## Sphere: -

In cartesian co-ordinate, A spherical surface with radius are centered on the co-ordinate origin is defined the set of points (x, y, z) such that the equation

x²+y²+z²=r²

we can additionally describe the spherical surface in parametric form using the latitude and longitude angles as
x = r cosφ cosθ
y = r cosφ sinθ
z = r sinφ
These above equations provide an asymmetric Range for the angular parametric θ and φ alternatively. We would write the parametric equation using standard spherical coordinates. Where φ has specified the angle between z-axis the coordinate. Then φ is defined over the range 0 ≤ φ ≤ θ ≤ π, and θ is often taken in the range φ ≤ θ ≤ π we would also set up the representation using parameters u and v defined over the vary from zero to one by substituting
Φ = π u And
Θ = 2 π v