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<(Courier) cf ><9 cs>The Henderson Library--<eop>
by Syam Gadde<eop>
and Bo Whong<eop>
<eop>
The Henderson Library is a toolkit with which one can use Functional Geometry,
as proposed by Peter Henderson in his paper "Functional Geometry". This is a s
cheme by which "Picture"s can be described in an abstract data type, and a numb
er of functions can be applied to it. This results in a very elegant method to
produce complex pictures from simple ones. The example Henderson uses is "Squ
are Limit" by M. C. Escher, which can be constructed with four simple pictures
.<eop>
<eop>
------------------------<eop>
ADTs and Type Synonyms<eop>
<eop>
The Picture data type is composed of eight different types of pictures. They a
re:<eop>
<eop>
data<eop>
Picture = Nil - empty picture<eop>
| Flip Picture - picture flipped on the y-axis<e
op>
| Beside Float Picture Float Picture - two pictures placed side by sid
e <eop>
- in accordance to the ratio of t
he<eop>
- two floats<eop>
| Above Float Picture Float Picture - two pictures placed one on top
of<eop>
- another in accordance to the ra
tio<eop>
- of the two floats<eop>
| Rot Picture - picture is rotated 90 degrees <
eop>
- counterclockwise<eop>
| File String - picture is stored as an externa
l<eop>
- file<eop>
| Overlay Picture Picture - two pictures are drawn such tha
t<eop>
- one lays on top of the other<eo
p>
| Grid Int Int SegList - picture type that contains the
list<eop>
- of picture's line segments alon
g<eop>
- with the size of the inital pic
ture<eop>
<eop>
The type synonyms are pretty much self explanatory.<eop>
<eop>
Hostname<tab><tab><tab>- a string of the hostname<eop>
Filename <tab>- a string of the filename<e
op>
IntPoint <tab>- a tuple of integers repres
enting<eop>
<tab>- the coordinates of a point
<eop>
IntSegment <tab>- a tuple of Intpoints repre
senting<eop>
<tab>- the endpoints of a line se
gment<eop>
IntSegList <tab>- a list of IntSegments <eop
>
Point <tab>- same as IntPoint except in
place of<eop>
<tab><tab><tab> <tab>- intergers, they are floating points<eop>
Segment <tab>- same as IntSegment except
in place<eop>
<tab><tab> <tab>- of intergers, they are floating <eop>
<tab><tab><tab>- points<eop>
SegList <tab>- same as IntsegList except
in place<eop>
<tab><tab><tab><tab>- of intergers, they are floating <eop>
<tab><tab><tab>- points<eop>
Vector <tab>- a tuple of floating points
to<eop>
<tab><tab><tab>- to represent a vector<eop>
Vtriple - a 3-tuple of Vectors<eop>
HendQuartet - a 4-tuple of Integers for the s
ize<eop>
- of the Henderson window<eop>
PEnv - a tuple of a Filename and a Pic
ture<eop>
- for storing already opened file
s in<eop>
- in order to save time and memor
y<eop>
- when a file needs to be opened
more<eop>
- than once<eop>
<eop>
-------------------------------------------------------------------------------
----<eop>
Function: create (an exported function from the HendersonLib)<eop>
<eop>
The purpose of the create function is to provide the user with a function to <e
op>
draw a picture from a graphics interface. The user may choose to create a pict
ure<eop>
file by inputing the the lines and points manually into a file or (s)he may cho
ose<eop>
to use the create function.<eop>
<eop>
Functionality of create:<eop>
create :: Hostname -<ra> Filaname -<ra> Int -<ra> Int -<ra> IO()<eop
>
<eop>
create takes as input a hostname, a filename, and two integers for the size of
the <eop>
window to be opened. Two windows should appear, one for the input of lines and
<eop>
another showing the current position of the mouse. These windows will be label
ed<eop>
accordingly.<eop>
To draw a line on the file window, move the cursor to the desired position, the
n<eop>
hit any key on the keybroad. This point will be the beginning of the line segme
nt.<eop>
Next move the cursor to the position of where the user wants the end of the lin
e<eop>
segment to be, then hit any key from the keyboard again. A line should appear.
