There are three kinds of lies: lies, damned lies, and statistics. -- Benjamin Disraeli (1804-1881), British politician


  * [[Livre]] http://rzr.online.fr/isbn/2746500329

===== THEORY =====

  * http://tfpsly.planet-d.net/Docs/3dIca/3dica.htm
  * http://www.geocities.com/SiliconValley/Park/9784/tut.html#math
  * http://en.wikipedia.org/wiki/Mathematics
  * http://mathworld.wolfram.com/
  * http://www.geocities.com/siliconvalley/2151/math3d.html
  * http://www.usenet-fr.net/fr.usenet.reponses/maths/maths-faq.html

Alt to KalmanFilter :

  * http://en.wikipedia.org/wiki/Linear-quadratic_regulator
  * http://en.wikipedia.org/wiki/Model_predictive_control#
  * http://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/#




====== [[Software]] ======

http://www.math.com/students/calculators/source/scientific.htm [[WebService]] ?

  * http://maxima.sourceforge.net/ [[ToDo]]

Mathematica
http://www.wolfram.com/

Maple
http://www.maplesoft.com/

GNU MP
http://www.swox.com/gmp/

Scilab
http://www.scilab.org/

MathLab
mathworks ?



==== [[Programming]] ====

  * http://www.thefreecountry.com/sourcecode/mathematics.shtml
  * http://en.wikipedia.org/wiki/Machine_epsilon


==== TRIGONOMETRY ====

  sin = Op / Hyp

  cos = Adj / Hyp

  tan = Op / Adj

Quaternions @ http://en.wikipedia.org/wiki/Quaternion

http://skal.planet-d.net/demo/matrixfaq.htm

Trigo : http://science.slashdot.org/article.pl?sid=05/09/17/1313249&from=rss


[[Java]]http://mrl.nyu.edu/~perlin/courses/fall97/improv-docs/improv.util.Quaternion.html

Rotation :
  * Vector + angle { x y z a }
  * Quaterion : { sin(a/2)* x , sin(a/2) * y , sin(a/2) * z , cos(a/2) }

==== LINEAR ALEBRA ====

norm :

  |AB| = sqrt( X^2 + Y^2 + Z^2 )

dot product (scalar) with a '.' :

  A . B = |A| * |B| * cos(A,B)
        = Ax*Bx + Ay*By + Az*Bz

props:

  X . Y = Y . X  # commutative
  ( a * X ) . Y  =  a * ( X . Y ) # associative
  X . ( Y + Z ) = ( X . Y ) + ( Y . Z ) # distributive


cross product (vect) with a 'x' : (result is called normal)

  A x B = ( Ay*Bz-By*Az , Az*Bx-Bz*Ax , Ax*By-Bx*Ay )

  | A x B | = |A| * |B| * sin(a,b)  (which is the area of the paralellogram)

props:

  A x A = 0
  A x B = -(B x A),
  r being a constant, (r * A) x B = r * ( A x B )
  A x (B + C) = A x B + A x C,
  ( A x B = C ) and respectively ( C x A = B ) and ( B x C = A )

==== APPLICATIONS ====

angle (A,B) :

  acos ( A.B / |A|*|B| )
  asin ( |AxB| / |A|*|B| )

normal:

  A x B is the normal of the 2 vectors (2 rights angles)
  order must be be anticlockwise for a (right hand direction)


projection: (of unit vectors)

  A'  = A projected on B = (A . B) * B

distance:

  within a Point P and a Unit Vector D staring in O :
  d = D x ( P - O  ) # check it
   = sqrt (
   ( Dy * ( Pz - Oz ) - Dz * ( Py - Oy ) )^2
  + ( Dz * ( Px - Ox ) - Dx * ( Pz - Oz ) )^2
  + ( Dx * ( Py - Oy ) - Dy x ( Px - Ox ) )^2
  )
  if we are in a 2D world :
  d = abs ( Dx * ( Py - Oy ) - Dy x ( Px - Ox ) )


=== OBJECTS ===

line:

  P = O + l * D

  # l is the parametric factor & O origin
  # D may be any vector including unit one or (M-O), M is anywhere on line

plane:

  define it by ( O & N  ) or ( N & k )
  N . P  = k # k is constant and N normal of plane
  ( Nx * Px ) + ( Ny * Py ) + ( Nz * Pz ) - k = 0

sphere :

  | P - C | = r # C is Center and r radius

distance point to plane : ( O is a Point of Plane)
  d = ( ( N . P ) - ( O . N ) ) / norm(N) # check it
   = N . ( P - O ) / norm(N)  # check it

intesection : line & plane

  [[ P.N = k
  [[ P = O + l * D

  l = ( k - ( O . N ) ) /  ( D . N )


intersection : plane & plane & plane

  [[ P.N1 = k1
  [[ P.N2 = k2
  [[ P.N3 = k3
  TODO, see matrix & inv mtx

intersection : plane & plane

  [[ P.N1 = k1
  [[ P.N2 = k2

intersection : line & sphere

  [[ P = O + l * D
  [[ | P - C | = r

  TODO , see quadratic


==== ROTATIONS MATRIX ====

around X :

  x' =   x
  y' =   (cos a * y) - (sin a * z)
  z' =   (sin a * y) + (cos a * z)

around Y :

  x' =   (cos a * x) + (sin a * z)
  y' =   y
  z' = - (sin a * x) + (cos a * z)

around Z :

  x' =   (cos a * x) - (sin a * y)
  y' =   (sin a * x) + (cos a * y)
  z' =   z


==== MATHS ====

question : comment determiner (n) a partir de (x)  sachant que :
  2^(n-1) < x << 2^n ?

  (n-1) log 2 < log x << n log 2
  (n-1) < log x/log 2 << n

  double n = log ( x  ) * 1. / log (2.) ;
  if ( n - ( (double) (int) n) ) n++;
  int m = 1<<(int) n;

Another solution is to use bitmask :

  1/ o = count '1' bits
  2/ if o = 1 return o's bit position
  3/ else shift right
  4/ return 1st '1' bit'position from left


===== MISC =====

  * http://gersoo.free.fr/calsci/calsci1.html
  * http://www2.hursley.ibm.com/decimal/decifaq.html
  * http://sympy.org/
  * http://sat.qc.ca/fr/chaos# ArT


===== MORE =====

@TaG: [[Science]] [[MathsSoftware]] [[Algebra]] [[Matrix]] [[fractal]]


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