Izometrijska preslikavanja ravnine
Author: Petar Piljić

Pika S është qendër e rrotacionit

Pika S është qendër e simterisë qendrore

 \vek{v } 

Vektor \, \vek{ v } \,\,është  \,\,vektor \,\,translacioni.

Drejtëza k është bosht i simetrisë

=SIMETRIJA QENDRORE

= SIMETRIJA BOSHTORE

=ROTACIONI

=TRANSLACIONI

Zgjidh_{Pasqyrimin} = 1 (slider from 1 to 4, step 1)
Numri_{pikave} = 1 (slider from 1 to 6, step 1)
A = (-0.4227350141656134, 1.5431430612850836)
S = (-2.5212529964011936, 1.0742702981603887)
b = Segment(A, Intersect[Circle[S, Distance[A, S] + 0.5], Ray[A, S]])
Hapi_{SQ} = 0 (slider from 0 to 3, step 1)
A' = Mirror(A, S)
B = (1.737178156127274, 3.7634469015603234)
d = Segment(B, Intersect[Circle[S, Distance[B, S] + 0.5], Ray[B, S]])
B' = Mirror(B, S)
e = Segment(A, B)
f = Segment(B', A')
C = (3.927715176066329, 3.5254618207272297)
g = Segment(C, Intersect[Circle[S, Distance[C, S] + 0.5], Ray[C, S]])
poly1, b_1, a_1, c_1 = Polygon(A, C, B)
C' = Mirror(C, S)
poly2, a', c', b' = Polygon(C', B', A')
D = (3.3472021193582897, 1.4281914854087088)
h = Segment(D, Intersect[Circle[S, Distance[D, S] + 0.5], Ray[D, S]])
poly3, a_2, b_2, c_2, d_1 = Polygon(A, B, C, D)
D' = Mirror(D, S)
poly4, a'_1, d', c'_1, b'_1 = Polygon(A', D', C', B')
E = (2.16, 0.32)
poly5, a_3, b_3, c_3, d_2, e_1 = Polygon(A, B, C, D, E)
i = Segment(E, Intersect[Circle[S, Distance[E, S] + 0.5], Ray[E, S]])
E' = Mirror(E, S)
poly6, d'_1, c'_2, b'_2, a'_2, e' = Polygon(D', C', B', A', E')
F = (0.1927272727272726, 0.48000000000000165)
poly7, a_4, b_4, c_4, d_3, e_2, f_1 = Polygon(A, B, C, D, E, F)
j = Segment(F, Intersect[Circle[S, Distance[F, S] + 0.5], Ray[F, S]])
F' = Mirror(F, S)
poly8, d'_2, e'_1, f', a'_3, b'_3, c'_3 = Polygon(D', E', F', A', B', C')
F_3 = (1.2138959903673263, 5.830749085998426)
G = (-3.4842210945524528, -1.581187184620356)
k = Line(F_3, G)
l = Segment(A, Intersect[Circle[Intersect[OrthogonalLine[A, k], k], Distance[A, k] + 0.5], Ray[A, Intersect[OrthogonalLine[A, k], k]]])
Hapi_{SB} = 0 (slider from 0 to 3, step 1)
p = Segment(B, Intersect[Circle[Intersect[OrthogonalLine[B, k], k], Distance[B, k] + 0.5], Ray[B, Intersect[OrthogonalLine[B, k], k]]])
q = Segment(C, Intersect[Circle[Intersect[OrthogonalLine[C, k], k], Distance[C, k] + 0.5], Ray[C, Intersect[OrthogonalLine[C, k], k]]])
r = Segment(D, Intersect[Circle[Intersect[OrthogonalLine[D, k], k], Distance[D, k] + 0.5], Ray[D, Intersect[OrthogonalLine[D, k], k]]])
s = Segment(E, Intersect[Circle[Intersect[OrthogonalLine[E, k], k], Distance[E, k] + 0.5], Ray[E, Intersect[OrthogonalLine[E, k], k]]])
t = Segment(F, Intersect[Circle[Intersect[OrthogonalLine[F, k], k], Distance[F, k] + 0.5], Ray[F, Intersect[OrthogonalLine[F, k], k]]])
