Program
for Drawing and
Analyzing Math Functions.
· Draw Functions and First derivatives
· Find
intersections (Regula Falsi)
· Numerical integration
(Simpson's Rule)
· Length of curve
· Volume
· Lateral surface
· Points of Gravity of:
- curves
- surfaces
- bodies
· Moments of Inertia from:
- surfaces
- bodies
Following User Interface Languages are available:
- English
- German
- DE - EDV (German without special characters)
- Bulgarian (Take care that 3rd-party software is needed to use Bulgarian on Palm)
- BG - LAT (Bulgarian uses Latin characters), so the Program can be used without 3rd party software)
- Internal Texteditor
- The complete POWER of PLUA can now be
accessed
trough the built-in MACROEDITOR
- Screenshot* - PGRaph can save the
screen contents in to a standart BMP file (which can be opened on
Desktop PC)
- HTML Report generator* - PGraph can create
standart HTML (wich can be viewed with any standart WEB browser) file
(+screenshot) that contains the result from the last calculation.
*-To use this functions you will need a Palm Device with External Memory Card (MMC / SD etc.)
Unpack PGRAPH.ZIP
Contents:
PGraph.prc - Program
PGT.pdb - Database
PluaRT.prc - run time environment
MathLib.prc - mathematics library
Liesmich.txt - Read Me German
Readme.txt - Read Me
ReadmeBG.txt - Read Me Bulgarian
FOLLOWING FILES MUST BE ON YOUR PALM:
1) PGraph.prc
2) PluaRT.prc
3) MathLib.prc
4) PGT.pdb
If you already have MathLib installed, it is not necessary to reinstall.
EARLIER VERSIONS OF PLUART.PRC AND PGRAPH.PRC MUST BE REMOVED!
PGraph is developed and tested with:
Palm Tungsten C
PalmOS Simulator
High resolution (320x320) Palm devices are supported. All other will run in Low-Res mode.
Start the programm. Draw...
Up - left on the screen is:
Menu:
Menu
- the same as About PGraph - displays
short Information
Help
- this here
f(x)=...
- opens input field where you can
input (edit) the function f(x)
g(x)=...
- the same
Only Plua expressions and functions with one variable are permitted.
Name of the variable is "x". The program uses "dostring(expression)".
Under "expression" is every Plua - expression to be understand. All
deviations from Plua - syntax lead to error message! Here a short
Manual.:
Square root: sqrt(Expression)
ln(x): log(Expression)
exp: exp(Expression)
Exponentiation:
(Expression)^Exponent
Root Extraction:
(Expression)^(1/Root)
Multiply:
(Expression)*(Expression)
Sum: (Expression)+(Expression)
Divide:
(Expression)/(Expression)
Subtract: (Expression) -
(Expression)
Arc functions:
asin(Expression), acos(Expression), atan(Expression)
Trigonometric functions:
sin(deg(Expression)),
cos(deg(Expression)), tan(deg(Expression))
WARNING - the Argument of
all
trigonometric
functions must first be converted trough deg()! Otherwise you will get
falsified values!
Hyperbolic functions and AREA functions:
sinh(x), cosh(x), tanh(x),
coth(x), arsinh(x), arcosh(x),
artanh(x),
arcoth(x)
Examples:
- sqrt(exp(sin(deg(x)))+cos(deg(x))) - !!! deg() !!!
- (x^3+3*x^2-x+16)/(x^5-x^8).
- (sinh(x)^2+tanh(x)^2)^(1/5)
Work with... -
switches between Curve,
Surface, Body (built trough Rotation of the selected function around
the X-Axis)
Built by...
- switches between f(x), g(x)
and f(x)-g(x)
- According to your choice in the those both positions different things
are drawn and can be calculated
Example: "Work with Surface" & "Built by f(x)" - draws surface
between f(x) and X-Axis and you can do all Surface-relevant calculation
types - Area, Point of Gravity, Moment of inertia
- Min. / Max. X / Y Axis
- ...
- Scale
- the distance for the grid
- Density
- Density of Points for
Drawing - lower Numbers results beautiful Graphs but takes more time to
draw. The programm calculates internal an suitable numer, but you can
change it.
- f(x)' draw and g(x)' draw
- changes
from "Yes" to "No" and again, makes what is written - draws (or not)
the according first Derivative on the screen.
- Lower and Upper Limits
- Limits for
Calculation (Integration, Regula Falsi etc.)- By choosing this entry,
the programm asks you if Regula Falsi should be started at last X
coordinates - according to the choice you make in Work with.../built
by..., for different intersections will be searched - after you say
"YES". As example "Work with Curve" "Built by f(x)-g(x)" looks for
intersection between f(x) and g(x). If you do not wish to use Regula
Falsi, an input field is shown and you can input suitable value.
