A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} -iteration 1- [Une courbe bidimensionnelle du type Hilbert définie avec {X1(...),Y1(...)} -itération 1-].
A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} -iteration 1- [Une courbe bidimensionnelle du type Hilbert définie avec {X1(...),Y1(...)} -itération 1-].
defined by means of 2 real functions of T
(T ∈ [0,1])
X1(T) ∈ [0,1] and Y1(T) ∈ [0,1]
such as
:
X1(T=0)=0 Y1(T=0)=0 (lower left corner)
X1(T=1)=1 Y1(T=1)=0 (lower right corner)
Ci(T) = {Xi(T),Yi(T)} ∈ [0,1]x[0,1] --> Ci+1(T) = {Xi+1(T),Yi+1(T)} ∈ [0,1]x[0,1]
if T ∈ [0,1/4[:
Xi+1(T) = Yi(4T-0)
Yi+1(T) = Xi(4T-0)
Transformation 1
if T ∈ [1/4,2/4[:
Xi+1(T) = Xi(4T-1)
Yi+1(T) = 1+Yi(4T-1)
Transformation 2
if T ∈ [2/4,3/4[:
Xi+1(T) = 1+Xi(4T-2)
Yi+1(T) = 1+Yi(4T-2)
Transformation 3
if T ∈ [3/4,1]:
Xi+1(T) = 2-Yi(4T-3)
Yi+1(T) = 1-Xi(4T-3)
Transformation 4
[See the used color set to display the parameter T]
 | ==> [iteration 11] |  |
 | ==> [iteration 10] |  |
 | ==> [iteration 9] |  |
 | ==> [iteration 10] |  |