A_1 = Mirror(A, k)
α = Angle(l, k)
β = Angle(k, p)
B_1 = Mirror(B, k)
a1 = Segment(A_1, B_1)
γ = Angle(q, k)
C_1 = Mirror(C, k)
poly9, c_5, a_5, b_5 = Polygon(A_1, B_1, C_1)
δ = Angle(r, k)
D_1 = Mirror(D, k)
poly10, a_6, b_6, c_6, d_4 = Polygon(A_1, B_1, C_1, D_1)
ε = Angle(s, k)
E_1 = Mirror(E, k)
poly11, a_7, b_7, c_7, d_5, e_3 = Polygon(A_1, B_1, C_1, D_1, E_1)
ζ = Angle(t, k)
F_1 = Mirror(F, k)
poly12, f_2, a_8, b_8, c_8, d_6, e_4 = Polygon(F_1, A_1, B_1, C_1, D_1, E_1)
H = (-1.4497391465037694, -1.3193487856899415)
I = (-6.139678577333198, 1.8037915846386146)
u = Vector(H, I)
Hapi_{TRAN} = 0 (slider from 0 to 3, step 1)
b1 = Segment(A, Intersect[Circle[A, Distance[H, I] + 0.5], Ray[A, u]])
A'' = Translate(A, u)
c1 = Segment(B, Intersect[Circle[B, Distance[H, I] + 0.5], Ray[B, u]])
d1 = Segment(C, Intersect[Circle[C, Distance[H, I] + 0.5], Ray[C, u]])
e1 = Segment(D, Intersect[Circle[D, Distance[H, I] + 0.5], Ray[D, u]])
f1 = Segment(E, Intersect[Circle[E, Distance[H, I] + 0.5], Ray[E, u]])
g1 = Segment(F, Intersect[Circle[F, Distance[H, I] + 0.5], Ray[F, u]])
B'' = Translate(B, u)
h1 = Segment(A'', B'')
C'' = Translate(C, u)
poly13, b'', a'', c'' = Polygon(A'', C'', B'')
D'' = Translate(D, u)
E'' = Translate(E, u)
F'' = Translate(F, u)
poly14, a''_1, d'', c''_1, b''_1 = Polygon(A'', D'', C'', B'')
poly15, a''_2, e'', d''_1, c''_2, b''_2 = Polygon(A'', E'', D'', C'', B'')
poly16, f'', e''_1, d''_2, c''_3, b''_3, a''_3 = Polygon(F'', E'', D'', C'', B'', A'')
Hapi_{ROT} = 0 (slider from 0 to 5, step 1)
Kend_{ROT} = 3.961897402027128 rad (slider from 0 to 6.283167853887067, step 0.017453292519943295)
i1 = Segment(A, S)
k1 = CircleArc(S, A, Rotate[A, Kend_{ROT} + 5°, S])
j1 = Segment(S, Rotate[A, Kend_{ROT}, S])
A_2 = Rotate(A, Kend_{ROT}, S)
θ = Angle(A, S, A_2)
p1 = CircleArc(S, B, Rotate[B, Kend_{ROT} + 5°, S])
l1 = Segment(S, B)
B_2 = Rotate(B, Kend_{ROT}, S)
m1 = Segment(B_2, S)
n1 = Segment(B_2, A_2)
q1 = CircleArc(S, C, Rotate[C, Kend_{ROT} + 5°, S])
r1 = Segment(C, S)
C_2 = Rotate(C, Kend_{ROT}, S)
s1 = Segment(C_2, S)
poly17, b_9, a_9, c_9 = Polygon(A_2, C_2, B_2)
t1 = Segment(D, S)
c2 = CircleArc(S, D, Rotate[D, Kend_{ROT} + 5°, S])
d2 = CircleArc(S, E, Rotate[E, Kend_{ROT} + 5°, S])
e2 = CircleArc(S, F, Rotate[F, Kend_{ROT} + 5°, S])
a2 = Segment(E, S)
b2 = Segment(F, S)
D_2 = Rotate(D, Kend_{ROT}, S)
E_2 = Rotate(E, Kend_{ROT}, S)
F_2 = Rotate(F, Kend_{ROT}, S)
f2 = Segment(D_2, S)
poly18, d_7, c_{10}, b_{10}, a_{10} = Polygon(D_2, C_2, B_2, A_2)
poly19, a_{11}, e_5, d_8, c_{11}, b_{11} = Polygon(A_2, E_2, D_2, C_2, B_2)
g2 = Segment(E_2, S)
h2 = Segment(F_2, S)
poly20, a_{12}, f_3, e_6, d_9, c_{12}, b_{12} = Polygon(A_2, F_2, E_2, D_2, C_2, B_2)
J = Midpoint(H, I)