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V=20 Dodecahedron. Images: A critical points scheme for Generating uniformly distributed points on a sphere
Auteur:
Roman Chijner
Onderwerp:
Algebra
,
Analyse
,
Cirkel
,
Verschil en helling
,
Differentiaalrekenen
,
Differentiaalvergelijking
,
Vergelijkingen
,
Optimalisatieproblemen
,
Meetkunde
,
Grafiek
,
Snijpunt
,
Wiskunde
,
Bol
,
Oppervlak
,
Vectoren
A system of points on a sphere S of radius R “induces” on the sphere S0 of radius R0 three different sets of points, which are
geometric medians (GM)
-local
maxima
,
minima
and
saddle
points sum of distance function f(x). The angular coordinates of the spherical distribution of a system of points -
local minima
coincide with the original system of points.
Distribution of points Pi
,
test Point
,
Max
/
min
/
saddle
-
Critical points
on a sphere. Vectors ∇f and ∇g at these points. max:
Icosahedron
min:
Dodecahedron
sad:
Icosidodecahedron
Distribution of points Pi
,
test Point
,
Max
/
min
/
saddle
-
Critical points
on a sphere. Vectors ∇f and ∇g at these points. max:
Icosahedron
min:
Dodecahedron
sad:
Icosidodecahedron
Two-variable function f(φ,θ) over a rectangular region: - π ≤φ ≤ π; -π/2≤θ≤π/2.
Intersection points of implicit functions over a rectangular region: - π ≤φ ≤ π; -π/2≤θ≤π/2.
Isolines and Intersection points of implicit functions over a rectangular region: - π ≤φ ≤ π; -π/2≤θ≤π/2.
Critical Points
Nieuw didactisch materiaal
apec
Silhouettes
Exploding cube
Nefroida
רישום חופשי
Ontdek materiaal
parallel lines
Rigid Motions: Question 5
rhombus
Triangle Median
Midpoint Spiral
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Wortel
Ellips
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