[size=85]A system of points on a sphere S of radius R “induces” on the sphere S[sub]0[/sub] of radius R[sub]0[/sub] three different sets of points, which are [color=#93c47d]geometric medians (GM)[/color] -local [color=#ff0000]maxima[/color], [color=#6d9eeb]minima[/color] and [color=#38761d]saddle[/color] points sum of distance function f(x). The angular coordinates of the spherical distribution of a system of points -[color=#0000ff] local minima[/color] coincide with the original system of points.[/size]
[color=#333333]Distribution of points Pi[/color][color=#ff0000], [color=#5b0f00]test Point[/color], [color=#ff0000]Max[/color]/[color=#0000ff]min[/color]/[color=#38761d]saddle[/color] -[color=#333333]Critical points[/color] on a sphere. Vectors ∇f and ∇g at these points.[br]max:[/color] n=14 [color=#0000ff]min:[/color] n=12 [color=#6aa84f]sad:[/color] n=24
[size=85]Two-variable function f(φ,θ) over a rectangular region: - π ≤φ ≤ π; -π/2≤θ≤π/2.[/size]
[size=85]Isolines and Intersection points of implicit functions over a rectangular region: - π ≤φ ≤ π; -π/2≤θ≤π/2.[/size]
[size=85]Critial Points, Intersections[/size]
[size=85]a,b,c Typen Rhombicuboctahedron[/size]
