An interpolation between a 'double sphere' and a torus [Une interpolation entre une 'double sphère' et un tore]
.X = Fx(u,v)
Y = Fy(u,v)
Z = Fz(u,v)with:
u ∈ [Umin,Umax]
v ∈ [Vmin,Vmax][Umin,Umax]*[Vmin,Vmax] then defined a bidimensional rectangular domain D.
v ^ | V |...... --------------------------- max | |+++++++++++++++++++++++++++| | |+++++++++++++++++++++++++++| | |+++++++++++++++++++++++++++| | |+++++++++++++++++++++++++++| | |+++++++++++++++++++++++++++| | |+++++++++++++++++++++++++++| | |+++++++++++++++++++++++++++| | |+++++++++++++++++++++++++++| | |+++++++++++++++++++++++++++| V |...... --------------------------- min | : : | : : O-------------------------------------------------> U U u min max
X = Mx(i,j)
Y = My(i,j)
Z = Mz(i,j)with:
i = f(u,Umin,Umax,Nu)
j = g(v,Vmin,Vmax,Nv)where 'f' and 'g' denote two obvious linear functions...