<eop>
The coordinates of the endpoints of each line drawn will also be printed out o
nto <eop>
standard output.<eop>
To signal completion of a file, press any button on the mouse. The user must <
eop>
remember though that this is only applicable after a completed drawing of a lin
e.<eop>
For example, pressing the mouse button will not work if one of the endpoints of
a<eop>
line is drawn but the other endpoint is not. create will not recognize the mous
e <eop>
button press event until a second endpoint is drawn.<eop>
<eop>
Advantages of create:<eop>
provides a quick and fun way to create a picture file.<eop>
<eop>
Disadvantages of create:<eop>
If the file does not exist, create will create the file and then store the pic
ture<eop>
to it. However, if the file exists, create will automatically delete the cont
ents<eop>
of that file before storing the new picture.<eop>
<eop>
-------------------------------------------------------------------------------
----<eop>
Function: modify (an exported function from the HendersonLib)<eop>
<eop>
The purpose of the modify function is to provide the user with a function make
<eop>
additions to an already existing picture file using a graphics interface. The
user<eop>
may choose to modify the picture file by adding the the lines and points manual
ly <eop>
into the file or (s)he may choose to use the modify function.<eop>
<eop>
Functionality of modify:<eop>
modify :: Hostname -<ra> Filaname -<ra> IO()<eop>
<eop>
modify takes as input a hostname and a filename. Tow windows should appear. Th
e <eop>
size of the draw window will be the same as the x and y coordinates already in
the<eop>
file. These windows will be labeled accordingly. The existing picture will app
ear<eop>
first before any input is allowed.<eop>
To draw a line on the file window, move the cursor to the desired position, the
n<eop>
hit any key on the keybroad. This point will be the beginning of the line segme
nt.<eop>
Next move the cursor to the position of where the user wants the end of the lin
e<eop>
segment to be, then hit any key from the keyboard again. A line should appear.
<eop>
The coordinates of the endpoints of each line drawn will also be printed out o
nto <eop>
standard output.<eop>
To signal completion of a file, press any button on the mouse. The user must <
eop>
remember though that this is only applicable after a completed drawing of a lin
e.<eop>
For example, pressing the mouse button will not work if one of the endpoints of
a<eop>
line is drawn but the other endpoint is not. modify will not recognize the mou
se <eop>
button press event until a second endpoint is drawn.<eop>
<eop>
Advantages of modify:<eop>
provides a quick and fun way to modify a picture file without having to go int
o<eop>
the file and manually add on the coordinates of the additional lines<eop>
<eop>
Disadvantages of modify:<eop>
Existing lines can not be deleted and any additional lines, whether intentiona
l or<eop>
unintentional, will be appended to the picture and stored in the file.<eop>
<eop>
--------------------------------------------------------<eop>
Function: sendToDraw<eop>
<eop>
Type of sendToDraw:<eop>
sendToDraw :: XWindow -<ra> XScreen -<ra> XDisplay -<ra> <eop>
XPixel -<ra> XPixel -<ra> Plot -<ra> IO()<eop>
<eop>
Usage:<eop>
sendToDraw win scn dis fg_color bg_color plt<eop>
<eop>
'sendToDraw' is the most primitive function in the part of the Henderson<eop>
library that deals with X windows, and therefore, can be used as a very<eop>
powerful tool. It draws a Plot plt (see 'plot' function) in the given XWindow<
eop>
win, and on the given XScreen and XDisplay scn and dis, drawing the lines in<eo
p>
the foreground color. This function allows the programmer to draw more than<eo
p>
one Picture to the same window.<eop>
<eop>
Arguments:<eop>
win - the XWindow in which to draw plt<eop>
