foot of perpendicular eyefoot2.htm

foot of perpendicular Update 2009-02-01
The Cauchy-Schwarz Master Class J. Michael Steele ★★★★★
This file is personal home work. Output
may contain error. Please verify first.
This file has three tools. 1, foot of perpendicular
2, Simple calculator. 3, Dec-Hex-General base converter
Please use MSIE browser to read this page.
This file is programmed with MSIE 6.0

Box 1, store debug information

Box 2, store debug information

Dimension 2 to 12

<a name=make_Line> create simple equation
I have a plane problem (3D problem OK), straight line
go through next two points.

t =	locate at	x component	y component	z component
	First point
	Second pt

Please help me build equation
(For 2D problem, click [del z] button)

foot of perpendicular and in/out interface separate [perpenfoot()].

<a name=eyefootDoc>
foot of perpendicular working record.

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This file is personal home work. Output 
may contain error. Please verify first. 

2009-01-22-19-42 begin
2008-11-03-20-15 click purchase button
2008-11-06-13-11 receive book

The Cauchy-Schwarz Master Class
J. Michael Steele
University of Pennsylvania
ISBN 978-0-521-54677-5 

2008-11-15-10-20 read to page 56, equation 4.5

line x=[x1,x2,x3] pass [0,0,0]
eye-point v=[v1,v2,v3] pass [0,0,0]
point on line x and most close to v is
p(v)=x*<x,v>/<x,x>
in which <a,b> is vector dot product.

There three motivation to write eyefoot2.htm
1. Read eqn. 4.5 find foot of perpendicular of
   one point to a line. Equation is in hand.
2. I need to calculate and find foot of
   perpendicular. example (Chinese page)
http://freeman2.com/tutc0005.htm#a00b20
   (click the button marked '9712022054'
    points 'L' and 'J' are foot of
    perpendicular. I hand calculate at
    that writing time.)
3. Around 2009-01-28 I paid attention that
http://freeman2.com/curve3d2.htm
   has ten examples, but none of them is 
   straight line. Science major reader can
   find straight line equation easily, but
   other reader may have trouble to find
   the easiest straight line equation. I
   need to provide an example. (9801301628)

2009-01-18-21-37 begin write foot of 
perpendicular program. (Chinese version)

This file URL
http://freeman2.com/eyefoot2.htm

File name
'eye' represent point is space. come from
http://freeman2.com/curve3d2.htm
Program use variable vp for eye point.

'v' in 'vp' come from ISBN 978-0-521-54677-5
page 56, equation 4.5, vector v
'p' in 'vp' means 'point'
Although 'vp' no 'eye' in it, but eye point
box use I00, I01. This 'I' means 'eye'.

Straight line equation box name E00; E01; E02 
'E' means 'equation'.

'foot' in eyefoot2.htm means foot of 
perpendicular.

I need to solve 2D problem, page 56, eqn. 4.5
is valid for 3D, 4D ... Use for loop to solve
2D and 3D problem, why not include 4D and higher?
This program set upper limit to 12D. 12D is
an arbitrary limit. 4D already no practical
application chance. 12D is out of reach.
Higher dimension is just for pure math reason.

3D straight line example is next

parametric equation 1: x(t) 3*t+1
parametric equation 2: y(t) t*8.2-2
parametric equation 3: z(t) -t+3.6

In which 't' is independent variable. 't' can
be only zeroth power (constant) or first power.
't' can not be second power. Because t*t is not
a straight line.

Program not allow to put 't' into math function
parametric '(...)' area. Because no math function
is a straight line.

'3' in 3*t+1 represent t change rate relative
to coordinate axis one.
'+1' in 3*t+1 represent parallel displacement
amount. Straight line equation must be
slope*t + constant
Program refuse 3*t*t
Program refuse sin(t)

-1.2-5.0*(t-2) is a reasonable straight line
equation. But this program can not expand
'-5.0*(t-2)' to '-5.0*t' and '+5.0*2'
this program can not handle some reasonable
straight line equation. Need user to cooperate
and use simple equation.

+1.6-4.*t+t*2.2-sin(1.5)  is a reasonable
straight line equation. sin(1.5) is just
a constant. sin(1.5) not contain 't'.
Program accept sin(1.5)

-4.*t+t*2.2 has a little trouble.
-4.*t pre-multiply '-4.'
t*2.2 post-multiply '2.2'.
Found solution for it. Now it is OK.

After done, tested few 2D problem, Output
look ok. If there is trouble equation,
I did not see it and I can not solve it
now. I will make correction in the future.

If you suspect error output. Please read box1
and box2 debug output. Those data will help 
you to locate trouble point.

Thank you for using eyefoot2.htm

Freeman 2009-01-22-20-35
2009-01-30-17-06 translate here.

This file is personal home work. Output 
may contain error. Please verify first. 

