Figure 7-4.
Sphere centered at origin and projections onto planes x= 0,y= 0 and z= 0.If α
(^2) +β (^2) +γ 2
4 −δ=
r^2 > 0 , then ris radius of sphere centered at
(
−α 2 ,−β 2 ,−γ 2)0 , then 0 is radius of sphere centered at
(
−α 2 ,−β 2 ,−γ 2)−r^2 < 0 , then no real sphere exists
In the case the right-hand side of equation (7.26) is negative, then a virtual sphere
is said to exist. A sphere centered at the point (x 0 , y 0 , z 0 )with radius r > 0 has the
form
(x−x 0 )^2 + (y−y 0 )^2 + (z−z 0 )^2 =r^2 (7 .27)The figure 7-4 illustrates a sphere and projections of the sphere onto the x= 0,y= 0
and z= 0 planes.
A sphere with constant radius r > 0 and cen-
tered at the origin can also be represented in the
parametric form
x=x(φ, θ) = rsin θcos φ,
y=y(φ, θ) = rsin θsin φ,
z=z(φ, θ) = rcos θ(7 .28)