scn - the screen which contains win<eop>
dis - the display which contains scn<eop>
fg_color - an XPixel the color of which the plt will be drawn in. Note that<
eop>
<tab>this allows the programmer to draw different plt's in different colors.<eo
p>
bg_color - unused, but required.<eop>
--------------------------------------------------------<eop>
Function: plot<eop>
<eop>
Type of 'plot':<eop>
plot :: Picture -<ra> VTriple -<ra> PEnv -<ra> ((Plot, PEnv) -<ra> IO()) -<ra
> IO()<eop>
<eop>
Usage:<eop>
plot pic (a,b,c) env func<eop>
<eop>
The 'plot' function is needed to create a Plot which would be normally sent to<
eop>
a function such as sendToDraw. 'plot' converts a Picture pic into a format<eop
>
that sendToDraw can deal with.<eop>
'plot' also takes three vectors which specify the bounding box in which the<eop
>
Picture is to be drawn. The first vector (a) specifies the upper left corner<e
op>
of the bounding box. The next two vectors specify the bounding box itself,<eop
>
with respect to the first vector. This allows for non-rectangular bounding<eop
>
boxes. For example, the vector triple ((50,50), (100,0), (0,100)) specifies<eo
p>
the following bounding box:<eop>
<eop>
(0,0)----------------------------------<eop>
|<eop>
| (50,50)<eop>
| _______________ (150,0) <eop>
| | |<eop>
| | |<eop>
| | |<eop>
| | |<eop>
| | |<eop>
| |_____________| (150,150)<eop>
| (0,150)<eop>
<eop>
<eop>
A vector triple of ((0,0), (100,300), (0,100)) would specify:<eop>
<eop>
(0,0)-------------------------------------<eop>
||\<eop>
|| \<eop>
|| \<eop>
(0,100)|| \<eop>
|\ \<eop>
| \ \<eop>
| \ \<eop>
| \ \ (100,300)<eop>
| \ | <eop>
| \ |<eop>
| \ |<eop>
| \| (100,400)<eop>
<eop>
Arguments: <eop>
pic - the Picture to be converted<eop>
a - a vector specifying the upper left corner of the bounding box<eop>
<tab>of the picture.<eop>
b - a vector understood to start at 'a' and specifying the upper edge of<eop>
<tab>the bounding box.<eop>
c - a vector understood to start at 'a' and specifying the left edge of<eop>
<tab>the bounding box.<eop>
--------------------------------------------------------<eop>
Function: draw<eop>
<eop>
Type of draw:<eop>
draw :: Hostname -<ra> Picture -<ra> VTriple -<ra> HendQuartet -<ra> IO()<eop
>
<eop>
Usage:<eop>
draw host pic (a,b,c) (m,n,p,q)<eop>
<eop>
'draw' is a higher-level function than sendToDraw, and is useful to use when<eo
p>
the programmer wishes only to draw one Picture on the screen. This function<eo
p>
does most of the work that the programmer would normally have to do when using<
eop>
sendToDraw. 'draw' opens a window at host with upper left coordinates m and n<
eop>
(on an X server that lets the user position any child window of the root<eop>
window, these coordinates mean nothing), and with width p and height q.<eop>
'draw' then calls 'plot' on pic and (a,b,c) and sends the result to sendToDraw,
<eop>
which finally draws the picture to the window.<eop>
<eop>
Arguments:<eop>
host - host on which to open a display, i.e. "tucan:0"<eop>
pic - the Picture to be drawn<eop>
(a,b,c) - the vector triple specifying the bounding box to be sent to<eop>
<tab>plot (see 'plot' function)<eop>
(m,n,p,q) - upper left corner x (m), upper left corner y (n), width (p),<eop>
<tab>and height (q), of window to be opened.<eop>
<eop>
-----------------------------------------------------------<eop>
<eop>
Module: SquareLimit<eop>
<eop>
This module is a sample user module that can be used to draw Square Limit, a wo
odcut by M. C. Escher. To draw "SquareLimit" on your host, run the dialogue:<e
op>
<tab>final host<eop>
where 'host' is the host running X, such as "turtle:0".<eop>
<eop>
To draw a slightly more interesting picture, tun the dialogue:<eop>
<tab>skewedfinal host<eop>
and it will draw "SquareLimit" in a bounding box shaped as a diamond.<eop>
<eop>
<textstream_end>
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