2009-01-30-18-29 translate begin
2009-01-24-13-20 begin
2009-01-23-17-52 write "Please help me build equation"

start from 2009-01-23-17-52
to 2009-01-24-09-52 create code help build
straight line equations.
2009-01-23 write 2D equation code
2009-01-24 write 3D equation code

2009-01-24-12-50 include code from
http://freeman2.biz/a1/dx880101.htm
to eyefoot2.htm
Purpose is to calculate the distance between
eye point and foot point. Make sure this
distance is shortest. When user click
"foot of perpendicular" button, program
auto write code to box 3, user click [click here]
button, output to box 4 bottom.
Key point is allow user to change value of
tiny0. 
 tiny0=0.0 should get shortest distance.
 tiny0=0.001 and tiny0=-0.001 get longer one.
2009-01-24-13-31 stop

2009-01-27-18-21 begin
Today, 2009-01-27 write "create simple equation"
add [x=t], [y=t], [z=t] button.

for example button [x=t] create simple line
equation.
y(x)=3*x-5

to simple parametric equation
x=t
y(t)=3*t-5

no need complicate equation.
x(t)= -0.25*t+(0.5)
y(t)= -0.75*t+(-3.5)
2009-01-27-18-29 stop


This file is personal home work. Output 
may contain error. Please verify first. 



2009-02-01-13-46 start
On 2009-02-01-12-10 open
http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/CSMC_index.html
read
[[
Finally, if you have a web page that deals
 with inequalities (or problem solving, or
 mathematical coaching), please add a link
 to this page. I'll happily reciprocate.
 In the era of Google, one lives or dies
 by links. Also, by learning that someone
 actually reads these pages, I'll have more
 incentive to keep scanning and posting more
 classics.
]]
Since this page
http://freeman2.com/eyefoot2.htm
receive equation from Professor J. Michael Steele
book. Professor Steele ask for link, On 2009-02-01
I made a link at top of this page.
2009-02-01-13-53 Stop

2009-02-01-14-23 start
When you check this program, please do NOT
rely upon the output message
[[
foot to eye vector dot with line vector should be zero:
5.329070518200751e-15
]]
Because if this program read line equation
coefficient wrong, then program solve another
problem. Another problem get vectors dot equal
to zero, it has no help.
2009-02-01-14-27 stop

<a name=addProg88>
Below is simple calculator come from dx880101.htm
Next is a simple calculator, input at box 3
click [click here] button. Output to box 4.
Program limitation is
First: one complete command must stay in one line.
for(){...} must stay in one line.
while(){...} must stay in one line.
Second: Line contain '=' not print value.
Line without '=' will print value.
Based upon this property, user can not use [var a0;],
user must use [var a0=0;], or use [var a0='';]
This program can do only small calculation.
Third: Use JavaScript language only. Can not use
other language.
Fourth: Can not insert blank lines.
Box 3 has default simple example code.
Button [example 1] has code which generate
x,y coordinate output and can be used to
plot curve. 9710171257

2008-10-16-21-24
Small calculator

Box 3

Box 4

Box 5

9710202058
Box 3 allow define variable name and assign equation.
Must be care about variable name. For example
 if , while , return are program reserved name.
and sin , cos , abs are math function name.
These name can not be used as variable name.
Better way to do is to add digit to variable name.
For example i0, i1, step0 etc. But in rare case
still get trouble. At this time, change (example)
 a0=12 to ab0=12, change all a0 to ab0 . This
rare error is caused by some elements used a0
as its ID name id=a0 That element can not assign
value.  a0=12 cause error. If use [var a0=12;]
it is possible to solve the problem. This time
a0 is local variable, it has nothing to do with
global a0. But use [var a0;] (no '=0') still
get error message. Because [var a0;] violate
this program eyefoot2.htm's rule. eyefoot2.htm
see one line without '=', then print value.
But [var] in [var a0;] make trouble. And a0 is
undefined. 9710202207

2008-10-16-21-20 begin to write small calculator
2008-10-17-00-29 done
2009-01-30-19-41 translate to here.

Box 6

<a name=9801241945>
2009-01-24-19-45 begin
Freeman consider above small calculator as
a hand-hold scientific calculator.
calculator has many push buttons. Above
simple calculator has just one button
[click here]. User must understand Java
Script language. simple calculator can do
most scientific calculator's job. (But lack
of statistic functions). After get data.
Copy data and paste to Space curve projector
http://freeman2.com/curve3d2.htm
Box 2. Or paste to
http://freeman2.com/graph03e.htm
Box 1. Adjust drawing board size. Let 
drawing board cover all curve. then
click [Draw 2D data] (curve3d2.htm)
click [Draw statistic data] (graph03e.htm)
These function combination can match those
of graphic scientific calculator.
2009-01-24-19-59 Stop
2009-01-30-19-53 break