TAKE CARE:
that all of the values (xmin,
xmax, limits) are tested to be suitable and if not the old value is
restored!
As example: you input lower limit that is bigger than the existing
upper limit, the old lower limit is restored. You should first change
the upper limit first.
- Find intersections (Regula Falsi)
- Numerical integration (Simpson)
- Length of curve
- Volume
- Lateral surface
- Points of Gravity of curves, surfaces and bodies
- Moments of inertia surfaces and bodies
Choosing one of these starts the calculation, an report is created with
the choosen calculation. This report (or parts of it) can be copied and
inserted (also into other programs). The result(s) from the last
calculation are stored into the variables Result 1 to 5 (depending from
the kind of the calculation - with Simpson, Regula Falsi only Result 1,
Point of gravity from curve Result 1, 2 & 3 etc.) and can be
called
up
Not all combinations are meaningful - e.g. lateral surface if you work
with curve or surface, volume of surface etc., ERROR MESSAGE is
displayed if you choose something like this.
Sincethe report is written in the Texteditor you can also save, edit
and open (saved) reports.
- Result 1 to 5 -
Result(s) from previous Calculation are
savedDBLK P here
- Memory 1 to 5 -
Memory places to save
Results or other Values
- "Colors" -
here you can change the
colors for drawing. Choose the element you wish to change. As example
f(x)-g(x) this means the color of the area between f(x) and g(x). The
saved color is shown automatically after you choose this item, use the
slide bars to change the color (you can compare previous / changed
color), the new value is saved automatically, "Back" goes back to the
"Draw" screen
- "User interface" -
I will surely win no
price for translation quality, neither German nor English are my native
language, so I give you the opportunity to change the used texts for
the UI. If you send me an optimised PGUIText, I can add it for next
PGraph versions (you can also translate PGraph into other Languages,
these is also welcome)
- Save / Load Settings
- the "Settings" -
this means all of the variables which controls the PGraphs behaviuor
are automatically saved in the PGini file (in this file not exists,
will be created every time you start PGraph), without your action, here
you can save/load your (customer) "INI" files, so you can easy change
between different functions/parameters - otherwise (without those
functions) you should every time hardly input all of the variables.
- "Texteditor"
- Here you can edit text (;-), load saved
reports, you can also open PalmDoc files (max 8 KB!). But take care -
by saving PGraph has only one option - StreamDB, this means you should
change the name of the opened PalmDoc file, otherwise the "DOC
structure" will be lost and you can open this file with PGraph/Plua
only (and no more with your preferred DocWiever/Editor!) StreamDBs can
be readed on Desktop PC without problems (I am using KWrite under
Linux/KDE)
- Run
- Runs single line of Plua code
- Run Macro
- Runs saved Plua macro
- Macroeditor -
Calls the texteditor in
"macro mode" so you can write your own macros
Here I am giving you very powerfull tool to extend the PGraph according
to your needs - you can do allmost all - define your own functions,
call PGraphs's functions, or even create completelly new programm!
But take care I am not able to make Programm-Routine to save you from
errors, if there are some errors the COMPLETE PGraph / Plua environment
will be exited (this means you must start PGraph again)
Here
briefly manual:
-- Comments are written this way in Lua / Plua
PGraph internal variables:
xmin - ...
xmax - ...
ymin - ...
ymax - ...
scl
- Scale
step
- Density of Points
Example:
xmin,xmax,ymin,ymax=-3,3,-3,3
-- take care of the multiple var set (typical for Lua), this here is
the same as:
xmin=-3
xmax=3
ymin=-3
ymax=3
ft[1] - f(x) as text
ft[2] - g(x) as text
Example:
ft[1]="sin(deg(x))
dostring("function f(x) return y="..ft[1].." end"])
-- You should call dostring("function f(x) return y="..ft[1].." end"])
in order to change f(x), the same for g(x)
ft[1],ft[2]=ft[2],ft[1]
-- tricky, switches the values of the both variables, ft[1] becomes the
value from ft[2], ft[2] from ft[1]
a - lower limit
b - upper limit
Example:
a=exp(1)
--sets a to 2.71828....
b=PI
--sets b to 3.14...
b=-a
-- tricky
text[1] ... text[60] the texts for the UI
fkr - internal screen faktor for Low / Hi Res devices, so you can place
everything on the right screen position without knowledge are we runing
on Hi Res or Low Res device.
using the pmode() command of Plua (as per Plua Manual)
pmode(): returns 4 numbers: screen width, screen height, screen depth
and 1 or 0 indicating if the screen supports color.
w,h,d,c=pmode()
--take care of the use of a,b,c,d,e=... this way you can take more than
one value returned from function
fkr=w/320
-- this way fkr is 1 on HiRes and 0.5 on LowRes devices
-- if you multiply the HiRes coordinate you wish to have with the fkr,
your object will be shown everytime at same (relative) screen position,
even you run the programm on 160x160 device.
xc - center of the grid X -component
yc - center of the grid Y -component
xf and yf are the correction factors for the X/Y axis.
