A program to display conformal maps.
This is a test program.
Copyright George S. Gordon Jr.

Description

With this program you make many windows that are related to each other by conformal maps. When you r draw in one window, the program draws the corresponding figure in the other windows. Conformal maps may be chained one after the other. Figures may be either drawn free hand, or one of several predefined figures may be drawn. Special drawing functions are available, such as drawing axis, or cuts, singularities, or special map dependent functions.

Documentation

This code draws figures in different windows, that correspond to different conformal maps of each other.

Running the code

The code can be run as either an application, or as an applet. To run as an applet either

use a Java enabled browser on "draw.html
appletviewer draw.html

to run as an application

Java draw

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enableing HELP feature.

To enable the help feature, this file must be converted to a txt file using netscape, (Outlook Express will not work as it does not put bullets in front ot list items.) This html file is edited with vi sed or the like

:%s///g
:%s/<\/h[34]>/
/g
:w d.html

Then d.html is converted to a txt file using nescape, and stored as draw.txt

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Operation of Program

The first Canvas will come up. You can draw into it, or bring up one of several menus. To draw into a window, move the mouse to the start point for the figure, then release the mouse for the second point in the figure. Some figures such as sectors or arc may require a second mouse depression and release to define third and fourth points.

A left click will bring up the "Control Menu"
This controls the look and drawing in the associated window, or in case of the ALL popup, of all windows.
A right click will bring up a new "New Canvas Menu"
This allows th creation of a new window which is related to the current window by the chosen Conformal Map. In ala, except a few simple cases, the inverse transform may be chosen with a click on the defining box which pops up as the window is created.
HELP In every menu there is a "HELP" option. When this option is activated, The normal function of all menu_choices is suspended, and replaces by popping up a help frame, that will explain that option. Normal operation of the menus resumes when the "HELP DONE" button on the main HELP frame is activated, and that frame is destroys. The other help frames can be left up if you wish.
The "HELP" option on the "Control Menu" can also be used to enter the help mode.
The help mode is exited by either clicking on the "HELP DONE" button on the help popup, the "HELP" button on the "Control Menu" or selecting "HELP on the "New Canvas Menu".

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"Control Menu"

control text

Name of Canvas
that this menu refers to.
size of pane
that is visible in pixels.
SIZE of CANVAS
that underlies the pane, in pixels
Real World"
is left side and length of the Real World coordinates the are referred to in the underlying Canvas.
The is the bottom and height of the real world coordinates.
(Changes to these become effective when the "DONE" button is clicked.)
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dxy
(if not zero) is the length of segments that straight lines are broken into, so the conformal map can follow a line more accurately. If equal to zero lines are not broken into segments.
ncir
number of segment circles are broken into. If zero, dxy will be used as a guide
nfill
number of lines used to fill in figures
tic
distance between tic marks, both for axis & draw tic. If zero, no ticks.
nfill2
number of lines used to fill in figures, second direction

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control buttons

The next two line's buttons apply only to this canvas, unless the "all" button on the next line is set, in which case they effect all canvases.

Clear
Clears this canvas
Axis
Draws a X & Y Axis
Print
print out info on this canvas & transform
Sectors
plots out sectors in different colors. All does not cause this to be done for all active mappings. Not defined for many mappings. Background and foreground colors may be ignored This is disabled in ALL menu.
Single
plots a mark at known singularity for this map
Cut
Draws any cut lines
Points
draws marks at important points for this transform
Special
draws special figures for this transform. May also send these to other Canvas if "local" is not set, and may write on caller's Canvas if "Pre Mark" is set. This function is not defined for many mappings. It is disables on all menu;

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control checkboxs

The next three lines effect the general processing

Local only
only plotted on this canvas, no transform done
All
Bring to the front the "ALL" Control menu.
Allow Drag
Allows mouse drags rather than just recording mouse press and release
Mark Pre
Mark on caller Canvas when the "special command is invoked
Fill In
Fills the interior of the figure being drawn.
Fill Out
Fills exterior, continues fill interior lines (even if interior lines are not drawn) their length on the exterior
Exact
Pops up a window on next draw so you can put in exact coordinates for the next figure.
Pos_xy
Pops up a panel which shows the real world coordinates (in x, y format) at the end of the last draw, but only if line is chosen on the line below
ToPoly
Treats figures drawn as polygons, and fills them in with a solid color.
Rotate
Allow figures such as Square and rectangle to be rotated from axisies. (Not yet implemented.)
PlotAny
Plots all points, even if they are possibly wrong.
Pos_rth
Pops up a panel which shows the real world coordinates (in R theta format) at the end of the last draw, but only if line is chosen on the line below

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Geometric figures that will be drawn in this canvas. Is effected by "Allow Drag, "length of dxy" etc.

