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1991-05-03
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3d Surface Grapher
3dGraph v1.0
by Dan Schikore
05/03/91
INDEX
1. Disclaimer - page 1
2. Shareware Notice - page 1
3. System Requirements - page 2
4. Definitions - page 2
5. The equation types - page 3
6. The Menu System - page 4
a) How to use it
b) The Surface Menu
c) The Graph Menu
d) The Options Menu
7. The Surface Menu Commands - page 5
8. The Graph Menu Commands - page 6
9. The Options - page 7
10. Graph Mode Commands - page 8
- page 1 -
1. Disclaimer
This program is provided without any warranty of any kind. The
author will not be responsible for any damage of any kind due to the use
of this program.
2. Shareware Notice
This program is Shareware. It is provided with full feature
capability for you to examine and determine if it is of any use to you.
You are encouraged to distribute it as long as all original files are
included unmodified (except the data file), and no charges other than
disk copying fees are charged. You are free to use the program for your
personal use for two weeks. If you would like to continue using it,
please register to encourage development of this and other shareware
programs. Registered users will be notified of update opportunities by
mail. To register a personal version, print or copy the file register.doc,
fill it out, and send it along with $10 check or money order to:
Dan Schikore
1983 Greenheath
Florissant, MO 63033
If 3dGraph is being registered for a network or use on other groups of
computers by different users, the registration is:
2- 5 computers - $15
6-10 computers - $25
11-19 computers - $35
20+ computers - $50
Comments and suggestions are welcome.
- page 2 -
3. System Requirements
This program will operate on any PC-compatible computer with a
minimum of 640K of memory. All major video modes are supported. The
printer functions were developed for use with 9 and 24 pin Star printers
and are compatible with most dot matrix printers. A coprocessor is
helpful but not necessary.
4. Definitions
Surface - A surface consists of a function of one or two variables,
from any of six types of equations, along with parameters which specify
the limits of the variables x and y, the skip values for x and y (Skip
values define how many lines of the grid surface will be graphed when in
Graph Mode, a skip of 2 means every second line will be graphed), the
number of data points to be used in the surface (increasing the number of
data points increases the accuracy of the representation of the graph, and
decreases the speed of calculations and drawing), and the center of the
surface (Specifies a translation of the surface so a sphere can be centered
at (1,0,0) by defining a sphere at the origin and setting the center of
the surface to (1,0,0) ).
Graph - a graph can contain up to six surfaces. All graphs must
contain at least one surface. 2d and 3d functions can be mixed in the
same graph.
- page 3 -
5. The equation types
There are six basic types of equations available:
i) y=f(x)
ii) z=f(x,y)
iii) T[x]=( f(x), g(x) )
iv) T[x,y]= ( f(x,y), g(x,y) )
v) T[x]=( f(x), g(x), h(x) )
vi) T[x,y]=( f(x,y), g(x,y), h(x,y) )
When specifying a domain for x and y, the limits must be constant
expressions. All operators and functions available in functions are
allowed but x and y are not. Constants e and pi are defined. Equation
types i) and ii) can be used for most functions, such as a paraboloid
( z=x^2 + y^2 ), however for graphs which appear circular, you may not get
the desired effect, and it would be better to use a parametric
representation of the surface. For a paraboloid, this would be
T[x,y] = ( ysin(x), ycos(x), y^2 ). For other surfaces, like a sphere,
there is really no choice. To graph the upper half of a sphere of radius 1,
we would have z=sqrt(1 - x^2 - y^2),
-1 <= x <= 1
-1 <= y <= 1
but at some places on this domain, such as (-1, 1), z would be undefined.
For some of the more popular equations, there are predefined equations that
can be used to create paraboloids, ellipses, tori, and others.
The equations for f, g, and h can contain the following operators:
+, - , *, /, ^
The functions recognized are:
abs, cos, cosh, sin, sinh, tan, tanh, sqrt, exp, ln, log
And the constants PI and E are defined.
The usual rules for precedence are observed.
In many cases, the * operator can be omitted, for equations like f(x)=5x.
Unless parentheses are used, the unary operators and functions
( -, cos, sin, tan ...) operate on only the next operator in the
equation. For example:
sin5x = (sin(5))*x, while
sin(5x) = sin(5*x)
- page 4 -
6. The menu system
a) How to use it - The menus can be controlled several ways.
The menu which is highlighted is the current menu. To pull down the
options for a menu, press <ENTER> or <DOWN>. <ESC> will remove the menu
and return to the top level. When a menu is pulled down, <UP> and <DOWN>
move the highlight bar within the menu. To make a selection, press <ENTER>.
<LEFT> and <RIGHT> will change the current menu.
b) The Surface menu - The surface menu contains all of the options
necessary to Create and Edit Surfaces in the current Graph. None of the
options in this menu can be used until a graph has been loaded or created
using either the Load or New options from the Graph Menu. The options
available are:
i) Add - Add a Surface to the current Graph
ii) Change - Change the current surface
iii) Delete - Delete a Surface from the current Graph
iv) Edit - Edit the current surface
v) Graph - Graph all surfaces in the current Graph
For more details on the Surface Menu commands see page 5
b) The Graph menu - The Graph menu will allow the user to create
new graphs, load a graph, or save the current graphs to the data file. All
the graphs actually remain in memory the entire time, so loading a graph
actually only selects the current graph. Available options:
i) Add - Add a new Graph
ii) Delete - Delete a Graph
iii) Load - Load a Graph
iv) Save - Save the graphs to the graph datafile
For more details on the Graph Menu commands see page 6
b) The Options menu - The Options menu can be used to configure
the program for your specific needs. Use this menu to set the printer
type, printer port, specify whether colors should be used, whether double
buffering should be used, and the increment of angles to be used when
rotating the graph in Graph Mode. Available options are:
i) Edit - Edit the current setup
ii) Display - Show the current setup
iii) Save Setup - Save the current setup
For more details on the options see page 7
- page 5 -
7. The Surface Menu Commands
i) Add - To add a surface to the current graph, select Add from
the Surface menu. A menu with the different equation types will appear.
Highlight the desired type of equation and press <ENTER>. If you choose
a predefined equation, you will be asked to supply various parameters
depending on what surface you choose. You will then be placed in the
Edit mode for the Surface which allows you to specify the other Surface
parameters.
ii) Change - Change allows