M0-M4 - Result 1 .. Result 5
M5-M9 - Memory 1 .. Memory 5 variables
Example
M5=M0-M1*PI
PGraph internal functions:
rf(a,b,n)
- calls Regula Falsi
-- a, b are the lower/upper limit (local variables for rf)
--n can be:
-- 0 - works with f(x) - means search intersection between f(x) and X -
Axis
-- 1 - works with g(x) - means search intersection between g(x) and X -
Axis
-- 2 - works with f(x)-g(x) - means search intersection between f(x)
and g(x)
returns the found x coordinate or 0 if nothing found
Example:
x=rf(0,1,0)
- searches for intersection from f(x) and X-axis
from 0 till 1
simpson(n)
- calls the Numerical integration
-- n has the same meaning as by rf(a,b,n) - "0" - works with f(x) -
area under f(x), "2" g(x), etc.
-- the variables a & b (global) must have the needed values
before
you call this function.
-- returns the Surface under the function / between functions in the M0
variable
Usage:
a=-1
b=1
simpson(1) --calculates the area
between g(x) and the X-Axis
volumen(n)
-- n has the same meaning as by rf(a,b,n)
-- the variables a & b (global) must have the needed values
before
you call this function.
-- returns the Volume of Rotation body in the M0 variable
schwerk(n) - Point of gravity
of Curve
-- n has the same meaning as by rf(a,b,n)
-- the variables a & b (global) must have the needed values
before
you call this function.
-- returns - returns the Point of gravity of Curve as follows
-- M0 - Length
-- M1 - Xs*Lenght
-- M2 - Ys*Lenght
-- M3=M1/M0 -Xs
-- M4=M2/M0 -Ys
schwerf(n) - Point of gravity
of Area
-- n has the same meaning as by rf(a,b,n)
-- the variables a & b (global) must have the needed values
before
you call this function.
-- returns the Point of gravity of Area as follows
-- M0 - Area
-- M1 - Xs*Area
-- M2 - Ys*Area
-- M3=M1/M0 -Xs
-- M4=M2/M0 -Ys
schwerb(n)
- Point of gravity of Body
-- n has the same meaning as by rf(a,b,n)
-- the variables a & b (global) must have the needed values
before
you call this function.
-- returns the Point of gravity of Body as follows
-- M0 - Xs
-- M1 - Volume
-- (Ys=Zs=0)
momentf(n)
- Moment of Inertia of Area
-- n has the same meaning as by rf(a,b,n)
-- the variables a & b (global) must have the needed values
before
you call this function.
-- returns the Moment of Inertia of Area as follows:
-- M0 - Ix
-- M1 - Iy
-- M2 =M1+M0 - Ip
momentb(n)- Moment of Inertia of
Body
-- n has the same meaning as by rf(a,b,n)
-- the variables a & b (global) must have the needed values
before
you call this function.
-- returns the Moment of Inertia of Body as follows:
-- M0 - Jx
wurzabl(n)
- returns the numerical solution of the integral from
sqrt(1-f'(x))
wurzabla(n)
- returns the numerical solution of the integral
from f(x)*sqrt(1-f'(x))
wurzablb(n)
- returns the numerical solution of the integral
from x*sqrt(1-f'(x))
-- n has the same meaning as by rf(a,b,n)
-- the variables a & b (global) must have the needed values
before
you call this function.
