where A is polar coordinate with range [0.π], B is azimuthally coordinate with range [0.2π] 1) r is the distance of the point from centre of sphere which is origin. 2) z-axis makes angle A with r . 3) Projection of r on x-y plane makes an angle B with x-axis. 4) Locus of points of same r making same angle A with z-axis makes a circle parallel to the circle in x-y plane with r as radius . 5) For 360> angle > 180 , use sin(180+A) = - sinA and cos (180 + A ) = - cosA;
(5) Any 4 points satisfying the below determinant condition uniquely describe a sphere.
| x2 +y2+ z2 x y z 1|
|x12+y12+z12 x1 y1 z1 1|
|x22+y22+z22 x2 y2 z2 1| = 0
|x32+y32+z32 x3 y3 z3 1|
|x42+y42+z42 x4 y4 z4 1|
(6) vol of sphere / (vol of sphere - vol. of circumscribed cylinder) =2