O

e_1

e_2

\text{Euklidovský priestor }\mathbb{E}_2\text{ určený repérom }\mathscr{R}=\left\langle O,e_1,e_2\right\rangle 

\text{Je daná osová afinita osou }o=PQ

\text{Postup

\text{Zostrojíme obraz repéru }\left\langle O,e_1,e_2 \right\rangle \text{ v osovej afinite.}\
\text{Pohybujete bodmi }P,Q.

e'_1

e'_2

M'

O_{1} = Intersect(xAxis, yAxis)
A_{1} = (0, 0)
B = (1, 0)
a = Vector(A_{1}, B)
C = (0, 0)
D: (0, 1)
b = Vector(C, D)
P = (3, 1)
Q = (-1, -2)
o = Line(P, Q)
O' = Mirror(O_{1}, o)
a'_{1} = Mirror(a, o)
b'_{1} = Mirror(b, o)
E: O'
E' = Translate(E, a'_{1})
a' = Vector(E, E')
F: O'
F' = Translate(F, b'_{1})
b' = Vector(F, F')
o1: x(O')
o2: y(O')
text1: "\text{Afinné lineárne zobrazenie - určené repérom}\\\\
 \;  \;  \;  \; \;   \;  O'=[ " + (LaTeX[o1]) + "   , " + (LaTeX[o2]) + "   ];\;  \; e'_1= " + (LaTeX[a'_{1}]) + "    ; \;  e'_2= " + (LaTeX[b'_{1}]) + "  "
a1: x(a')
a2: y(a')
b1: x(b')
b2: y(b')
A1: a1
B1: a2
A2: b1
B2: b2
A: {{A1, B1}, {A2, B2}}
A6: o1
B6: o2
text3: "\text{Maticový zápis afinnej transformácie }f:(x,y)↦(x',y')  \\\\
 \; \left( x' \;\; y' \right) =\left(  x  \;\; y \ \right) ×\left( \begin{array}{}   " + (LaTeX[a1]) + "&" + (LaTeX[a2]) + "  \\ " + (LaTeX[b1]) + " &" + (LaTeX[b2]) + "  \\ \end{array}   \right) +\left(  " + (LaTeX[o1]) + "  \;\;  " + (LaTeX[o2]) + "   \right)"
M = (1, 2)
m1: x(M)
A4: m1
m2: y(M)
B4: m2
X: {{A4, B4}}
O: {{A6, B6}}
X': (X * A) + O
text4: "\text{Transformačné rovnice pre: }M(x,y)→M'(x',y') \\\\
 \; x'=" + (LaTeX[a1]) + "·x+" + (LaTeX[a2]) + "·y+" + (LaTeX[o1]) + " \\ \; y'=" + (LaTeX[b1]) + "x+" + (LaTeX[b2]) + "·y+" + (LaTeX[o2]) + ""
M' = Point(X')
u = Vector(M, M')
M'_{1} = Mirror(M, o)
A_t = Transpose(A)
m3: (A * A_t)
text8: "A×A^T=" + (LaTeX[A]) + "×" + (LaTeX[A_t]) + "=" + (LaTeX[m3]) + ""