Line
Draw a straight line. (The default)
circle
Draw a circle centered at mouse press, with radius to mouse release
rectangle
Draw a rectangle
square
Force a rectangle to a square
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parallel
Draw parallelogram.
sector
Draw a sector of a circle.
mouse press at center then release at end of first radius. Press again on the interior of the sector, releasing on the second radius of the sector.
sector2
Draw the difference in two sectors with the same radii.
mouse press at center then release at interior point of first radius. Press again on the interior of the sector,but at the distance of the max radius. Release on the second radius.
poly
draws polygon, and fills. Press the mouse, than drag the outline of the polygon. on release the polygon is filled.
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point
Draws a point on button release
arc
Draws an arc. Center on button down, first edge on button up, button down interior of arc, release governs radial line for end of arc

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control colors

Back_Ground
a drop-down menu to set the color of the background
Fore_Ground
a drop-down menu to set the color of the foreground
Polygon_Fill
Drop down menu for the fill color of the polygon.
Polygon_Border
Drop down menu for the border color of the polygon. The color is also used for the XORing if that is used.
Figure_Fill
Drop down menu for the fill color of figures.
Figure_Border
Drop down menu for the border color of figures.
XOR_color
Set the XOR Mode color, if null use Paint Mode.
Bad_color
drop down menu to set the color use when the data point is suspected to be bad.
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control finial

finial three buttons

HELP
This will bring up the First HELP Frame, and suspend the normal menu functions until this HELP window is removed
DO
Does the top half of the menu.
DONE
Does the top half of the menu, and makes the menu invisible.
(A left click will make it visible again.)
DELETE
Deletes this Canvas. This will delete children canvases.

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control end

"New Canvas Menu"

This drop down menu let you select the next canvas (conformal map) that will be done from this Canvas. This is a multi level dropdown menu. At present the following Conformal maps are implemented

Bilinear_type
- bilinear
  page 3, formula 3.1
  z = ( a*w + b)/(c*w + d)
  A pop up window will request you to put in the wanted complex values for a, b, c, d. Indicate that the proper values are in by clicking on the "DO" button.
  - a
    as in above formula
  - b
    as in above formula
  - c
    as in above formula
  - d
    as in above formula
  _______________________________
- cir_cir
  This is a different form of the bilinear transform. This map, maps one circle onto another circle.
  page 20
  - Z0
    center of circle in base window
  - W0
    center of circle in generated window
  - r
    radius of circle in base window
  - R
    radius of circle in generated window
  - th
    angle of rotation of generated plot
  - alpha
    a control parameter, if abs( alpha) < 1 map inside to inside, if abs( alpha) > 1 map inside to outside.
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- p3_p3
  maps three point into three points
  page 16, eq 5.1
  - point1
    first point in generated window
  - point2
    second point in generated window
  - point3
    third point in generated window
  - POINT1
    first point in base window
  - POINT2
    second point in base window
  - POINT3
    third point in base window
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- trans_rot
  Does a translation, rotation and expansion. First panel requests order of Translation, rotation and expansion. (All need not be done) Upon clicking on Continue, the popup is expanded to request the amounts of Translation, Rotation & expansion to be done.
  - Translation
    amount of translation in real & imaginary directions
  - Rotation
    Rotation angle in radians.
  - Expansion
    Scale factor.
- Algebraic_type
  - ztoa
    
    w = z^alpha
    page 40, eq 6.2 A pop up window will request you to put in the wanted complex values for a, b, c, d. Indicate that the proper values are in by clicking on the "DO" button.
    - alpha
      as in above formula
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  - sector
    onto upper half plan First half of sector maps inside of unit half circle. Second half of sector maps outside of unit half circle
    
    z = c (( w^0.5 + 1)/(w^0.5 - 1))^( a/pi)
    page 51
    - c
      length of side of sector
    - a
      angle of sector
  - half_plane
    
    w = a * z + b/z
    page 58, eq 8
    - a
      as in above formula
    - b
      as in above formula
  - Exp_&_Log_type
    Formulas containing exp & log.
    - exp
      
      w = exp( z)
      page 85, eq 10.1
      - Cut Angle
        Angle of Cut in radians
    - tanh
      hyperbolic tangent
      w = tanh( z)
      page 88 eq 10.2
      - Cut placement
        Angle of Cut in radians radial box
        
        out side
        Cut is on real line outside of (-1, 1)
        in side
        Cut is on real line inside of [-1, 1]
        Other
        Cut Along an arc between real [-1, 1] Causes the popup to expand to request the "Cut Angle for exp. Minus pi ==> outside Zero ==> Inside other values cause arcs between -1 & 1
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- DEBUG_type
  These vary from time to time, and as the name suggests they are being debugged. Thus they are more error prone.
- Simple_type
  These do not pop up any info frame, and do not have an inverse option;
  - equal
    This is just the identity transform
  - half
    This transform just half s all the coordinates
  - double
    This transform just doubles all coordinates
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Description

Documentation

Running the code

enableing HELP feature.

Operation of Program

"Control Menu"

control text

Name of Canvas

size of pane

SIZE of CANVAS

Real World"

__________________________

dxy

ncir

nfill

tic

nfill2

control buttons

Clear

Axis

Print

Sectors

Single

Cut

Points

Special

control checkboxs

Local only

All

Allow Drag

Mark Pre

Fill In

Fill Out

Exact

Pos_xy

ToPoly

Rotate

PlotAny

Pos_rth

Line

circle

rectangle

square

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parallel

sector

sector2

poly

__________________________

point

arc

control colors

Back_Ground

Fore_Ground

Polygon_Fill

Polygon_Border

Figure_Fill

Figure_Border

XOR_color

Bad_color

control finial

HELP

DO

DONE

DELETE

control end

"New Canvas Menu"

Bilinear_type

bilinear

z = ( a*w + b)/(c*w + d)

a

b

c

d

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cir_cir

Z0

W0

r

R

z = ( aw + b)/(cw + d)