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9801022039
Java Script Bible
[[
884 Part IV ✦ JavaScript Core Language Reference
Table 28-1: JavaScript Math Properties
Property Value Description
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 π
Math.SQRT1_2 0.7071067811865475727 Square root of 0.5
Math.SQRT2 1.414213562373095145 Square root of 2
Because these property expressions return their constant values, you use them in your regular
arithmetic expressions. For example, to obtain the circumference of a circle whose diameter
is in variable d, employ this statement:
circumference = d * Math.PI;
Perhaps the most common mistakes scripters make with these properties are failing to capitalize
the Math object name and observing the case-sensitivity of property names.
Methods
Methods make up the balance of JavaScript Math object powers. With the exception of the
Math.random() method, all Math object methods take one or more values as parameters.
Typical trigonometric methods operate on the single values passed as parameters; others
determine which of the numbers passed along are the highest or lowest of the group. The
Math.random() method takes no parameters but returns a randomized, floating-point value
between 0 and 1 (note that the method does not work on Windows or Macintosh versions of
Navigator 2). Table 28-2 lists all the Math object methods with their syntax and descriptions
of the values they return.
Table 28-2: Math Object Methods
Method Syntax Returns
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 x and y
Math.ceil(val) Next integer greater than or equal to val
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 val
Math.log(val) Natural logarithm (base e) of val
Math


885 Chapter 28 ✦ The Math, Number, and Boolean Objects
Method Syntax Returns
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
HTML is not exactly a graphic artist’s dream environment, so using trig functions to obtain a
series of values for HTML-generated charting is not a hot JavaScript prospect. Only with the
advent of positionable elements have scripters been able to apply their knowledge of using
these functions to define fancy trajectories for flying elements. For scripters who are not
trained in programming, math is often a major stumbling block. But as you’ve seen so far, you
can accomplish a great deal with JavaScript by using simple arithmetic and a little bit of
logic—leaving the heavy-duty math for those who love it.
Creating random numbers
The Math.random() method returns a floating-point value between 0 and 1. If you design a
script to act like a card game, you need random integers between 1 and 52; for dice, the range
is 1 to 6 per die. To generate a random integer between zero and any top value, use the following
formula:
Math.floor(Math.random() * n)
Here, n is the top number. To generate random numbers between a different range, use this
formula:
Math.floor(Math.random() * (n – m + 1)) + m
Here, m is the lowest possible integer value of the range and n equals the top number of the
range. For the dice game, the formula for each die is
newDieValue = Math.floor(Math.random() * 6) + 1;
Math object shortcut
In Chapter 31, you see details about a JavaScript construction that enables you to simplify
the way you address multiple Math object properties and methods in statements. The trick is
to use the with statement.
In a nutshell, the with statement tells JavaScript that the next group of statements (inside the
braces) refers to a particular object. In the case of the Math object, the basic construction
looks like this:
with (Math) {
//statements
}
Math

886 Part IV ✦ JavaScript Core Language Reference
For all intervening statements, you can omit the specific references to the Math object.
Compare the long reference way of calculating the area of a circle (with a radius of six units)
result = Math.pow(6,2) * Math.PI;
to the shortcut reference way:
with (Math) {
result = pow(6,2) * PI;
}
Though the latter occupies more lines of code, the object references are shorter and more
natural when reading the code. For a longer series of calculations involving Math object properties
and methods, the with construction saves keystrokes and reduces the likelihood of a
case-sensitive mistake with the object name in a reference. You can also include other fullobject
references within the with construction; JavaScript attempts to attach the object
name only to those references lacking an object name. On the downside, the with construction
is not particularly efficient in JavaScript because it must perform a lot of internal tracking
in order to work.

]]


hyperbolic cosine use
0.5*(exp(x)+exp(-x))

hyperbolic sine use
0.5*(exp(x)-exp(-x))
 9507211232



2009-01-31-09-55
This file eyefoot2.htm has Gamma function
y(t)=gamma(t)
and has step function
y(t) = 
-3.097*stepf(t,-2)*(1-stepf(t,2))*sin(t)+stepf(t,2)*(1-stepf(t,5))*exp(-(t-PI))*sin(t-PI)+stepf(t,5)*(1-stepf(t,8))*(t*t*t/108.75-1)
2009-01-31-09-56

<a name=addProg92>
Below is general-base and ten-base (decimal) convert program. Take from dx920101.htm
General base: 2 to 36 ; frequently used base:2,8,10,16

Java Script program index
http://freeman2.com/jsindex2.htm

foot of perpendicular eyefoot2.htm
is created on 2009-01-28-15-29
First upload 2009-01-31

URL of this page is
http://freeman2.com/eyefoot2.htm
Chinese version is
http://freeman2.com/eyefoot1.htm

Thank you for visiting Freeman's page
Freeman
2009-01-28-15-33