# index - Homniserv/pointillism Wiki

<title>Pointillism</title>

# Pointillism

V20
Mathematical pointillism
MathML
Visible under Firefox only !
In mathematics field, relative to spots, dots science : included spots constraints Normal metric : x 2 4 x 4 0
``````<apply>
<sqrt/>
<apply>
<plus/>

<apply>
<power/>
<mi>x</mi>
<mn>2</mn>
</apply>

<apply>
<power/>
<mi>y</mi>
<mn>2</mn>
</apply>
</apply>

</apply>

[/itex]
,
<br>
<!--    https://www.w3.org/Math/whatIsMathML.html
``````

d(x,y,z) = x2 +

``````        <msup><mi>y</mi><mn>2</mn></msup>
<mo>+</mo>

<msup><mi>z</mi><mn>2</mn></msup>
</mrow>
</msqrt>

[/itex]
``````

Proposition(
Exhaustive for comprehension
x = d(U,V)*cos(U),y = d(U,V)* sin(U), z = R*sin(((2*pi* d(U,V))/(2*pi*R))*(2*pi))
``````)
<br>
``````

Surface metrics distances (surface integrals, minimal path, geodesics (https://moueza.github.io/geodesics/)):

Constraints on the surface : sphere, donut(tore) + iso-distance

OR-tools, Scilab Scicos
Example 1 : 3 dots iso-distance on sphere gives a triangle
Example 2 : known a cone equation, find equilateral triangle whose (max za - min zc) > 10 for instance

or .........................................................whose a=(xa,ya,za)
Example 3 : known 5 locations on Earth, find 3 36000 altitude satellites, so that average distance(sum(sum, by satellites of distances)) is minimal
Example 4 : d(x,y)>1 AND d(x,y)<2

Relative to CP i.e. Constraint Programming(Python Google ORtools), graphs, GPS(Earth locations, satellites best spread), CSP and COP

``````  Example 5 : density, chemistry Pauli orbitals distributions
``````

Example 6 : Penrose related : with France frontiers, find gravity point, 100km*100km squares (or less by frontiers) so that number of squares is minimal, or average real polygone surface is max, and so on.

By Peter MOUEZA