2006-11-11-21-00 (9511112100)
There are many program draw math curves.
These programs can not be used in web page.
Web site use web page to display message.

The special point of this program
http://freeman2.com/graph09c.htm
is that it draw math curve in web page.
If author use graph09c.htm structure to
write web page, allow visitor to modify
equation coefficients, allow visitor to
bend curves. In this way, your web page
is more attractive to your visitor.

If write home work, or write report, it
has nothing to do with internet visitor,
in this case you can use expert program
to draw curves.

If you write web page for your visitor,
you need to use Javascript code to draw
curves.

Expert program draw faster, and better
quality. But expert program can not be 
used on web page.

Javascript code to draw curves, it can
be used in web page, it can be used in
any platform.
Javascript code to draw curves which is
slow. Simple curve can use graph09c.htm
interface. But complicate curve, you
must write Javascript code.

If write home work, or write report, 
do not use graph09c.htm. There are many
program run faster than Javascript based
graph09c.htm.

If you write web page for your visitor,
suggest reader keep this program graph09e.htm 
2006-11-11-21-18

95,06,13,23,44
Javascript support the following math functions
[[
Math.E 2.718281828459045091 Euler's constant
Math.LN2 0.6931471805599452862 Natural log of 2
Math.LN10 2.302585092994045901 Natural log of 10
Math.LOG2E 1.442695040888963387 Log base-2 of E
Math.LOG10E 0.4342944819032518167 Log base-10 of E
Math.PI 3.141592653589793116  PI
Math.SQRT1_2 0.7071067811865475 Square root of 0.5
Math.SQRT2 1.414213562373095145 Square root of 2
Math.random() method takes no parameters
Math.abs(val) Absolute value of val
Math.acos(val) Arc cosine (in radians) of val
Math.asin(val) Arc sine (in radians) of val
Math.atan(val) Arc tangent (in radians) of val
Math.atan2(val1, val2) Angle of polar coordinates
Math.ceil(val) Next integer greater than or equal
Math.cos(val) Cosine of val
Math.exp(val) Euler's constant to the power of val
Math.floor(val) Next integer less than or equal to
Math.log(val) Natural logarithm (base e) of val
Math.max(val1, val2) The greater of val1 or val2
Math.min(val1, val2) The lesser of val1 or val2
Math.pow(val1, val2) Val1 to the val2 power
Math.random() Random number between 0 and 1
Math.round(val) N+1 when val >= n.5; otherwise N
Math.sin(val) Sine (in radians) of val
Math.sqrt(val) Square root of val
Math.tan(val) Tangent (in radians) of val
]]

for 
hyperbolic cosine, use
0.5*(Math.exp(x)+Math.exp(-x))

hyperbolic sine, use
0.5*(Math.exp(x)-Math.exp(-x))


Step function: stepf(a,b)
If a<b return 0 (close)
otherwise return 1 (open)
Any number multiply by 0 get 0
that is to close.
Any number multiply by 1 get itself
that is to open.
Above is to multiply stepf()
If add or subtract stepf() then it
is shift curve up/down.
One of a,b must be variable. If
both a and b are constant, then
stepf() has no meaning. 9507211227


Gamma function  gamma(t)
If t is an integer gamma(t) is (t-1)!
gamma(t) let factorial become
continuous.
gamma(t) is searched from Internet.
9507211232




2006-06-23-12-41 start
This program is received on 2006-06-12

2006-06-12-18-14
http://www.bigwebmaster.com/3051.html

2006-06-12-18-21
http://www.structura.info/XYGraph/XYGraph.zip

=====

2006-10-23-09-08 start
Start from 2006-10-17 write this program.
Its URL is
http://freeman2.com/graph09e.htm
This file has same source as previous
http://freeman2.com/graph03e.htm
Both from XYGraph v2.3
http://www.structura.info/XYGraph/XYGraphDemo.htm
Freeman take their source code write a
better version.
graph03e.htm is mainly introduction
        All graph use one drawing board.
graph09e.htm is for application. Each
        graph has its own drawing board.
"has its own drawing board" is Freeman's
need. This function allow user to draw
multiple graph in one web page. Now
upload this program to Internet let
everyone use. Please click "Draw 606"
to see how to use.

graph09e.htm can dynamically create input
form and also one more change

graph03e.htm must use "Math.cos(t)"
          Where "Math." can not drop.
graph09e.htm allow to use cos(t)
          "Math." can be dropped.
Because graph09e.htm add 
[[
9510222211 use 'with(Math){' and '}'
]]
graph03e.htm follow XYGraph v2.3
             must use "Math."
graph09e.htm modified by Freeman
             no need to use "Math."

graph09e.htm still has limitation.
Curve allow maximum 5.
Arrow allow maximum 1.
Label allow maximum 1.
Equation can not be modified
Especially equation constant and 
number of terms.

graph03e.htm allow variable constant
             'a', 'b' to have five
             different values. (one
             equation family five
             members)
graph09e.htm broader this property to
             five arbitrary functions.

