Posunutie

repér

vzor

Posunutie

repér

obrazy

Pohyblivý

bod - L

\textbf{Prvky matice transformácie sú určené \red{obrazmi repéra}}.

U = (1, 0)
V = (2, 2)
v = Vector(U, V)
O = Intersect(xAxis, yAxis)
E_1 = Point(xAxis)
u = Vector(O, E_1)
E_2 = Point(yAxis)
w = Vector(O, E_2)
E'_1 = Translate(E_1, v)
E'_2 = Translate(E_2, v)
O' = Translate(O, v)
a = Vector(O', E'_1)
b = Vector(O', E'_2)
A2: 0
A3: 0
A4: 1
B2: 1
B3: 0
B4: 1
C2: 0
C3: 1
C4: 1
A6: x(v)
A7: y(v)
A8: 1
B6: x(v) + B2
B7: y(v) + B3
B8: 1
C6: x(v) + C2
C7: y(v) + C3
C8: 1
L = (-2, 1)
A11: x(L)
A12: y(L)
A13: 1
M: {{A2, B2, C2}, {A3, B3, C3}, {A4, B4, C4}}
M': {{A6, B6, C6}, {A7, B7, C7}, {A8, B8, C8}}
R: (M' * Invert[M])
a11 = SurdText(Element[R, 1, 1])
a12 = SurdText(Element[R, 1, 2])
a13 = SurdText(Element[R, 1, 3])
a21 = SurdText(Element[R, 2, 1])
a22 = SurdText(Element[R, 2, 2])
a23 = SurdText(Element[R, 2, 3])
text1: "\textbf{Matica posunutia}\\
 \;  \;\textbf{\red{ " + (LaTeX[R]) + "}}"
text2: "\textbf{Rovnice}\\\\
   \;\textbf{\red{x'= x+ " + (LaTeX[a13]) + "}}\\
   \;\textbf{\red{y'= y+" + (LaTeX[a23]) + " }"
L': (x(L) + x(v), y(L) + y(v))