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<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>	     
			
  </math>
  , 
<br>
  <!--    https://www.w3.org/Math/whatIsMathML.html 

https://developer.mozilla.org/en-US/docs/Web/MathML/Authoring -->

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>
		
  </math>

Proposition(
R : radius of sphere
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

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