Isometric coordinate system and Ein-Stein-Tile
f(x,y), I(u,v) - Isometric Coordinate System
XGrid - Vertices in ICS
XGrid={(0,0), (1,-1), (1,-3/2), (2,-2), (5/2,-3), (2,-3), (3/2,-5/2), (1,-3), (0,-5/2), (0,-2), (-1/2,-3/2), (0,-1), (-1/2,0)}
YGrid - Reflected vertices in ICS
YGrid={(0,0), (-1,1), (-3/2,1), (-2,2), (-3,5/2), (-3,2), (-5/2,3/2), (-3,1), (-5/2,0), (-2,0), (-3/2,-1/2), (-1,0), (0,-1/2)}
XFig, YFig - Vertices in Cartesian Coordinates
D + reflected vertices rotate angle 210°
Fig_D=Polygon(D + Rotate(YFig, 210°))
Make a positiv form Pos2 and a negtive form Neg1 Isometric Coordinate System
Abzählen der Koordinaten I(2,-4), I(1.5,-3)
CAS Input
I(u,v):=u (cos(30°), sin(30°)) + v (cos(-30°), sin(-30°))
pos:={(0,0), I(4, -2), I(2, -4), I(1.5, -3), I(0.5, -2.5), I(0, -1.5), I(0.5, -1)}
neg:={(0,0), I(4, -2), I(2, -4), I(1.5, -3), I(2, -2.5), I(1.5, -1.5), I(0.5, -1)}
Construction of Polygons with move points Pos2/Neg1
Polygon(Pos2 + pos)
Polygon(Neg1 + neg)
Polygon(Nev2 + neg (-1))
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AlgebraView
f(u,v)=Surface(u (cos(30°), sin(30°)) + v (cos(-30°), sin(-30°)), u, -10, 10, v, -10, 10)
f - KO grid u,v ∈ [-10,10]
posf:={(0,0), f(4, -2), f(2, -4), f(1.5, -3), f(0.5, -2.5), f(0, -1.5), f(0.5, -1)}
vertices/Eckpunkte der Figur
Rotate 180°: pos*(-1), neg*(-1)
Rotate 90°: ApplyMatrix({{1, 0}, {0, -1}}, neg)
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www.geogebra.org/calculator