
A mixing -maximum- of a sphere and of a 'thick' helix defined by means of three bidimensional fields [Un mélange -maximum- d'une sphère et d'une hélice 'épaissie' défini à l'aide de trois champs bidimensionnels].
Many surfaces -bidimensional manifolds- in a tridimensional space
can be defined using a set of three equations:
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
If D is sampled by means of a bidimensional rectangular grid (made of Nu.Nv points),
the three {X,Y,Z} coordinates can be defined by means of three rectangular matrices:
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...
[for more information about this process]
[Plus d'informations sur ce processus]
For a mixing -maximum- of a sphere and a 'thick' helix, the three {X,Y,Z} fields/matrices are as follows:
- max(
,
) =
Fx
- max(
,
) =
Fy
- max(
,
) =
Fz
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