A 'crumpled' sphere defined by means of three bidimensional fields [Une sphère 'froissée' définie à l'aide de trois champs bidimensionnels].
A 'crumpled' sphere defined by means of three bidimensional fields [Une sphère 'froissée' définie à l'aide de trois champs bidimensionnels].
X = F (u,v)
x
Y = F (u,v)
y
Z = F (u,v)
z
with:
u E [U ,U ]
min max
v E [V ,V ]
min max
[Umin,Umax]x[Vmin,Vmax] then defined a bidimensional rectangular domain D.
v ^
|
V |...... ---------------------------
max | |+++++++++++++++++++++++++++|
| |+++++++++++++++++++++++++++|
| |+++++++++++++++++++++++++++|
| |+++++++++++++++++++++++++++|
| |+++++++++++++++++++++++++++|
| |+++++++++++++++++++++++++++|
| |+++++++++++++++++++++++++++|
| |+++++++++++++++++++++++++++|
| |+++++++++++++++++++++++++++|
V |...... ---------------------------
min | : :
| : :
O------------------------------------------------->
U U u
min max
X = M (i,j)
x
Y = M (i,j)
y
Z = M (i,j)
z
with:
i = f(u,U ,U ,N )
min max u
j = g(v,V ,V ,N )
min max v
where 'f' and 'g' denote two obvious linear functions...
Fx
Fy
Fz
) being applied only on the radius coordinate.
u E [0,pi]when:
v E [0,2.pi]
See the perfect sphere.