if the input is a valid image color
</menu>

The first group of functions creates basic shapes (<code>Image</code>):
<menu>
<li><code>{(idx rectangle)} :  Number Number Mode Color -> Image </code><br>
 to create a rectangle using the given width, height, mode, and color

<li><code>{(idx circle)} : Number Mode Color -> Image</code><br>
 to create a circle using the given radius, mode, and color

<li><code>{(idx ellipse)} : Number Number Mode Color -> Image </code><br>
 to create an ellipse using the given width, height, and color

<li><code>{(idx triangle)} : Number Mode Color -> Image</code><br>
 to create an upward pointing equilateral triangle using the given edge size and color

<li><code>{(idx star)} : Number[>=2] Number[>=1] Number[>=1] Mode Color -> Image</code><br>
 to create a multi-pointed star; the first number specifies
 the number of points, the second specifies the radius where
 the points begin and the third specifies the radius where they end.

<li><code>{(idx line)} : Number Number Color -> Image </code><br> to create an
 image with a colored line from (0,0) to the point with the given
 coordinates

<li><code>{(idx add-line)} : Image Int Int Int Int Color -> Image </code><br>
 to add a line to an existing image, drawn between the two given points

<li><code>{(idx text)} : String Size Color -> Image </code><br>
 to create an image of the text in the given string, with the point size,
 and color specified by the last two arguments 
</menu>

Images have many properties. To understand how functions manipulate and
create images, we need to understand one of these properties immediately:
<em>pinholes</em>. Each image, including primitive shapes, come with a
pinhole. Usually the pinhole is in the center of the shape except for those
created from <code>line</code> and <code>text</code>, which have pinholes
at the top left. When in doubt you can always find out where the pinhole is
and even place it somewhere else: 
<menu>
<li><code>{(idx pinhole-x)}</code> :  Image -> Int </code><br>
 to determine the x coordinate of the pinhole, measuring from
 the left of the image

<li><code>{(idx pinhole-y)} :  Image -> Int </code><br>
 to determine the y coordinate of the pinhole, measuring down from 
 the top of the image

<li><code>{(idx put-pinhole)} :  Image Int Int -> Image </code><br>
 to put the pinhole in the location specified by the arguments, counting
 from the left and down from the top, respectively.

<li><code>{(idx move-pinhole)} :  Image Int Int -> Image </code><br>
 to move the pinhole down and to the right (by the specified amounts) of 
 its current location. Use negative numbers to move it up or to the left.
</menu>

The next group of functions build images from images:
<menu>
<li><code>{(idx overlay)} : Image Image Image ... -> Image </code><br> 
 to add the pixels of the second Image onto the first image. The operation
 lines up the images via their pinholes. 

<li><code>{(idx overlay/xy)} : Image Int Int Image -> Image </code><br> to
 add the pixels of the second image onto the first image. Instead of lining
 up on the pinhole, the second image's pinhole is lined up with an offset
 from the first image's pinhole. The two coordinates specify how far down
 and to the right the offset should be. The pinhole of the resulting image
 is the same place as the pinhole in the first image.
</menu>

For composite images, it is always possible to determine whether one occurs
in the other and where: 
<menu>
<li><code>{(idx image-inside?)} : Image Image -> Boolean </code><br>
 to determine whether the pixels of the second image appear in the first.

<p>Be careful when using this function with jpeg images. If you use an
image-editing program to crop a jpeg image and then save it,
<code>image-inside?</code> will not recognize the cropped image, due to
standard compression applied to JPEG images. </p>

<p>Use PNG images instead whenever possible. </p>

<li><code>{(idx find-image)}</code> : Image Image -> Posn </code><br>
 to determine where the pixels of the second image appear in the first, with
 respect to the pinhole of the first image.
</menu>

Two more properties of images are useful for image manipulations: their
width and height. The two functions for extracting these properties are: 
<menu>
<li><code>{(idx image-width)} :  Image -> Int </code><br>
 to obtain an Image's width in pixels
<li><code>{(idx image-height)} :  Image -> Int </code><br>
 to obtain an image's height in pixels
</menu>

Data definition: 
<pre>
<code>
;; <em>List-of-color</em> is one of:
;; -- empty
;; -- (cons Color List-of-color)
</code>
</pre>
Interpretation: represents a sequence of colors 

It is possible to extract an image's colors and pixels and to create images
from a list of colors:
<menu>
<li><code>{(idx image->color-list)} : Image -> List-of-color </code><br>
 to convert an image to a list of colors

<li><code>{(idx color-list->image)} : List-of-color Nat Nat Nat Nat -> Image </code><br>
 to convert a list of colors to an image with the given
 width and height, and pinhole coordinates (the pinhole
 coordinates are with respect to the top-left of the image).

</menu>

The shrink functions trim an image by eliminating extraneous pixels.
<menu>
<li><code>{(idx shrink-tl)} : Image Number Number -> Image </code><br>
to shrink the image, starting from the top-left corner. The
two numbers indicate how many pixels to save.
The pinhole of the resulting image is in the middle of the image.
</li>

<li><code>{(idx shrink-tr)} : Image Number Number -> Image </code><br>
to shrink the image, starting from the top-right corner. The
two numbers indicate how many pixels to save.
The pinhole of the resulting image is in the middle of the image.
</li>

<li><code>{(idx shrink-bl)} : Image Number Number -> Image </code><br>
to shrink the image, starting from the bottom-left corner. The
two numbers indicate how many pixels to save.
The pinhole of the resulting image is in the middle of the image.
</li>

<li><code>{(idx shrink-br)} : Image Number Number -> Image </code><br>
to shrink the image, starting from the bottom-right corner. The
two numbers indicate how many pixels to save.
The pinhole of the resulting image is in the middle of the image.
</li>

<li><code>{(idx shrink)} : Image Number Number Number Number -> Image </code><br>
to shrink an image around its pinhole. The numbers are the
pixels to save to left, above, to the right, and below the
pinhole, respectively. The pixel directly on the pinhole is
always saved.
</li>
</menu>
 
The last group of functions extracts the consitiuent colors from an image
and combine colors into an image, but the functions provide alpha-channel
information as well. Alpha channels are a measure of transparency; 0
indicates fully opaque and 255 indicates fully transparent.

<menu>
<li><code>{(idx image->alpha-color-list)} : image -> list-of-alpha-color </code><br>
 to convert an image to a list of alpha colors
<li><code>{(idx alpha-color-list->image)} : list-of-alpha-color int int int int -> image </code><br>
 to convert a list of alpha colors to an image with the given
 width and height, and pinhole coordinates (the pinhole
 coordinates are with respect to the top-left of the image).
<li><code>{(idx make-alpha-color)} : int int int int -> color </code><br>
 to construct an alpha color
<li><code>{(idx alpha-color?)} : anything -> boolean </code><br>
 to determine if its input is a color
<li><code>{(idx alpha-color-alpha)} : color -> int </code><br>
 to extract the alpha value of a color
<li><code>{(idx alpha-color-red)} : color -> int </code><br>
 to extract the red component of a color
<li><code>{(idx alpha-color-green)} : color -> int </code><br>
 to extract the green component of a color
<li><code>{(idx alpha-color-blue)} : color -> int </code><br>
 to extract the blue component of a color"
</menu>