-- these are used in the calculating of Curvelenght and Lateral surface
Usage:
var=wurzabl(1)
--integral from sqrt(1-f'(x))
var=wurzabla(2)
--integral from g'(x)*sqrt(1-g'(x))
Plua functions:
palert("TEXT")
-- displays small window with "TEXT" and OK Button, you can use numbers
instead of text
var=pinput("text",
initial_value)
-- displays input field, var becomes the value inputed or NIL if Cancel
was pressed
Sample macro:
-- shows the calculated point of gravity of Curve or Area
-- before startting the macro you should have an Curve/Area defined and
run "Point of gravity" option in the menu
-- the values are then in the M3 and M4, for Xs and Ys respektivelly
pcolor(prgb(245,45,178))
-- set color to have 245 for Red , 45 for Green and 178 for Blue
component.
pline(0, yc-M4*yf, 320*fkr,
yc-M4*yf)
pline(xc+M3*xf,320*fkr,xc+M3*xf)
-- this draws two lines with color as defined, directly trough the
calculated Point of gravity
For better / further information please take a look in the very well
documented Lua / Plua projects (simply type Lua or Plua at google...).
-
About PGraph - ... ;-)
For improvement suggestions, bug reports etc. etchekov@yahoo.de
LICENSE:
PGraph is Freeware.
PGraph is called in the following software.
LIMITED WARRANTY:
THIS SOFTWARE IS PROVIDED 'AS-IS' AND WITHOUT WARRANTY OF ANY KIND,
EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES
WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT
ADVISED OF THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY,
ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
SOFTWARE, EXCEPT TO THE EXTENT OF ANY UNAVOIDABLE STATUTARY LIABILITY.
USE AND DISTRIBUTION OF THIS SOFTWARE IS FREE:
YOU ARE HEREBY LICENSED TO MAKE AS MANY COPIES OF THIS SOFTWARE AS YOU
WISH; GIVE EXACT COPIES OF THE ORIGINAL VERSION TO ANYONE; AND
DISTRIBUTE IN ITS UNMODIFIED FORM VIA ELECTRONIC MEANS. THERE IS NO
CHARGE FOR ANY OF THE ABOVE. YOU ARE
AUTHORIZED TO FREELY USE THIS SOFTWARE.
Copyright (C) 2004 Emil
Tchekov. All rights reserved.
PGraph uses
two approximation methods which I will try
to
describe. For deep-going information, please look into all good
mathematics books. This text serves only
as extension for the PGraph operating instructions, other purposes are
not intended.
The so
called "Wrong rule" (or Secant Method) is a
procedure for determination of intersections
(Method for solving equations).
We look for
the x - value, that makes F(x) to 0
(intersection of F(x) and the x
- Axis). F(x) is replaced by the secant, so the
formula:
supplies us an approximate value (the intersection of the
secant
with the x axis).
If we repeat this procedures often enough with values x1 and x3 or x2
and x3 (PGraph
makes this 1000 times, or until F(x1)=F(x2))- we will become an Value
that is very
close to the real one . The approximation is sufficient for ordinary
purposes, mathematical is it however
NOT correct. These procedure
functions only if some basic conditions are given - for further
information please look
into the appropriate books.
PGraph example: We look for the 1. solution of the equation
sin(x)=1/x-1. So we
input for f(x) sin(deg(x)) and for g(x) 1/x-1. First we want to take a
look over
these Functions, then we should click somewhat left from the 1.
Intersection (the 1.
Solution) and take the value (about 0.5...) for the lower bound, for
upper limit
you can input 1 (we
can also draw the function one more time, so we were able to click this
time right from the intersection
and receive a value for the upper limit). Then we are so far and can
call Regula Falsi
->
The
procedures for numeric determination of surface
under function (integration) are based on the same basic principle:
The surface must be divided into many strips, finding the surface or
every
single strip, and then sum of all strips.
The Simpson
procedure uses parabola as upper
delimitation of the
stripes (other procedures use straight lines). This supplies better
approximate values.
To define a parabola we needs at least 3 points, also Simpson Method
uses double strips.
First the surface is divided at even number of stripes (PGraph - uses
100), then
find the strip width h. Afterwards the three sums are created (Summe1 =
first + last strips, Summe2 = sum of the odd strips, Summe3 = sum of
the
even strips). Then the last formula is used and we receives a numeric
approximate value for the surface under the function.
Example in PGraph: How
big is the surface between the
functions sqrt(1 x^2) and sqrt(1 x^2)?
First we must shift the functions into the upper quadrants, otherwise
we will get we falsified values (there
is visibly a surface present, but we will become 0). So we must take
1+sqrt(1 x^2) and
1-sqrt(1-x^2) instead. Thus both functions stand above the x axis. It
is easy to recognize that we
have a circle with r=1, so the lower limit is -1, upper limit is 1, the
surface is equal to a natural constant - ...
p.
All further
abilities of PGraph, which are based on
integration, develop on the Simpson procedure.
Marcio Miguelleto de Andrade - for the development of PLua
TeCeGraf and PUC Rio - for the development of Lua
My wife and my children for their PATIENCE with my additional job.