If you need function exceed above 
limitation, you must write code for it.
Examples can be found at
http://freeman2.com/graph03e.htm
find function Calculate0(PlotID){.....}
five examples.

Expect graph09e.htm will be used in
http://freeman2.com/tutc0004.htm
This is Freeman's tutor page in Chinese.

Welcome visit Freeman site often.
Freeman 2006-10-24-18-01

=====

9510242029
Out side of table [Draw 601] button
and inside of table [Draw] button
are different. They both draw curve,
but
[Draw 601] button create input form
     NOT open input form. carry out
     plot curve, then close form to
     save system resources.
[Draw] button NOT create input form
     because already exist. Carry 
     out plot curve, then let form
     remain open.

Out side of table [Wipe 601] button
     delete both graph and input form.
Inside of table [Wipe] button delete
     graph only.
9510242039

9510251736
If you want drop arrow temporary.
click "delArrow" delete ALL arrow
data, then no arrow drawn. But
if you want to reuse arrow, you 
have to fill back all arrow data.
If you clear "arrow x" box, then
no arrow drawn, reuse arrow is
much simpler. All data (but one)
are in place.

Clear "label x" box is same for
label.
9510251740


9510281051
2006-10-28-10-51 start

One caution:
If you input

function 1 x(t) [ sin(x) ]

this equation look like

x(t) = sin(x)

This is confuse, because left hand side
independent variable is 't' [x(t)]
right hand side independent variable is
x [sin(x)]
This different variable 'equation' has
no meaning.

graph09e.htm use 't' as independent 
variable. In many case x=t identically
graph09e.htm convert 'x' to 't' let
user free to use y(x) = 2*sin(x+3.14)

Please be understand that
x(t) = sin(x)
has no meaning,

and
x = sin(x)
is to find solution, NOT to plot curve.

To find solution of
x = sin(x)
please construct

x(t) = t
y(t) = t
and
x(t) = t
y(t) = sin(t)

input the following

function 1 x(t) t
function 1 y(t) t
function 2 x(t) t
function 2 y(t) sin(t)

One point is common to both red and
blue lines, that is solution at (0,0)

*** Please use 't' as independent
*** variable
*** 'x' behave as if it were 't'
*** side effect
*** x(t) = sin(x)
*** has no meaning.

2006-10-28-11-05 stop
9510281105

<!-- Begin 606  Begin 606  Begin 606 
2006-10-22-22-30
Please copy above code about 16 lines
change all 601 to 606

This is just to create user interface.
An input form. All boxes value must
copy from a default data bank. As an
author (you), you need define curve
equations and line properties and
arrow/label etc. Please find key
string
if(eqnID==601)
{
.....
}
Read what it does there (about 130 lines)
then create your own
else
if(eqnID==606)
{
.....
}
If smooth, you can create your drawing
quickly.

User can change value in input form
easily. User can not easily change 
value in data bank, unless he open
source code. If user modified and
want to return to original problem
He can click "Reuse default" to
recover data. This design let your
visitor change easily and recover
default easily.

Before you modify this program,
please make a back up copy first.
In case modify wrong, you still
have one working copy.
2006-10-22-22-51

2006-10-24-08-12
** Must use    else if(eqnID==606){.....}
** Can NOT use      if(eqnID==606){.....}
** can not drop "else" otherwise first
** few curve fall to last no-if
** else{.....} and get unexpected result.
2006-10-24-08-17
<!-- End 606  End 606  End 606 -->

2006-11-09-06-42 start
If your equation can not draw, there are
two possibilities.

First: program code can not take care special
       case. Need to modify code. Most user
       do not know how to modify code. You
       can only wait for update version.
       If you know how to code, you can debug
       the code.

Second: Improper input data
       Freeman experience the next three cases

       2A sqrt(t-sin(t)) can draw
          sqrt(t-sin(t)  can not draw
          because missing one ')'.

       2B Freeman visited the following page
          [[
            2006-11-08-20-45-11
            http://163.32.131.20/samax/instpage.php?r=&w=100%25&h=800&url=163.32.131.200/math/form.php
            Title: Praise for answer (in Chinese)
            Author Samax 
            Question 573*x*x+11*x−584=0 find X = ?
          ]]
          Freeman copy equation from screen
          573*x*x+11*x−584 can not draw
          573*x*x+11*x-584  can draw
          Because the problem equation use Unicode '−'
          instead of regular '-'.

       2C function 1 x(t)  100*cos(t)
          function 1 y(t)  100*sin(t)
          can not draw
          Because the radius is 100, but drawing
          board range define to be from -10 to +10
          in both x and y axis.
          Goto the bottom of input form find
          min X    max X    min Y    max Y 
          assign range -100 to +100 for both
          x and y axis, then solve problem.
2006-11-09-07-07 stop